SSC MTS 2025 Official Paper (Held On: 06 Feb, 2026 Shift 2) (Previous Year Paper)

Given:

Total number of days = 6

Formula Used:

Average = Sum of all observations ÷ Total number of observations

Calculation:

According to the question,

⇒ Total sum of new users = 180 + 150 + 135 + 190 + 65 + 115

⇒ Total sum = 835

⇒ Average number of new users = Total sum ÷ Total number of days

⇒ Average = 835 ÷ 6

⇒ Average = 139.1666...

⇒ Average ≈ 139.17

∴ The correct answer is 139.17.

Given:

Number of hotels in S1 = 4400

Formula Used:

Total Number of Hotels = (Number of hotels in a State ÷ Percentage of that State) × 100

Number of hotels in a State = Total Number of Hotels × (Percentage of that State ÷ 100)

Calculation:

According to the question,

⇒ Number of hotels in S1 = 4400

⇒ Percentage of hotels in S1 = 22%

⇒ 22% of Total Hotels = 4400

⇒ Total Hotels = (4400 ÷ 22) × 100

⇒ Total Hotels = 200 × 100 = 20,000

Now, we need to find the state where the number of hotels is 2400.

⇒ Let the required percentage be x%

⇒ x% of 20,000 = 2400

⇒ (x ÷ 100) × 20,000 = 2400

⇒ 200 × x = 2400

⇒ x = 2400 ÷ 200

⇒ x = 12%

From the table/chart, 12% corresponds to State S2.

∴ The correct answer is S2.

Given:

Total number of nurses in H5 and H1 = 3240

Formula Used:

Value of a sector = (Degree of sector ÷ 360°) × Total Value

Percentage less = [(Higher Value − Lower Value) ÷ Higher Value] × 100%

Calculation:

According to the question,

⇒ Total degree sum for H5 and H1 = 54° + 54° = 108°

⇒ Given that 108° corresponds to 3240 nurses

⇒ Value of 1° = 3240 ÷ 108 = 30

⇒ Number of nurses in H1 = 54° × 30 = 1620

⇒ Number of nurses in H4 = 72° × 30 = 2160

Now, calculate the percentage by which nurses in H1 are less than those in H4:

⇒ Difference = 2160 − 1620 = 540

⇒ Percentage less = (Difference ÷ Number of nurses in H4) × 100%

⇒ Percentage less = (540 ÷ 2160) × 100%

⇒ Percentage less = (1 ÷ 4) × 100%

⇒ Percentage less = 25%

Alternatively, using degrees directly:

⇒ Percentage less = [(72° − 54°) ÷ 72°] × 100%

⇒ Percentage less = (18 ÷ 72) × 100% = 25%

∴ The correct answer is 25% (Option 4).

Shortcut Trick

Angle Bisector Theorem: The bisector of an angle divides the opposite side in the ratio of the other two sides.

Ratio BD : DC = AB : AC = 28 : 42 = 2 : 3

Total parts = 2 + 3 = 5 units

Given 5 units = 50 cm ⇒ 1 unit = 10 cm

BD = 2 units = 2 × 10 = 20 cm

∴ The correct answer is 20 cm.

Alternate Method

Given:

In ΔABC, AB = 28 cm, AC = 42 cm, BC = 50 cm.

AD is the internal angle bisector of ∠A meeting BC at D.

According to the Internal Angle Bisector Theorem:

⇒ BD / DC = AB / AC

Let BD = x cm, then DC = (50 − x) cm

⇒ x / (50 − x) = 28 / 42

⇒ x / (50 − x) = 2 / 3

⇒ 3 × x = 2 × (50 − x)

⇒ 3x = 100 − 2x

⇒ 5x = 100

⇒ x = 20

∴ The correct answer is 20 cm.

Additional Information

Internal Angle Bisector Theorem

The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the corresponding sides: BD/DC = AB/AC.

Length of Angle Bisector

The length of the internal bisector AD is given by AD² = (AB × AC) − (BD × DC). For this triangle, AD = √(28 × 42 − 20 × 30) = √576 = 24 cm.

External Angle Bisector Theorem

If AD' is the external bisector of ∠A meeting BC produced at D', then BD'/CD' = AB/AC.

Shortcut Trick

Profit Ratio (Kamal : Harshit) = (4800 × 4 + 6000 × 8) : (6000 × 4 + 4800 × 8)

⇒ Ratio = 67200 : 62400 = 672 : 624 = 14 : 13

Harshit's share (13 units) = ₹2600 ⇒ 1 unit = ₹200

Kamal's share (14 units) = 14 × 200 = ₹2800

∴ The correct answer is ₹2800.

Alternate Method

Given:

Kamal initial investment = ₹4800 | Harshit initial investment = ₹6000

After 4 months, Kamal adds ₹1200 | Harshit withdraws ₹1200

Annual profit of Harshit = ₹2600

Formula:

Profit Ratio = (Investment₁ × Time₁) : (Investment₂ × Time₂)

Calculations:

⇒ Total Investment value for Kamal = (4800 × 4) + (4800 + 1200) × 8

⇒ Kamal = 19200 + 48000 = ₹67200

⇒ Total Investment value for Harshit = (6000 × 4) + (6000 − 1200) × 8

⇒ Harshit = 24000 + 38400 = ₹62400

⇒ Ratio (Kamal : Harshit) = 67200 : 62400

⇒ Ratio = 672 : 624 = 28 : 26 = 14 : 13

⇒ Harshit's profit share = (13 / 27) × Total Profit = ₹2600

⇒ 13 units = ₹2600

⇒ 1 unit = 2600 ÷ 13 = ₹200

⇒ Kamal's profit share = 14 units = 14 × 200 = ₹2800

∴ The correct answer is ₹2800.

Additional Information

Partnership Profit Rule

In any business partnership, the profit is distributed among partners in the ratio of the product of their investments and the time duration: P₁ : P₂ = C₁ × T₁ : C₂ × T₂.

Compound Partnership

When partners invest different amounts for different periods of time, it is called a compound partnership. The effective capital is calculated by summing the products of various capitals and their respective time periods.

Ratio Simplification

To simplify the profit ratio, find the Highest Common Factor (HCF) of the calculated investment-time products and divide both sides by it.

Shortcut Trick

Let Cost Price (CP) = 100. Then Marked Price (MP) = 100 + 35% = 135.

Price after first 20% discount = 135 × 0.8 = 108.

Overall Profit = 8%, so Required Selling Price = 100 + 8% = 108.

Since the price after the first discount (108) is already equal to the target selling price (108), the second discount y must be 0%.

∴ The correct answer is 0%.

Alternate Method

Given:

Markup Percentage = 35%

First Discount (d₁) = 20%

Overall Profit Percentage = 8%

Calculations:

⇒ Let Cost Price (CP) = ₹100

⇒ Marked Price (MP) = 100 + 35% of 100 = ₹135

⇒ Price after 1^st discount = 135 − (20/100) × 135 = 135 − 27 = ₹108

⇒ Required Final Selling Price (SP) for 8% overall profit = 100 + 8% of 100 = ₹108

⇒ Let the second successive discount be y%.

⇒ SP after second discount = 108 × (1 − y/100) = 108

⇒ 1 − y/100 = 108 ÷ 108 = 1

⇒ y/100 = 0

⇒ y = 0

∴ The correct answer is 0%.

Additional Information

Successive Discounts Formula

For two successive discounts d₁% and d₂%, the effective discount D% = d₁ + d₂ − (d₁ × d₂) ÷ 100.

CP, MP and Profit Relation

The relationship between Cost Price and Marked Price is given by: MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

Effective Profit Percentage

Profit% = Markup% − Discount% − (Markup% × Discount%) ÷ 100. This formula calculates profit directly from markup and discount rates.

Shortcut Trick

Initial Ratio (Juice : Water) = 5 : 2 → (Multiply by 3) → 15 : 6

New Ratio (Juice : Water) = 8 : 3 → (Multiply by 2) → 16 : 6

Increase in Juice = 16 − 15 = 1 unit

Given: 1 unit = 15 L

Initial Total = 15 + 6 = 21 units = 21 × 15 L = 315 L

∴ The correct answer is 315 L.

Alternate Method

Initial ratio of grape juice and water = 5 : 2

Let the initial volume of grape juice be 5x and water be 2x.

Initial total volume = 5x + 2x = 7x

After adding 15 litres of juice, the new amount of juice = 5x + 15

The amount of water remains the same = 2x

According to the question:

⇒ (5x + 15) / 2x = 8 / 3

⇒ 3 × (5x + 15) = 8 × 2x

⇒ 15x + 45 = 16x

⇒ 16x − 15x = 45

⇒ x = 45

Initial total volume of the mixture = 7x

⇒ 7 × 45 = 315 L

∴ The correct answer is 315 L.

Additional Information

Ratio Balancing Method

When one component in a mixture is added or removed, the other component remains constant. Equating the ratio parts of the constant component simplifies the calculation.

Alligation Rule

Used to find the ratio in which two ingredients at different prices or concentrations are mixed to produce a mixture of a desired price or concentration.

Component Percentage

Concentration of a component = (Quantity of component ÷ Total Quantity) × 100.

Shortcut Trick

Total ratio units = 2 + 3 + 5 = 10 units.

10 units = ₹1,500 ⇒ 1 unit = ₹150.

A share = 2 × 150 = ₹300.

B share = 3 × 150 = ₹450.

C share = 5 × 150 = ₹750.

∴ The correct answer is A = ₹300, B = ₹450, C = ₹750.

Alternate Method

Given:

Total Sum = ₹1,500

Ratio of A : B : C = 2 : 3 : 5

Formula Used:

Individual Share = (Individual Ratio / Total Ratio Parts) × Total Sum

⇒ Total Ratio Parts = 2 + 3 + 5 = 10

⇒ Share of A = (2/10) × 1,500 = 2 × 150 = ₹300

⇒ Share of B = (3/10) × 1,500 = 3 × 150 = ₹450

⇒ Share of C = (5/10) × 1,500 = 5 × 150 = ₹750

∴ The correct answer is A = ₹300, B = ₹450, C = ₹750.

Additional Information

Ratio and Proportion

A ratio is a comparison of two or more quantities of the same kind. If A:B = x:y, then A/x = B/y = k (constant).

Direct Proportion

When quantities are divided in a given ratio, each part is directly proportional to its respective ratio term.

Inverse Ratio

The inverse ratio of a : b is 1/a : 1/b, which simplifies to b : a.

Given:

Formula Used:

Total number of tenants = Sum of tenants in all given towns

Total tenants = T1 + T2 + T3 + T4 + T5 + T6

Calculation:

According to the question,

⇒ Total number of tenants = 120 + 100 + 80 + 120 + 100 + 140

⇒ Total number of tenants = (120 + 80) + (100 + 100) + (120 + 140)

⇒ Total number of tenants = 200 + 200 + 260

⇒ Total number of tenants = 400 + 260

⇒ Total number of tenants = 660

∴ The correct answer is 660.

Shortcut Trick

Simplify square roots: √144 = 12, √36 = 6, and √49 = 7.

Apply calculation: x = (12 ÷ 6) × 7 = 14.

Calculate x²: 14² = 196.

∴ The correct answer is 196.

Alternate Method

Given:

x = √144 ÷ √36 × √49

Formula Used:

Simplification using BODMAS rule and square root values.

Calculations:

⇒ x = 12 ÷ 6 × 7

⇒ x = 2 × 7

⇒ x = 14

⇒ x² = 14 × 14

⇒ x² = 196

∴ The correct answer is 196.

Additional Information

BODMAS Rule

Simplification always follows the priority order of Brackets, Orders (powers and roots), Division, Multiplication, Addition, and Subtraction.

Square Roots and Squares

Common squares are essential for speed: 12² = 144, 13² = 169, 14² = 196, and 15² = 225.

Property of Powers

If x = a, then x² = a × a. This operation is performed after the expression for x is fully simplified.

Shortcut Trick

Use the algebraic identity: (a + b)² + (a − b)² = 2(a² + b²)

Here, a = 1 and b = √5

⇒ 2(1² + (√5)²) − 6

⇒ 2(1 + 5) − 6 = 12 − 6 = 6

∴ The correct answer is 6.

Alternate Method

Given expression: (1 + √5)² + (1 − √5)² − 6

Formula used: (a + b)² = a² + b² + 2ab and (a − b)² = a² + b² − 2ab

⇒ [(1)² + (√5)² + 2(1)(√5)] + [(1)² + (√5)² − 2(1)(√5)] − 6

⇒ [1 + 5 + 2√5] + [1 + 5 − 2√5] − 6

⇒ 6 + 2√5 + 6 − 2√5 − 6

⇒ (6 + 6 − 6) + (2√5 − 2√5)

⇒ 6 + 0

⇒ 6

∴ The correct answer is 6.

Additional Information

Sum and Difference of Squares

(a + b)² + (a − b)² = 2(a² + b²) and (a + b)² − (a − b)² = 4ab.

Squaring of Surds

The square of a square root of a number is the number itself: (√x)² = x.

BODMAS Rule

Always solve exponents first, then perform addition and subtraction from left to right.

Shortcut Trick

Apply the algebraic identity: (a + b)² + (a − b)² = 2(a² + b²).

Here, a = 4 and b = √2.

Sum of squares = 2 × (4² + (√2)²) = 2 × (16 + 2) = 36.

Final Value = 36 − 20 = 16.

∴ The correct answer is 16.

Alternate Method

Given: (4 + √2)² + (4 − √2)² − 20

Using formulas: (a + b)² = a² + b² + 2ab and (a − b)² = a² + b² − 2ab

⇒ (4² + (√2)² + 2 × 4 × √2) + (4² + (√2)² − 2 × 4 × √2) − 20

⇒ (16 + 2 + 8√2) + (16 + 2 − 8√2) − 20

⇒ 18 + 8√2 + 18 − 8√2 − 20

⇒ 36 − 20

⇒ 16

∴ The correct answer is 16.

Additional Information

Sum and Difference Identities

The sum of squares (a + b)² + (a − b)² simplifies to 2(a² + b²), while the difference (a + b)² − (a − b)² simplifies to 4ab.

Radical Square Property

For any non-negative number x, (√x)² = x. For example, (√2)² = 2.

BODMAS Rule

Always solve brackets and exponents before performing addition and subtraction in simplification problems.

Shortcut Trick

Breadth of the rectangle = Area ÷ Length = 54 ÷ 9 = 6 cm.

Perimeter = 2 × (Length + Breadth) = 2 × (9 + 6) = 2 × 15 = 30 cm.

∴ The correct answer is 30 cm.

Alternate Method

Given:

Area of rectangle = 54 cm²

Length (L) = 9 cm

Formula Used:

Area = Length × Breadth

Perimeter = 2 × (Length + Breadth)

Calculations:

⇒ Area = Length × Breadth

⇒ 54 = 9 × Breadth

⇒ Breadth = 54 ÷ 9

⇒ Breadth = 6 cm

⇒ Perimeter = 2 × (Length + Breadth)

⇒ Perimeter = 2 × (9 + 6)

⇒ Perimeter = 2 × 15

⇒ Perimeter = 30 cm

∴ The correct answer is 30 cm.

Additional Information

Properties of Rectangle

Opposite sides are equal and parallel, and each internal angle is 90°.

Diagonal of Rectangle

The length of the diagonal d = √(L² + B²), where L is length and B is breadth.

Square Area vs Perimeter

For a square of side a, Area = a² and Perimeter = 4 × a.

Shortcut Trick

Divisibility rule for 3: Sum of digits must be a multiple of 3.

Sum of digits for 39P6 = 3 + 9 + P + 6 = 18 + P.

Since 18 is already divisible by 3, P must be 0, 3, 6, or 9.

Among the options, 7 is the only value that makes the sum (18 + 7 = 25) not divisible by 3.

∴ The correct answer is 7.

Alternate Method

Given: The number 39P6 is divisible by 3.

Property: A number is divisible by 3 if the sum of its digits is divisible by 3.

⇒ Sum of digits = 3 + 9 + P + 6 ⇒ Sum = 18 + P ⇒ Since 39P6 is divisible by 3, (18 + P) mod 3 = 0 ⇒ For P = 0: 18 + 0 = 18 (18 ÷ 3 = 6, Remainder = 0) ⇒ For P = 3: 18 + 3 = 21 (21 ÷ 3 = 7, Remainder = 0) ⇒ For P = 6: 18 + 6 = 24 (24 ÷ 3 = 8, Remainder = 0) ⇒ For P = 7: 18 + 7 = 25 (25 ÷ 3 = 8, Remainder = 1) ⇒ Since the remainder is not 0 for P = 7, the number is not divisible by 3.

∴ The correct answer is 7.

Additional Information

Divisibility by 9

Similar to the rule for 3, a number is divisible by 9 if the sum of its digits is a multiple of 9.

Divisibility by 4

A number is divisible by 4 if the last two digits of the number are divisible by 4 or if the last two digits are 00.

Divisibility by 11

Subtract the sum of the digits in the even positions from the sum of the digits in the odd positions. If the result is 0 or divisible by 11, the original number is divisible by 11.

Shortcut Trick

Identify the Pythagorean Triplet: (5, 12, 13).

If Length = 5 cm and Diagonal = 13 cm, then Width = 12 cm.

Area = Length × Width = 5 × 12 = 60 cm².

∴ The correct answer is 60 cm².

Alternate Method

Given: Length (l) = 5 cm, Diagonal (d) = 13 cm

Formula: Diagonal² = Length² + Width² (Pythagoras Theorem)

⇒ 13² = 5² + w²

⇒ 169 = 25 + w²

⇒ w² = 169 − 25 = 144

⇒ w = √144 = 12 cm

⇒ Area = Length × Width

⇒ Area = 5 × 12 = 60 cm²

∴ The correct answer is 60 cm².

Additional Information

Perimeter of a Rectangle

The total boundary of the rectangle is given by P = 2 × (length + width).

Common Pythagorean Triplets

Standard integer sets satisfying a² + b² = c² include (3, 4, 5), (8, 15, 17), and (7, 24, 25).

Diagonal Property

The diagonal of a rectangle bisects it into two congruent right-angled triangles.

Shortcut Trick

Ratio of Length : Breadth = 3 : 1.

Perimeter units = 2 × (3 + 1) = 8 units.

8 units = 64 cm ⇒ 1 unit = 8 cm.

Sides are 24 cm (Length) and 8 cm (Breadth).

Diagonal = 8 × √(3² + 1²) = 8√10 cm.

∴ The correct answer is 8√10 cm.

Alternate Method

Given:

Perimeter of rectangle = 64 cm

Length (L) = 3 × Breadth (B)

Formula Used:

Perimeter = 2 × (L + B)

Diagonal = √(L² + B²)

Calculations:

⇒ Let the Breadth be x cm. Then Length = 3x cm.

⇒ 2 × (3x + x) = 64

⇒ 2 × 4x = 64

⇒ 8x = 64 ⇒ x = 8

⇒ Breadth = 8 cm and Length = 3 × 8 = 24 cm.

⇒ Diagonal = √(24² + 8²)

⇒ Diagonal = √(576 + 64)

⇒ Diagonal = √640

⇒ Diagonal = √(64 × 10) = 8√10 cm.

∴ The correct answer is 8√10 cm.

Additional Information

Area of Rectangle

The total space occupied by the rectangle is calculated as Area = Length × Breadth.

Diagonal Property

The diagonals of a rectangle are equal in length and bisect each other at the point of intersection.

Pythagoras Theorem

In any right-angled triangle formed by the sides and diagonal, Diagonal² = Length² + Breadth².

Shortcut Trick

The average of n consecutive numbers is the middle term of the series.

For 8 consecutive numbers, the average (57) lies exactly between the 4^th and 5^th terms.

4^th term = 57 − 1 = 56 (since even numbers have a gap of 2).

3^rd term = 4^th term − 2 = 56 − 2 = 54.

∴ The correct answer is 54.

Alternate Method

Given: Average of 8 consecutive even natural numbers = 57.

Let the 8 consecutive even numbers in ascending order be x, x+2, x+4, x+6, x+8, x+10, x+12, x+14.

⇒ Sum of 8 numbers = 57 × 8 = 456

⇒ x + (x+2) + (x+4) + (x+6) + (x+8) + (x+10) + (x+12) + (x+14) = 456

⇒ 8x + 56 = 456

⇒ 8x = 400

⇒ x = 50

⇒ 3^rd number = x + 4 = 50 + 4 = 54

∴ The correct answer is 54.

Additional Information

Average of Arithmetic Progression

For any series in AP, Average = (First term + Last term) ÷ 2. This applies to consecutive even/odd numbers as well.

Middle Term in Even Count

If the number of terms (n) is even, the average is the arithmetic mean of the (n/2)^th and (n/2 + 1)^th terms.

Sum of Even Numbers

The sum of the first n even natural numbers is given by the formula n(n + 1).

Shortcut Trick

In any sequence of consecutive natural numbers (Arithmetic Progression), the average is always the middle value.

The average is also equal to the mean of the first and last terms.

Formula: Average = (Smallest number + Largest number) ÷ 2

Given: Average = A

Sum of smallest and largest = 2 × Average = 2 × A = 2A

∴ The correct answer is 2A.

Alternate Method

Given: Total consecutive terms (n) = 19, Average = A

Formula: Average = (First term + Last term) ÷ 2

⇒ Let the 19 consecutive natural numbers be x, (x + 1), (x + 2), ..., (x + 18).

⇒ Average = [Sum of all terms] ÷ 19

⇒ In an AP, Average = (Smallest + Largest) ÷ 2

⇒ A = [x + (x + 18)] ÷ 2

⇒ A = (2x + 18) ÷ 2

⇒ 2A = 2x + 18

⇒ Sum of smallest and largest = x + (x + 18) = 2x + 18

⇒ From the previous step, 2x + 18 = 2A

∴ The correct answer is 2A.

Additional Information

Average of AP

For any sequence in Arithmetic Progression, the Average = (First Term + Last Term) ÷ 2 = Middle Term (if n is odd).

Sum of n Consecutive Numbers

The sum of n consecutive natural numbers starting from x is S = (n ÷ 2) × [2x + (n − 1)].

Middle Term Location

If the number of terms n is odd, the middle term is the [(n + 1) ÷ 2]^th term, which represents the average.

Shortcut Trick

In parallel lines, corresponding angles are equal.

∠RSD = ∠PRB = 74°

Angles on a straight line (linear pair) sum to 180°.

∠DSQ = 180° − ∠RSD = 180° − 74° = 106°

∴ The correct answer is 106°.

Alternate Method

Given: AB || CD, ∠PRB = 74°.

Formula Used: Corresponding angle property and Linear pair property.

⇒ Since AB || CD and PQ is the transversal, ∠PRB and ∠RSD are corresponding angles.

⇒ ∠RSD = ∠PRB = 74°

⇒ Now, S lies on the transversal line PQ, making ∠RSD and ∠DSQ a linear pair.

⇒ ∠RSD + ∠DSQ = 180°

⇒ 74° + ∠DSQ = 180°

⇒ ∠DSQ = 180° − 74°

⇒ ∠DSQ = 106°

∴ The correct answer is 106°.

Additional Information

Corresponding Angles

Angles in the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, corresponding angles are equal.

Linear Pair

A pair of adjacent angles formed by intersecting lines. The sum of the angles in a linear pair is always 180°.

Alternate Interior Angles

Angles between the parallel lines on opposite sides of the transversal. They are always equal (∠ARS = ∠RSD).

Co-Interior Angles

Angles on the same side of the transversal between the two parallel lines. Their sum is always 180° (∠BRS + ∠RSD = 180°).

Shortcut Trick

Draw a line parallel to AB passing through point C.

Angle between BC and the parallel line = 180° − 120° = 60° (Consecutive Interior Angles).

Angle between CD and the parallel line = 180° − 120° = 60° (Consecutive Interior Angles).

The total angle at point C on a straight line is 180°.

∠BCD = 180° − (60° + 60°) = 60°.

∴ The correct answer is 60°.

Alternate Method

Given:

∠ABC = 120°

∠EDC = 120°

AB ∥ DE

Step-by-step Calculation:

⇒ Let us draw a line PCQ passing through C such that PQ ∥ AB ∥ DE.

⇒ Since AB ∥ PQ, then ∠ABC + ∠BCP = 180° (Sum of consecutive interior angles).

⇒ 120° + ∠BCP = 180°

⇒ ∠BCP = 180° − 120° = 60°

⇒ Since DE ∥ PQ, then ∠EDC + ∠DCQ = 180° (Sum of consecutive interior angles).

⇒ 120° + ∠DCQ = 180°

⇒ ∠DCQ = 180° − 120° = 60°

⇒ Now, PCQ is a straight line, so ∠BCP + ∠BCD + ∠DCQ = 180°.

⇒ 60° + ∠BCD + 60° = 180°

⇒ ∠BCD + 120° = 180°

⇒ ∠BCD = 180° − 120° = 60°

∴ The correct answer is 60°.

Additional Information

Consecutive Interior Angles

When two parallel lines are intersected by a transversal, the pairs of angles on the same side of the transversal inside the parallel lines are supplementary (Sum = 180°).

Alternate Interior Angles

Angles located between parallel lines and on opposite sides of the transversal are equal (∠1 = ∠2).

Angle on a Straight Line

The sum of all angles formed at a point on one side of a straight line is always 180°.

The logic followed here is:

thus, "464" will replace the question mark in the given series.

Hence, the correct option is "Option 3".

The Logic followed here is:

For, ZNV : WKS

For, QIP : NFM

Now for, TEY : ?

Therefore, the related cluster for TEY is QBV.

Hence, the correct answer is Option 2.

The logic followed here is:

So, 'JZ' will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

The Logic followed here is:

For, (FA, BV, XQ)

For, (HL, DG, ZB)

Now checking the options:

Option 1: (QV, NU, IM)

Option 2: (YG, RA, MX)

Option 3: (AQ, YO, TH)

Option 4: (GY, CT, YO)

Therefore, the set (GY, CT, YO) follows the same logic.

Hence, the correct answer is Option 4.

The logic followed here is:

Given: January 5 was Wednesday in a leap year.

From January 26 to January 31 = 5 days

So, Wednesday + 5 days = Monday

Therefore, January 31 = Monday

February 1 = Tuesday

Total Thursdays = 4

Total Saturdays = 4

Here, Total Saturdays and Thursdays = 4 + 4 = 8

Hence, the correct answer is "Option 3".

The logic followed here is:

**Given:**1924 was a leap year.

January 1, 1924 was Tuesday.

So, Tuesday + 4 days = Saturday

Total Thursdays in March 1924 = 4

So, Tuesday + 2 days = Thursday

Total Thursdays in May 1924 = 5

Statement Result

I. March 1924 had 5 Thursdays Incorrect

II. May 1924 had 5 Thursdays Correct

Hence, the correct answer is "Option 2".

Given: Five persons C, D, F, G and H are sitting in a row facing north.

Only C and F are to the left of D.

Only H is to the right of G.

F is at one of the extreme ends of the row.

Now, persons between F and G =  2 persons.

Hence, the correct answer is "Option 3".

The logic followed here is:

Given:

R is taller than only four girls.

Since, there are 6 girls in total, R must be the 2^nd tallest.

U is taller than both S and P.

S and P both are taller than both Q and T.

So, the general order becomes: U > R > {S, P} > {Q, T}

Now check the given sequences.

I. U > R > S > P > T > Q

This satisfies all conditions.

So, Sequence I is possible.

II. U > R > P > S > Q > T

This also satisfies all conditions.

So, Sequence II is possible.

Hence, the correct answer is Option 3.

The Logic followed here is:

For, SK18 : TM36

For, BN25 : CP50

Now for, ? : AV60

Therefore, the missing letter-number cluster is ZT30.

Hence, the correct answer is Option 2.

The Logic followed here is:

For, BI320 : GB450

For, EK240 : JD370

Now for, DJ110 : ?

Therefore, the related cluster for DJ110 is IC240.

Hence, the correct answer is Option 1.

The Logic followed here is:

Logic:  The pattern observed is (First Number − 42) = Second Number

For, 9165 : 9123

9165 − 42

= 9123

For, 874 : 832

874 − 42

= 832

Now for, 5630 : ?

5630 − 42

= 5588

Therefore, the missing number is 5588.

Hence, the correct answer is Option 3.

The Logic followed here is:

Logic:  The pattern observed is (First Number − 278) = Second Number

For, 910 : 632

910 − 278

= 632

For, 412 : 134

412 − 278

= 134

Now for, 415 : ?

415 − 278

= 137

Therefore, the missing number is 137.

Hence, the correct answer is Option 4.

The logic followed here is:

Logic: Each letter of the word is replaced by the next letter in the English alphabetical series (+1).

Here, JAMB → KBNC

Similarly, BOND → CPOE

Now, applying the same pattern to COIR:

So, COIR → DPJS

Hence, the correct answer is "Option 2".

The logic followed here is:

Given: WP14, XT28, YX42, ZB56, AF70, BK84

Here, BK84 is wrong among the given terms.

Hence, the correct answer is Option 2.

The logic followed here is:

So, VQD814 will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

The logic followed here is:

Given: The minute hand and hour hand overlap whenever the angle between them becomes 0°.

The hands overlap 11 times in 12 hours because the overlap at 12:00 is common for two adjacent intervals.

So, Total overlaps = 11 + 11

Total overlaps = 22

Therefore, the minute and hour hands overlap 22 times in 24 hours.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: Angle between hour hand and minute hand is calculated using:

Angle = |30 × H − 5.5 × M|

Now, calculating:

For J at 3:05

= |30 × 3 − 5.5 × 5|

= |90 − 27.5|

= 62.5°

For K at 11:55

= |30 × 11 − 5.5 × 55|

= |330 − 302.5|

= 27.5°

Difference between J and K

= |62.5° − 27.5°|

= 35°

Hence, the correct answer is Option 2.

The logic followed here is:

Logic: In each step, all three symbols move one position clockwise along the border of the square and flip vertically.

So in the next figure:

Barred Arrow moves to Top-Left and points downward.

T-shape moves to Bottom-Center and becomes inverted (⊥).

Simple Arrow moves to Bottom-Right and points upward.

Hence, the correct answer is Option 1.

The logic followed here is:

Logic: The main arrow rotates 45° counter-clockwise in each step, while the circle colors alternate between white and black.

In the next figure:

Main arrow points West.

Two black circles are above the arrow.

One white circle is below the arrow.

Hence, the correct answer is Option 1.

The logic followed here is:

Logic: If the sum and difference of ages are known, then:

Elder person’s age = (Sum + Difference) ÷ 2

Younger person’s age = (Sum − Difference) ÷ 2

Now, calculating:

Present age of S

= (50 + 8) ÷ 2

= 58 ÷ 2

= 29 years

Present age of T

= (50 − 8) ÷ 2

= 42 ÷ 2

= 21 years

6 years ago:

S = 29 − 6 = 23 years

T = 21 − 6 = 15 years

Required ratio = 23 : 15

Hence, the correct answer is Option 2.

The correct answer is Cinnabar.

Key Points

• Cinnabar is the primary and most common ore of mercury (Hg).
• Chemically, it is known as Mercury(II) sulfide and its chemical formula is HgS.
• It typically appears as a bright red or brownish-red crystalline solid, which has been historically used as a pigment known as vermilion.
• The extraction of mercury from cinnabar involves roasting the ore in a furnace. During this process, sulfur in the ore combines with oxygen to form sulfur dioxide, and the mercury vaporizes.
• The mercury vapor is then cooled and condensed to collect liquid mercury.

Additional Information

• Bauxite:
• It is the principal ore of Aluminium (Al).
• It is not a specific mineral but a sedimentary rock with high aluminum content, primarily consisting of gibbsite, boehmite, and diaspore.
• Australia is the world's largest producer of bauxite, while in India, the state of Odisha is the leading producer.
• Magnetite:
• It is one of the most important ores of Iron (Fe).
• Its chemical formula is Fe3O4 and it is known for its natural magnetic properties, often called lodestone.
• It has a very high iron content, approximately 72.4%, making it a high-quality ore.
• Malachite:
• It is a copper carbonate hydroxide mineral with the formula Cu2CO3(OH)2.
• It is a minor ore of Copper (Cu) and is easily recognizable by its distinct bright green color.
• It was often used as a mineral pigment in green paints in ancient times.

Important Points

• Mercury (Hg): It is also known as quicksilver and is the only common metal that is liquid at standard temperature and pressure.
• Applications: Due to its uniform thermal expansion, mercury is used in thermometers, barometers, and manometers. It is also used in fluorescent lighting and dental amalgams.
• Amalgams: Mercury can dissolve many other metals (like gold and silver) to form alloys called amalgams. However, it does not form amalgams with iron, which is why it is often stored in iron flasks.
• Toxicity: Mercury is highly toxic to humans. Minamata disease is a neurological syndrome caused by severe mercury poisoning, famously occurring in Japan in the 1950s.

p- The correct answer is United Kingdom.

Key Points

• The Durgapur Steel Plant (DSP) is one of the integrated steel plants of Steel Authority of India Limited (SAIL), located in Durgapur, in the Paschim Bardhaman district of West Bengal.
• It was set up in the late 1950s with the help of a consortium of British companies known as ISCON (Indian Steelworks Construction Co. Ltd.).
• The establishment of this plant was a major part of the Second Five Year Plan (1956-1961), which focused on the development of heavy industries and capital goods in India.
• The plant was initially designed with an annual capacity of 1 million tonnes of crude steel, which was later expanded in various phases.
• It serves as a critical industrial hub in Eastern India, contributing significantly to the production of railway materials like wheels and axles, as well as structural steel.

Additional Information

• Second Five Year Plan (1956-1961):
• This plan was based on the P.C. Mahalanobis Model, which emphasized rapid industrialization with a focus on heavy industries.
• Under this plan, three major integrated steel plants were established in the public sector with foreign collaboration: Bhilai, Rourkela, and Durgapur.
• Bhilai Steel Plant:
• Located in Bhilai, Chhattisgarh, it was set up in 1955 with the collaboration of the Soviet Union (now Russia).
• It is an eleven-time winner of the Prime Minister's Trophy for the best integrated steel plant in the country.
• Rourkela Steel Plant (RSP):
• Located in Odisha, it was the first integrated steel plant in the public sector in India, set up in 1959.
• It was established in collaboration with German firms, specifically Krupp and Demag.
• Bokaro Steel Plant:
• Located in Bokaro, Jharkhand, it was the fourth integrated public sector steel plant in India.
• It was established in 1964 with the assistance of the Soviet Union during the Third Five Year Plan.
• Steel Authority of India Limited (SAIL):
• SAIL is a government-owned steel producer headquartered in New Delhi.
• It was incorporated in 1973 and currently holds the status of a Maharatna Central Public Sector Enterprise.

The correct answer is Aravali.

Key Points

• Himadri, also known as the Great Himalayas or Inner Himalayas, is the northernmost and most continuous range of the Himalayan mountain system. It contains the highest peaks in the world, such as Mount Everest and Kanchenjunga, with an average elevation of 6,000 meters.
• Himachal, or the Lesser Himalayas, lies to the south of the Himadri. This range is mainly composed of highly compressed and altered rocks, with an altitude varying between 3,700 and 4,500 meters. It is famous for its hill stations like Shimla, Mussoorie, and Nainital.
• Shiwalik is the outermost range of the Himalayas. It extends over a width of 10-50 km and has an altitude varying between 900 and 1,100 meters. These ranges are composed of unconsolidated sediments brought down by rivers from the main Himalayan ranges located farther north.
• Aravali is one of the oldest fold mountain ranges in the world and is located in the western part of India, primarily in Rajasthan. It is not part of the Himalayan mountain system, which is a much younger geological formation. Hence, Aravali is NOT a division of the Himalaya.

Additional Information

• Himalayan Mountain System:
• The Himalayas are geologically young and structurally fold mountains that stretch across the northern borders of India.
• They run in a west-east direction from the Indus River to the Brahmaputra River, covering a distance of about 2,400 km.
• The width of the Himalayas varies from 400 km in Kashmir to 150 km in Arunachal Pradesh.
• Aravali Range:
• The Aravali Range dates back to the Proterozoic Era, making it significantly older than the Himalayas, which were formed during the Tertiary Period.
• It spans approximately 692 km, starting from Gujarat, passing through Rajasthan and Haryana, and ending in Delhi.
• The highest peak of the Aravali Range is Guru Shikhar, located on Mount Abu, with an elevation of 1,722 meters.
• The range serves as a barrier preventing the eastward expansion of the Thar Desert.

Important Points

• Longitudinal Valleys (Duns): The longitudinal valleys lying between the Lesser Himalayas (Himachal) and the Shiwaliks are known as Duns. Well-known examples include Dehra Dun, Kotli Dun, and Patli Dun.
• Trans-Himalayas: Located immediately north of the Great Himalayan range, this region includes the Karakoram, Ladakh, and Zanskar ranges. It is also known as the Tethys Himalayas.
• Regional Divisions: Apart from longitudinal divisions, the Himalayas are also divided from west to east:
• Punjab Himalayas (between Indus and Sutlej).
• Kumaon Himalayas (between Sutlej and Kali).
• Nepal Himalayas (between Kali and Teesta).
• Assam Himalayas (between Teesta and Dihang).

The correct answer is Iron.

Key Points

• The Harappan Civilization, also known as the Indus Valley Civilization (IVC), belonged to the Bronze Age (circa 3300 BCE to 1300 BCE).
• While the Harappans were highly advanced in metallurgy, Iron was unknown to them. The use of iron in the Indian subcontinent began much later, during the Vedic Period around 1000 BCE. Hence, option 1 is the correct answer.
• Archaeological excavations at major sites like Harappa, Mohenjo-daro, and Lothal have revealed a wide variety of artifacts made of Copper, Bronze, Gold, and Silver, but no iron implements have been discovered.
• The Harappans produced Bronze by mixing Copper with Tin. Copper was sourced from the Khetri mines in Rajasthan, while Tin was likely imported from Afghanistan.
• The absence of Iron suggests that the Harappans relied on softer metals and stone tools for agriculture, construction, and warfare.

Additional Information

• Use of Copper and Bronze:
• Copper was the first metal to be used extensively by the Harappan people. They manufactured tools like axes, saws, knives, and spearheads.
• The invention of Bronze allowed for the creation of more durable tools and artistic figures, marking a significant technological leap.
• Precious Metals (Gold and Silver):
• Gold was used to create elaborate jewelry, including necklaces, bangles, and earrings. It is believed to have been sourced from Southern India (modern-day Karnataka) and Afghanistan.
• Silver was also widely used for making vessels and ornaments. The Harappans were among the earliest people in the world to use silver.
• Lead and Tin:
• The Harappans were aware of Lead and Antimony. Tin was a rare commodity and its scarcity is reflected in the limited number of high-quality bronze artifacts compared to copper ones.
• Trade and Metallurgy:
• The civilization maintained active trade links with Mesopotamia (modern-day Iraq) and Oman, exchanging metal goods for other commodities.

Important Points

• Technological Limitations: Smelting Iron requires a much higher temperature (approx 1538°C) compared to Copper (approx 1085°C). The Harappans had not yet developed the advanced furnace technology required to extract iron from its ore.
• Lost-Wax Technique: One of the most famous metal artifacts of this era is the "Dancing Girl" statue found at Mohenjo-daro, created using the Cire Perdue or lost-wax casting method.
• Transition to Iron Age: The Iron Age in India is associated with the Painted Grey Ware (PGW) culture. Early evidence of iron usage has been found at sites like Atranjikhera in Uttar Pradesh, dating back to approximately 1000 BCE, which is long after the decline of the mature Harappan phase.
• Agricultural Implements: Due to the lack of Iron, Harappan farmers used wooden plows and copper/bronze sickles for harvesting crops like wheat and barley.

The correct answer is By transpiration.

Key Points

• Transpiration is the biological process through which plants eliminate excess water in the form of water vapor from their aerial parts, primarily the leaves.
• Approximately 97-99% of the water absorbed by a plant's roots is not utilized for growth or photosynthesis but is instead released into the atmosphere via this process.
• This process mainly occurs through microscopic pores called stomata, which are located on the underside of the leaves and are regulated by guard cells.
• Transpiration serves several vital functions, including the creation of a transpirational pull (suction force) that aids in the upward transport of water and minerals from the soil to the top of the plant.
• It also helps in thermoregulation, providing a cooling effect to the plant during hot weather, similar to sweating in humans.
• Hence, the correct option is By transpiration.

Additional Information

• Types of Transpiration:
• Stomatal Transpiration: This is the most common type, accounting for about 80-90% of the total water loss through stomata.
• Cuticular Transpiration: Occurs through the cuticle (waxy layer) of the leaf, contributing to about 5-10% of water loss.
• Lenticular Transpiration: Water loss that happens through lenticels, which are small openings in the bark of woody stems.
• Factors Affecting Rate:
• Light: Increases the rate as stomata open in the presence of sunlight.
• Temperature: A higher temperature increases the rate of evaporation, thereby increasing transpiration.
• Humidity: If atmospheric humidity is high, the rate of transpiration decreases because the air is already saturated with moisture.
• Wind Speed: Moving air removes water vapor from the leaf surface, increasing the rate.
• Guttation: This is another method of water loss where water is released in liquid droplets from the edges of leaves through specialized structures called hydathodes. It usually occurs at night or early morning when soil moisture is high and transpiration is low.

Important Points

• Xylem: This is the specialized vascular tissue responsible for the conduction of water and nutrients from the roots to the rest of the plant.
• Cohesion-Tension Theory: This scientific theory explains how water moves upwards against gravity. It relies on the cohesive forces between water molecules and the tension created by transpiration in the leaves.
• Potometer: A laboratory instrument used by botanists to measure the rate of transpiration in a plant shoot.
• Adaptations: Xerophytes (plants in dry climates, like cacti) have adapted features such as sunken stomata, thick cuticles, or leaves modified into spines to minimize water loss.
• Environmental Impact: Transpiration is a key component of the water cycle, as it contributes significantly to atmospheric moisture and rainfall patterns.

The correct answer is Neither I Nor II.

Key Points

• Article 26 of the Indian Constitution provides the freedom to manage religious affairs. It states that every religious denomination has the right to establish and maintain institutions for religious and charitable purposes, manage its own affairs in matters of religion, and own and acquire movable and immovable property. Hence, statement I is incorrect.
• Article 27 of the Constitution relates to the freedom as to payment of taxes for promotion of any particular religion. It mandates that no person shall be compelled to pay any taxes, the proceeds of which are specifically used for the promotion or maintenance of any particular religion or religious denomination. Hence, statement II is incorrect.
• Both articles are part of the Right to Freedom of Religion, which is a Fundamental Right guaranteed under Part III of the Constitution of India.
• The statements provided in the question have swapped the definitions of the two articles, making both descriptions factually wrong in the context of the Article numbers mentioned.
• Hence, the correct answer is Neither I Nor II.

Additional Information

• Right to Freedom of Religion (Articles 25–28):
• Article 25: Guarantees freedom of conscience and the right to freely profess, practice, and propagate religion to all citizens. This right is subject to public order, morality, and health.
• Article 26: Protects collective religious rights. It allows religious denominations to manage their own internal affairs without state interference, provided they do not violate public order.
• Article 27: Prevents the State from using taxpayer money to favor one religion over another, upholding the secular character of the Indian polity.
• Article 28: Prohibits religious instruction in educational institutions wholly maintained out of State funds. In other institutions recognized by the State or receiving aid, religious instruction is permitted only with the consent of the individual (or guardian).

Important Points

• Difference between Tax and Fee:
• Under Article 27, the State is prohibited from levying a tax for religious promotion. However, the courts have clarified that the State can levy a fee to provide secular services, such as providing safety, health, and sanitation facilities for pilgrims during festivals or at religious sites.
• Religious Denominations:
• For a group to be considered a religious denomination under Article 26, it must be a collection of individuals who have a system of beliefs (doctrines) which they regard as conducive to their spiritual well-being, a common organization, and a distinctive name.
• Secularism in India:
• The inclusion of these articles reinforces the Positive Concept of Secularism in India, where the State maintains an equal distance from all religions and gives equal respect to all faiths, rather than a total separation of state and religion seen in Western models.

The correct answer is 47.

Key Points

• The Concurrent List, also known as List III, is one of the three lists defined in the Seventh Schedule of the Constitution of India.
• The last subject mentioned in the Concurrent List is officially numbered as 47. While the total number of items has increased due to amendments, the numbering still concludes at 47.
• This list contains subjects of common interest to both the Union Government and the State Governments, allowing both levels of government to legislate on them.
• The concept of the Concurrent List in the Indian Constitution was borrowed from the Constitution of Australia.
• Under Article 246, the Parliament and the State Legislatures have concurrent powers to make laws with respect to any of the matters enumerated in this list.

Additional Information

• The Seventh Schedule and Three Lists:
• The Seventh Schedule provides for the distribution of legislative powers between the Union and the States.
• Union List (List I): Originally contained 97 subjects, currently it has 100 subjects. These include defense, foreign affairs, and banking.
• State List (List II): Originally contained 66 subjects, currently it has 61 subjects. These include police, public health, and agriculture.
• Concurrent List (List III): Originally contained 47 subjects, currently it has 52 subjects. The subjects added include Education and Forests.
• The 42^nd Amendment Act, 1976:
• This landmark amendment moved five subjects from the State List to the Concurrent List to ensure national uniformity.
• The transferred subjects are Education, Forests, Weights and Measures, Protection of Wild Animals and Birds, and Administration of Justice (excluding the Supreme Court and High Courts).
• Legislative Supremacy and Article 254:
• If there is a conflict between a law made by the Parliament and a law made by a State Legislature on a subject in the Concurrent List, the Central law prevails.
• However, if the State law has been reserved for the consideration of the President and has received his assent, the State law prevails in that particular state.
• Residuary Powers:
• Subjects that are not mentioned in any of the three lists are called Residuary Subjects.
• According to Article 248, the power to legislate on these subjects is vested solely in the Union Parliament.
• Examples of Concurrent List Subjects:
• Key subjects include Criminal Law, Marriage and Divorce, Bankruptcy and Insolvency, Trusts and Trustees, Civil Procedure, Contempt of Court, and Vital Statistics (including registration of births and deaths).
• The final entry, number 47, specifically relates to fees in respect of any of the matters in the list, excluding fees taken in any court.

The correct answer is Mizoram.

Key Points

• Chawng Laizawn is a popular and vibrant folk dance that originates from the North-Eastern state of Mizoram.
• This dance is specifically associated with the Pawi community, also known as the Lai tribe, who primarily inhabit the Lawngtlai district of Mizoram.
• The dance is traditionally performed on two distinct occasions: to celebrate a successful hunt (specifically when a warrior/hunter returns with a trophy) or during the Pawl Kut festival, which is a post-harvest festival.
• It is a rhythmic performance where drums and gongs serve as the primary musical instruments to provide the beat.
• The performance involves a group of dancers, often both men and women, who move in a synchronized and circular fashion, reflecting the cultural heritage and social cohesion of the Mizo people.

Additional Information

• Mizoram:
• The state is famous for the Cheraw Dance, popularly known as the Bamboo Dance, where dancers move between horizontally placed bamboo poles.
• Other prominent folk dances of Mizoram include Khuallam (dance of the guests), Chheihlam, and Sarlamkai (a warrior dance).
• The major festivals of the state are known as Kuts, such as Chapchar Kut (celebrated in March), Mim Kut, and Pawl Kut.
• Assam:
• The most famous dance is Bihu, performed during the three Bihu festivals (Rongali, Kongali, and Bhogali).
• Sattriya is a Classical Dance of India that originated in the Sattras (monasteries) of Assam, founded by the saint Srimanta Sankardev in the 15^th century.
• Other folk dances include Bagurumba (performed by the Bodo community) and Jhumur.
• Ladakh:
• Shondol is known as the 'Royal Dance' of Ladakh and was historically performed for the King of Ladakh on special occasions.
• Jabro is a traditional folk dance of the Nomadic people of the Tibetan plateau living in the Changthang region of Ladakh.
• Chhattisgarh:
• Panthi is a famous folk dance of the Satnami community, performed on the birth anniversary of Guru Ghasidas.
• Raut Nacha is a traditional dance performed by the Yaduvanshi (cowherds) community, typically during the Dev Uthani Ekadashi festival.
• Karma dance is another significant folk dance performed by tribal groups like the Gonds, Baigas, and Oraons.

Important Points

• Cultural Significance: In Mizo culture, dances are not merely for entertainment but are deeply intertwined with rituals and community milestones.
• Lai Tribe: The Lai people have a distinct dialect and cultural practices within the broader Mizo identity, and Chawng Laizawn is a key marker of their specific ethnic pride.
• Instruments: Traditional Mizo music heavily relies on percussion. The Khuang (drum) is considered the most important instrument and is used in almost all folk dances.
• Mizoram Statehood: Mizoram became the 23^rd state of the Indian Union on 20 February 1987, following the Mizo Accord of 1986.

The correct answer is Uttar Pradesh.

Key Points

• Kajri is one of the most prominent folk song and dance genres of India, predominantly famous in the state of Uttar Pradesh and some parts of Bihar.
• It is traditionally associated with the monsoon season, specifically the months of Shravan and Bhadrapada (typically July, August, and September), when the dark clouds bring relief from the summer heat.
• The origin of Kajri is believed to be the city of Mirzapur in Eastern Uttar Pradesh. Legend suggests it evolved from the longing of a woman for her husband during the rainy season.
• The performance of Kajri is a vital part of the Teej festival, where women gather, sing, and dance while enjoying swings in the rain.
• It is usually sung in the Bhojpuri and Maithili dialects, reflecting the local culture and rural lifestyle of the Gangetic plains. Hence, the correct answer is Uttar Pradesh.

Additional Information

• Assam:
• This state is world-famous for the Bihu dance, which is performed during the three Bihu festivals: Rongali Bihu, Kongali Bihu, and Bhogali Bihu.
• Another significant dance is Sattriya, which is one of the eight Classical Dances of India, introduced by the great saint Srimanta Sankardev in the 15^th century.
• Other folk forms include Bagurumba (of the Bodo community) and Ojapali.
• Punjab:
• Punjab is renowned for its high-energy folk dances such as Bhangra, traditionally performed by men during the harvest festival of Vaisakhi.
• Giddha is the female counterpart to Bhangra, characterized by rhythmic clapping and singing of folk verses called Boliyan.
• Other traditional dances include Jhumar, Luddi, and Sammi, reflecting the agrarian life of the Five Rivers region.
• Maharashtra:
• The most iconic folk dance of Maharashtra is Lavani, which combines powerful rhythm, traditional Dholak beats, and expressive lyrics.
• The Koli dance is performed by the fishing community, mimicking the movement of waves and the casting of nets.
• Other notable forms include Dhangari Gaja (shepherd dance), Lezim, and Povada, which is a narrative song form praising historical heroes like Chhatrapati Shivaji Maharaj.
• Uttar Pradesh (Other Dances):
• Apart from Kajri, the state is the cradle of Kathak, a major Classical Indian Dance form.
• Folk forms like Charkula (popular in the Braj region), Raslila (depicting the life of Lord Krishna), and Nautanki (a form of folk theater) are widely practiced across the state.

Important Points

• Musical Styles of Kajri: There are two main versions of Kajri. The Dhunmun Kajri is the rustic folk style performed in villages, while the Benares Kajri has been refined into a semi-classical musical form often included in Thumri and Dadra recitals.
• Thematic Focus: The lyrics of Kajri often center on themes of Biraha (separation), romance, the beauty of the monsoon clouds, and the swing (Jhoola).
• Instruments: Traditional musical instruments used during the performance include the Dholak, Majira (cymbals), Harmonium, and sometimes the Sarangi or Shehnai.
• Geographical Spread: While Mirzapur is the heart of Kajri, it is also popular in Varanasi, Prayagraj (Allahabad), and Lucknow.

The correct answer is June.

Key Points

• Ganga Dussehra, also known as Gangavataran, is a major Hindu festival celebrated to commemorate the descent of the holy River Ganga from heaven to earth.
• The festival is observed on the Dashami (10^th day) of the Shukla Paksha (waxing phase of the moon) during the Hindu month of Jyeshtha.
• In the Gregorian calendar, this auspicious day typically falls in the month of June, though occasionally it may begin in late May depending on the lunar cycle.
• The festival marks the successful culmination of the intense penance performed by King Bhagiratha, who sought to bring the river to earth to liberate the souls of his ancestors. Hence, the statement regarding the month is correct.
• It is believed that on this specific day, the goddess Ganga descended from the heavens, making it one of the most sacred days for purification and spiritual merit.

Additional Information

• Significance of the Name: The word Dussehra is derived from the Sanskrit words 'Dasha' (ten) and 'Hara' (to destroy/remove). It signifies the removal of ten types of sins (three physical, four verbal, and three mental) through the grace of the river.
• Prominent Locations: The festival is celebrated with immense fervor at the Ghats of the Ganga in holy cities such as Varanasi, Haridwar, Rishikesh, Prayagraj, and Garhmukteshwar. Devotees gather in thousands to take a ritualistic holy dip in the waters.
• The Role of Lord Shiva: According to ancient Puranas, the force of the falling Ganga was so powerful that it could have swept the earth away. To prevent this, Lord Shiva caught the river in his matted locks (Jata), releasing her in gentle streams.
• Rituals and Traditions: On this day, pilgrims perform the Ganga Aarti at dusk, offering earthen lamps (diyas) and flowers to the river. Many devotees also observe fasts and engage in charitable activities (Daana) to earn spiritual merit.
• Difference from Ganga Jayanti: It is important to distinguish this festival from Ganga Jayanti (or Ganga Saptami), which is celebrated in the month of Vaisakha (April/May) and marks the day the river was reborn after being consumed by Sage Jahnu.

Important Points

• Duration: While the main festival is on the tenth day, the celebrations often span ten days leading up to the Dashami, involving continuous prayers and religious discourses.
• Cultural Impact: In states like Uttar Pradesh, Bihar, and West Bengal, the festival is a vital part of the cultural fabric, promoting the ecological and spiritual preservation of the National River of India.
• Environmental Awareness: In recent years, the government and local bodies use the occasion of Ganga Dussehra to promote the Namami Gange project and other initiatives aimed at cleaning and rejuvenating the river ecosystem.

The correct answer is West Bengal.

Key Points

• According to the Census 2011, West Bengal was identified as the fourth most populous state in India, with a total population of approximately 91,276,115 (9.13 crore).
• Among the options provided, West Bengal holds the highest population figure, significantly exceeding Tamil Nadu, which recorded 72,147,030 inhabitants.
• Rajasthan, the largest state by area, had a population of 68,548,437, placing it below the population count of West Bengal in the 2011 Census records.
• Karnataka recorded a population of 61,095,297, making it the state with the lowest population among the four given choices.
• West Bengal also exhibited a high decadal growth rate of 13.84 percent between 2001 and 2011 and remains one of the most densely populated regions in the country.

 Additional Information

• The 2011 Census was the 15^th National Census of India and the 7^th after independence, conducted under the slogan Our Census, Our Future.
• Population Hierarchy in 2011:
• Uttar Pradesh: Ranked first with a population of about 19.98 crore.
• Maharashtra: Ranked second with 11.24 crore.
• Bihar: Ranked third with 10.41 crore.
• West Bengal: Ranked fourth with 9.13 crore.
• Demographic Facts:
• Highest Density: Bihar had the highest population density with 1,106 persons per sq km, followed by West Bengal with 1,028.
• Lowest Population: Sikkim was the least populous state, while Lakshadweep was the least populous Union Territory.
• Sex Ratio: The overall sex ratio for India was 943 females per 1,000 males.

The correct answer is study Earth's spectral and polarimetric properties from lunar orbit.

Key Points

• The SHAPE payload stands for Spectro-polarimetry of Habitable Planet Earth.
• Unlike other payloads on the lander or rover, SHAPE was integrated into the Propulsion Module of the Chandrayaan-3 mission.
• Its primary objective is to study the Earth from the lunar orbit to identify the unique spectral and polarimetric signatures of a habitable planet.
• The data collected helps scientists understand the characteristics of light reflected by Earth, which serves as a benchmark for searching for habitable exoplanets outside our solar system.
• It operates in the Near-Infrared (NIR) wavelength range, specifically from 1.0 to 1.7 μm, to observe the disk of the Earth.

 Additional Information

• Lander Payloads (Vikram):
• ChaSTE (Chandra's Surface Thermophysical Experiment): Measures the thermal conductivity and temperature of the lunar surface near the south pole.
• ILSA (Instrument for Lunar Seismic Activity): A seismometer designed to detect moonquakes and seismic vibrations around the landing site.
• RAMBHA-LP (Radio Anatomy of Moon Bound Hypersensitive Ionosphere and Atmosphere - Langmuir Probe): Analyzes the plasma density (ions and electrons) and its variations over time.
• Rover Payloads (Pragyan):
• APXS (Alpha Particle X-ray Spectrometer): Used to determine the elemental composition of the lunar soil and rocks.
• LIBS (Laser Induced Breakdown Spectroscope): Employs laser pulses to determine the chemical and mineralogical composition of the lunar surface.
• Mission Success: Chandrayaan-3 successfully landed near the Lunar South Pole on August 23, 2023, making India the first country to reach this specific region.

The correct answer is 1000.

Key Points

• The unit kJ represents a kilojoule, which is a multiple of the base unit of energy, the joule (J).
• In the International System of Units (SI), the prefix kilo- is used to denote a factor of 10³ or 1000.
• The joule is defined as the amount of energy transferred to an object when a force of one newton acts on that object in the direction of the force's motion through a distance of one meter.
• Mathematically, the relationship is defined as 1 kilojoule = 1000 joules. This conversion is fundamental in thermodynamics, physics, and chemistry when measuring heat or work.

 Additional Information

• Metric System Multiples:
• Mega (M): Represents 10⁶ or 1,000,000 units. Therefore, 1 MJ = 1,000,000 J.
• Giga (G): Represents 10⁹ or 1,000,000,000 units.
• Milli (m): Represents 10⁻³ or 1/1000 of a unit. Therefore, 1 mJ = 0.001 J.
• Historical Context:
• The unit is named after the English physicist James Prescott Joule, who demonstrated the mechanical equivalent of heat in the 19^th century.
• Energy Conversions:
• 1 calorie (cal) is equivalent to approximately 4.184 joules.
• 1 kilowatt-hour (kWh), often used for electrical energy billing, is equal to 3,600,000 joules or 3600 kJ.
• The joule can also be expressed in terms of other SI units as 1 kg·m²/s² or 1 Watt-second.

The correct answer is Mahatma Gandhi.

Key Points

• Hind Swaraj, also known as 'Indian Home Rule', is a seminal work written by Mohandas Karamchand Gandhi in 1909 while he was traveling from London to South Africa.
• The entire manuscript was written on the ship SS Kildonan Castle using the ship's stationery; Gandhi famously wrote with his left hand when his right hand became exhausted.
• The book was originally composed in Gujarati and was subsequently published in the columns of Indian Opinion in South Africa before being released as a book.
• It is written in a dialogic form, consisting of a conversation between an Editor (representing Gandhi's voice) and a Reader (representing the extremist nationalist viewpoint of the time).
• The text serves as a manifesto for Swaraj (Self-Rule), where Gandhi argues that India can only achieve true independence by rejecting modern Western civilization and adopting Satyagraha (non-violent resistance).
• In 1910, the British authorities in India banned the Gujarati edition of the book, labeling it as seditious literature, which prompted Gandhi to publish the English translation.

 Additional Information

• Ravindra Nath Tagore
• He was a polymath who reshaped Bengali literature and music; he was the first non-European to win the Nobel Prize in Literature in 1913 for his collection Gitanjali.
• Tagore founded the Visva-Bharati University at Shantiniketan and is the author of the national anthems of both India and Bangladesh.
• Gopal Krishna Gokhale
• A prominent Moderate leader of the Indian National Congress, he was considered the political mentor or 'guru' of Mahatma Gandhi.
• He founded the Servants of India Society in 1905 with the aim of training Indians to devote their lives to the cause of the nation.
• Bal Gangadhar Tilak
• Known as the 'Father of Indian Unrest', he was a key Extremist leader who famously declared, 'Swaraj is my birthright and I shall have it'.
• During his six-year imprisonment in Mandalay Jail, he authored the famous commentary on the Bhagavad Gita titled Gita Rahasya.

The correct answer is Digantara.

Key Points

• The SCOT mission, which stands for Space-based Compact Optical Tracker, was developed by Digantara, a leading Indian space-technology startup based in Bengaluru.
• The mission was successfully launched in January 2025 as part of the SpaceX Transporter-12 rideshare mission from the United States.
• The primary objective of the SCOT payload is to advance Space Situational Awareness (SSA) by providing high-resolution, in-situ tracking of space objects and space debris from orbit.
• This launch represents a major step for India's private space sector, as it is one of the first commercial space-based sensors designed to monitor the orbital environment directly from space rather than from the ground.
• The data collected by the SCOT sensor will be integrated into Digantara’s proprietary Space-MAP (Space-Mission Assurance Platform) to help satellite operators avoid potential collisions.

Additional Information

• Digantara:
• Founded by Anirudh Sharma and Rahul Rawat, the company is headquartered in Bengaluru, Karnataka.
• It focuses on building a comprehensive infrastructure for space surveillance and space traffic management to ensure the sustainability of outer space activities.
• Space Situational Awareness (SSA):
• SSA involves the detection, tracking, and characterization of all objects in Earth's orbit, including active satellites and space junk.
• With the rapid increase in satellite constellations, SSA has become critical to preventing Kessler Syndrome, a scenario where the density of objects in Low Earth Orbit (LEO) is high enough that collisions could cause a cascade of debris.
• Other Notable Private Space Companies in India:
• Skyroot Aerospace: Based in Hyderabad, they gained fame for launching Vikram-S, India's first privately developed rocket, in November 2022.
• Agnikul Cosmos: A Chennai-based startup that developed the Agnibaan rocket and the world's first 3D-printed semi-cryogenic engine.
• Pixxel: A space-data company that specializes in building a constellation of hyperspectral imaging satellites to provide detailed planetary health data.
• Transporter Missions:
• These are dedicated rideshare missions operated by SpaceX, allowing multiple small satellites from various organizations and countries to be launched together at a lower cost.

Important Points

• The SCOT payload is designed to detect objects as small as 1 centimeter in size, which are often invisible to ground-based radar systems but still pose a significant threat to spacecraft.
• The Government of India, through IN-SPACe (Indian National Space Promotion and Authorization Centre), has been actively supporting private players like Digantara to boost India's share in the global space economy.
• The launch in January 2025 reinforces India's position as a hub for cost-effective and innovative space solutions under the Make in India initiative.

The correct answer is BharatGPT.

Key Points

• BharatGPT is India's first indigenously developed Large Language Model (LLM), created by the Bengaluru-based conversational AI startup CoRover.ai.
• It was designed specifically to bridge the language gap in India, supporting over 14 Indian languages and more than 22 languages in total across text, voice, and video formats.
• The model is developed in collaboration with the National Language Translation Mission (NLTM), also known as BHASHINI, under the Ministry of Electronics and Information Technology (MeitY).
• Unlike many global LLMs, BharatGPT is fine-tuned to understand the cultural nuances and diverse linguistic dialects of the Indian population, making it a "Sovereign AI" solution.
• The platform integrates with Google Cloud’s Vertex AI to provide scalable, secure, and high-performance generative AI capabilities for both government and private enterprises.

Additional Information

• CoRover.ai: Founded in 2016, it is a leading conversational AI company that powers several high-traffic virtual assistants, including IRCTC’s AskDISHA, Linguistic University, and Max Life Insurance.
• Multi-modal Capabilities: BharatGPT is not limited to text; it features voice-to-voice interaction, which is crucial for accessibility among the non-literate or semi-literate populations in rural India.
• Data Sovereignty: A key feature of BharatGPT is that it ensures all data stays within the geographical boundaries of India, complying with the Digital Personal Data Protection (DPDP) Act, 2023.
• Bhashini Mission: This is a government initiative aimed at providing all Indians easy access to the internet and digital services in their own language. BharatGPT serves as a significant technological pillar for this mission.
• Applications: The LLM is being deployed across sectors such as Healthcare, Education, Banking, and E-governance to provide automated, human-centric support in regional languages like Hindi, Kannada, Tamil, Telugu, and Marathi.

Important Points

• Comparison with Global Models: While ChatGPT (OpenAI) and Gemini (Google) are trained on vast global datasets, BharatGPT focuses on Indian context, legal frameworks, and socio-economic data points.
• Launch Timeline: The model gained significant attention in 2023 and 2024 as India pushed for self-reliance (Atmanirbhar Bharat) in the field of Artificial Intelligence.
• AskDISHA 2.0: The upgraded version of the IRCTC chatbot utilizes CoRover’s technology to handle millions of queries daily, proving the scalability of the BharatGPT framework.
• Efficiency: The model is designed to be more computationally efficient for Indian languages compared to Western models, which often struggle with the complex scripts and syntax of Indic languages.

The correct answer is less, decrease.

Key Points

• Population change refers to the change in the number of people during a specific time period. This is a dynamic process influenced by three main factors: births, deaths, and migration.
• The Birth rate is the number of live births per 1,000 people in a year, while the Death rate is the number of deaths per 1,000 people in a year.
• When the birth rate is less than the death rate, it signifies that the number of people dying exceeds the number of babies being born. As a result, the total population will decrease over that period, assuming no significant inward migration. Hence, the statement aligns with the logic of natural decrease.
• The difference between the birth rate and the death rate of a country is called the natural growth rate. If the death rate is higher, the natural growth rate becomes negative.
• Until the 1800s, the world's population grew steadily but slowly because, although many babies were born (high birth rate), the death rate was also high due to poor health facilities and food shortages.
• In modern times, many developed nations have seen a population decline because their birth rate has fallen below the death rate, a phenomenon often observed in countries with aging populations.

Additional Information

• Components of Population Change:
• There are three primary components: Births, Deaths, and Migration. While births and deaths are natural causes, migration is a man-made or induced cause of change.
• Natural Increase occurs when the birth rate is higher than the death rate. This was the primary reason for the population explosion in the 20^th century.
• Migration Dynamics:
• Migration is the movement of people across boundaries. It can be internal (within the country) or international (between countries).
• Immigration is when a person arrives in a new country, increasing its population, while Emigration is when a person leaves a country, decreasing its population.
• Countries like the United States of America and Australia have gained in-numbers by in-migration or immigration.
• Demographic Transition:
• This is a model used to represent the transition from high birth and death rates to low birth and death rates as a country develops from a pre-industrial to an industrialized economic system.
• In the final stage of demographic transition, both birth and death rates decline significantly, often leading to a stable or declining population.
• Factors Influencing Rates:
• Birth rates are influenced by social factors, education levels (especially of women), and economic stability.
• Death rates have plummeted globally due to advancements in medicine, better sanitation, and improved nutrition.
• The World Population reached 8 billion in November 2022, largely driven by high natural increase in developing regions.

Important Points

• Statistical Facts:
• A stationary population occurs when the birth rate is exactly equal to the death rate and there is no net migration.
• The Infant Mortality Rate (IMR) and Maternal Mortality Rate (MMR) are critical subsets of the death rate that reflect the socio-economic development and healthcare quality of a nation.
• The Replacement Level Fertility is the total fertility rate—the average number of children born per woman—at which a population exactly replaces itself from one generation to the next, without migration. This value is roughly 2.1 in most countries.

The correct answer is Manufacturing.

Key Points

• The Primary Sector of the economy includes all those activities the end purpose of which consists of exploiting natural resources. It forms the base for all other products that we subsequently make.
• Fishing is a primary activity because it involves the direct extraction of aquatic resources from nature without significant chemical or mechanical transformation at the point of harvest. Hence, it is included in the primary sector.
• Mining involves the extraction of minerals and ores directly from the earth's crust. Since it deals with raw earth materials, it is classified under the primary sector. Hence, it is included in the primary sector.
• Forestry involves activities such as logging, timber production, and the collection of wild-grown forest products. It relies entirely on the biological and environmental growth of forests. Hence, it is included in the primary sector.
• Manufacturing refers to the process of converting raw materials into finished goods using machinery, tools, and labor. This activity adds value to primary products and is categorized under the Secondary Sector. Hence, statement 3 is not included in the primary sector and is the correct answer.

Additional Information

• Sectors of Economy:
• Primary Sector: This sector is also known as the Agriculture and Related Sector. It includes Agriculture, Dairy, Fishing, Forestry, and Mining. In developing countries like India, it remains a significant provider of employment.
• Secondary Sector: This sector covers activities in which natural products are changed into other forms through ways of manufacturing. It is also called the Industrial Sector. Examples include Textile mills, Steel plants, and Automobile assembly.
• Tertiary Sector: Often called the Service Sector, it provides support to the primary and secondary sectors. It includes Transport, Banking, Insurance, Education, and Health Services. It currently contributes the highest share to India's GDP.
• Advanced Classifications:
• Quaternary Sector: This is a knowledge-based part of the economy, including services such as Information Technology (IT), Research and Development (R&D), and Financial planning.
• Quinary Sector: This includes the highest level of decision-making in a society or economy. This includes top officials in Government, Science, and Universities.
• Indian Context:
• In India, while the primary sector employs nearly 45-50% of the workforce, its contribution to the Gross Value Added (GVA) is relatively lower compared to the service sector, highlighting the issue of disguised unemployment in rural areas.

Important Points

• Workers in the primary sector are often called Red-collar workers due to the outdoor nature of their work.
• Workers in the secondary sector (specifically physical labor) are known as Blue-collar workers.
• The transition of an economy from primary to secondary and then to tertiary is known as Structural Transformation. In India, there has been a direct jump from the primary to the tertiary sector in terms of GDP share, bypassing a dominant manufacturing phase.

The correct answer is Preeti Shenoy.

Key Points

• The book 'When Love Came Calling' is authored by Preeti Shenoy, who is one of India's most popular and highest-selling contemporary writers.
• Published in September 2020 by HarperCollins Publishers India, the novel is a story about two starkly different individuals, Puja and Arush, exploring themes of love, self-discovery, and finding one's purpose.
• Preeti Shenoy has the distinction of being nominated for the Forbes India Celebrity 100 list multiple times since 2013, highlighting her influence in the Indian literary landscape.
• The narrative of 'When Love Came Calling' is set against the backdrop of life in India and the UK, focusing on the pressures faced by the youth regarding career choices and social expectations.
• This book is considered her 15^th book, adding to her repertoire of national bestsellers that often deal with human emotions and relationships in a relatable manner.

Additional Information

• Preeti Shenoy:
• She is an Indian author and artist, born in 1971.
• Her notable works include 'Life is What You Make It', 'The Secret Wish List', and 'A Hundred Little Flames'.
• She is often praised for her simple yet evocative prose and has received several awards, including the Indian of the Year award by Brands Academy.
• Aruni Kashyap:
• He is an Indian-American writer and translator from Assam.
• He is well-known for his debut novel 'The House with a Thousand Stories' (2013), which is set against the backdrop of the insurgency in Assam.
• He also writes in Assamese and serves as an Associate Professor of Creative Writing.
• Chetan Bhagat:
• An Indian author and columnist, he is famous for his books that cater to the Indian youth.
• His best-known works include 'Five Point Someone', 'The 3 Mistakes of My Life', and 'One Indian Girl'.
• Many of his novels have been adapted into Bollywood movies, such as '3 Idiots' and '2 States'.
• Tanya Selvaratnam:
• She is an Emmy-nominated producer, activist, and author based in the United States.
• She authored the book 'Assume Nothing: A Story of Intimate Violence' (2021), which is a powerful memoir regarding her personal experiences.
• She is also the author of 'The Big Lie: Motherhood, Feminism, and the Reality of the Biological Clock'.

Important Points

• Literary Context: Preeti Shenoy's writing style is frequently categorized as popular fiction or commercial fiction, making it highly accessible to a broad audience in India.
• Target Audience: 'When Love Came Calling' specifically targets the Young Adult (YA) demographic, focusing on the transitional phase of teenagers entering adulthood.
• Publisher Details: HarperCollins India is a subsidiary of News Corp and has been a primary publisher for many of Shenoy's recent titles, emphasizing her commercial success.
• Societal Themes: The book highlights the volunteering culture and the gap between parental ambition and child’s passion, which is a prevalent theme in modern Indian literature.

The correct answer is Leather Industry.

Key Points

• The Production Linked Incentive (PLI) scheme was launched by the Government of India to boost domestic manufacturing, increase exports, and make India a global supply chain hub under the Atmanirbhar Bharat initiative.
• The scheme initially targeted three industries in March 2020 but was later expanded to cover 14 key sectors with a total outlay of approximately ₹1.97 lakh crore.
• Manufacturing of Medical Devices is a recognized sector under the PLI scheme, specifically aimed at reducing import dependence on high-end medical equipment like radiology and imaging devices, anaesthetics, and cancer care equipment. Hence, statement 1 is covered under the scheme.
• Automobiles and Auto Components were included in the scheme in September 2021 with a financial outlay of ₹25,938 crore to incentivize the production of Advanced Automotive Technology (AAT) products and Electric Vehicles (EVs). Hence, statement 3 is covered under the scheme.
• Drones and Drone Components were approved under the PLI scheme in 2021 to position India as a global drone hub by 2030, providing an incentive of 20% of the value addition made by the manufacturer. Hence, statement 4 is covered under the scheme.
• The Leather Industry is not one of the 14 sectors currently covered under the PLI scheme. While the government supports this sector through the Indian Footwear and Leather Development Programme (IFLDP), it does not fall under the specific PLI framework. Hence, the Leather Industry is the correct answer.

Additional Information

• List of 14 Sectors: The 14 sectors under the PLI scheme include Mobile Manufacturing, Medical Devices, Critical Key Starting Materials (KSMs)/Drug Intermediaries, Automobiles and Auto Components, Pharmaceutical Drugs, Specialty Steel, Telecom and Networking Products, Electronic/Technology Products, White Goods (ACs and LEDs), Food Products, Textile Products (MMF segment and Technical Textiles), High-Efficiency Solar PV Modules, Advanced Chemistry Cell (ACC) Battery, and Drones.
• Objectives: The primary goal is to provide financial incentives to companies based on their incremental sales from products manufactured in domestic units, encouraging Foreign Direct Investment (FDI) and large-scale manufacturing.
• Implementation: Different ministries manage specific sectors. For example, the Ministry of Heavy Industries oversees Automobiles and Drones, while the Department of Pharmaceuticals manages Medical Devices and Drugs.
• Economic Impact: The scheme is expected to contribute significantly to India's GDP, create employment opportunities for millions, and significantly reduce the trade deficit by promoting import substitution.

Important Points

• Tenure: The duration of the PLI schemes varies by sector, typically ranging from 4 to 6 years, starting from the base year 2019-20 or 2021-22.
• Eligibility: Incentives are provided to both MSMEs and Large Enterprises that meet specific investment and production thresholds defined for each category.
• Recent Developments: In 2023, the government considered expanding the PLI to other sectors like Toys and Bicycles, but as of the current official list, the Leather Industry remains excluded from the PLI umbrella.

The correct answer is Both I and II.

Key Points

• A service in volleyball is the act of putting the ball into play by the right-back player, placed in the service zone. It is the only technical action where a player has total control over the ball without interference from teammates or opponents.
• Jump Serve (Jump and Serve): This is an advanced type of serve where the player increases the power and height of the serve by jumping to hit the ball. The server tosses the ball high, takes a rhythmic approach, and strikes the ball in mid-air. This technique generates high velocity and a steep downward angle, making it difficult for the receiving team to pass. Hence, statement I is correct.
• Floating Serve (Floater): A floating serve is hit with very little to no spin. Because of the lack of rotation, the ball's path becomes unpredictable as it interacts with the air currents, causing it to "dance" or move suddenly to the left, right, or drop down. This makes it extremely challenging for the defensive players to track and handle accurately. Hence, statement II is correct.
• Both the Jump Serve and the Floating Serve are fundamental strategies used in modern competitive volleyball to gain an advantage right from the start of the rally.
• Hence, the correct answer is Both I and II.

Additional Information

• History of Volleyball:
• Volleyball was invented in 1895 by William G. Morgan, a physical education director at the YMCA in Holyoke, Massachusetts. It was originally called "Mintonette" and was designed as an indoor sport for businessmen who found basketball too vigorous.
• The game was added to the Olympic Games program for the first time during the 1964 Tokyo Olympics.
• Basic Rules and Court Dimensions:
• A standard volleyball court measures 18 meters in length and 9 meters in width. It is divided by a net into two 9m x 9m halves.
• The height of the net is 2.43 meters for men and 2.24 meters for women.
• Each team consists of 6 players on the court. A team is allowed a maximum of three hits to return the ball over the net.
• Common Volleyball Terminology:
• Ace: A serve that results directly in a point because it hits the floor untouched or the receiving team cannot keep it in play.
• Libero: A specialized defensive player who wears a different colored jersey and can substitute for any back-row player without notice to the officials.
• Dig: The act of preventing the ball from hitting the floor after an attack or spike by the opponent.
• Set: A tactical pass, usually the second contact, that directs the ball towards a hitter to spike it into the opponent's court.

Important Points

• Governing Body: The Fédération Internationale de Volleyball (FIVB) is the international governing body for all forms of volleyball. It was founded in 1947 and is headquartered in Lausanne, Switzerland.
• Variations of Serves: Besides jump and floating serves, players also utilize the Underhand Serve (often for beginners), the Overhand Serve, and the Topspin Serve (which rotates forward rapidly to drop quickly into the court).
• Scoring System: Modern volleyball uses the Rally Point System, where a point is scored on every single rally, regardless of which team is serving. Matches are typically played as the best of five sets, with the first four sets played to 25 points and the fifth set (if necessary) played to 15 points.

The correct answer is 5.

Key Points

• The Dilwara Temples are a world-famous group of Svetambara Jain temples located about 2.5 kilometers from the Mount Abu hill station, the only hill station in Rajasthan.
• There are 5 distinct temples in the complex, each dedicated to a different Jain Tirthankara and possessing its own unique architectural identity.
• These temples were built between the 11^th and 16^th centuries (specifically between 1031 AD and 1582 AD) during the reign of the Chaulukya dynasty (Solanki rulers).
• The complex is globally renowned for its extraordinary architecture and stunning marble stone carvings, often considered superior to the Taj Mahal in terms of intricate detailing.
• The five temples included in the complex are Vimal Vasahi, Luna Vasahi, Pittalhar, Parshvanath, and Mahavir Swami.

Additional Information

• Vimal Vasahi Temple:
• Built in 1031 AD by Vimal Shah, a minister of the Solanki King Bhimdev I.
• It is dedicated to the first Jain Tirthankara, Lord Rishabha (also known as Adinath).
• The temple is famous for its "Rang Mandap," a central hall supported by 12 decorated pillars and a magnificent carved dome.
• Luna Vasahi Temple:
• Constructed in 1230 AD by two brothers, Vastupal and Tejpal, who were ministers of Raja Vir Dhawal of Gujarat.
• It is dedicated to the 22^nd Tirthankara, Lord Neminatha.
• The temple is noted for its "Hathishala" (elephant cell), featuring 10 marble elephants, and its incredibly delicate pendant carvings in the central dome.
• Pittalhar Temple:
• This temple was built by Bhima Shah, another minister from Gujarat, during the 14^th-15^th century.
• It is dedicated to Lord Adinath and houses a massive statue of the deity cast in five metals (Panchaloha), with brass (Pittal) being the dominant metal, giving the temple its name.
• Parshvanath Temple (Khartar Vasahi):
• Built between 1458 and 1459 by the Mandlika family, it is the tallest shrine in the Dilwara complex.
• It is dedicated to the 23^rd Tirthankara, Lord Parshvanath, and consists of a three-story building with grey stone carvings on the exterior walls.
• Mahavir Swami Temple:
• Completed in 1582, it is the smallest and newest temple in the complex, dedicated to the 24^th and last Tirthankara, Lord Mahavira.
• Despite its small size, it features beautiful wall paintings on the upper walls of the porch, dating back to 1764.

Important Points

• Architectural Style: The temples are built in the Maru-Gurjara style of architecture, which originated in Western India. This style is characterized by ornate carvings, multiple shrines, and vaulted ceilings.
• Material Sourcing: The white marble used for the construction was transported from the Arasuri hills near Ambaji in Gujarat, which was a massive logistical feat at the time.
• Location: Situated at a high altitude in the Aravalli Range, the site provides a serene environment conducive to meditation and religious activities.
• Preservation: The complex is managed by the Seth Kalyanji Paramanandji Pedhi trust and remains a vital pilgrimage site for the Jain community worldwide.

The correct answer is The sum of the atomic masses of all atoms in a molecule.

Key Points

• The molecular mass of a substance is defined as the sum of the atomic masses of all the atoms present in a single molecule of that substance. Hence, option 3 is correct.
• It is the relative mass of a molecule compared to 1/12^th of the mass of one carbon-12 atom.
• Calculation Method: To find the molecular mass, we multiply the atomic mass of each element by the number of its atoms in the chemical formula and then add the results. For example, in Water (H2O), the mass is (2 x 1u) + (1 x 16u) = 18u.
• The total number of atoms in a molecule is known as its atomicity, not its molecular mass. For instance, the atomicity of Phosphorus (P4) is 4. Hence, statement 1 is incorrect.
• The valency of an atom is its combining capacity. The sum of valencies is used to determine chemical formulas but does not represent the mass of the molecule. Hence, statement 2 is incorrect.
• The volume occupied by a molecule relates to its physical state and conditions like temperature and pressure, as described by Avogadro's Law, rather than its mass. Hence, statement 4 is incorrect.

Additional Information

• Atomic Mass Unit (u): Also known as the unified mass, it is the standard unit used for expressing atomic and molecular weights. It is exactly 1/12^th the mass of an unbound neutral atom of carbon-12 at rest and in its ground state.
• Molar Mass: While molecular mass refers to the mass of a single molecule (in u), molar mass refers to the mass of one mole of the substance (6.022 x 10^23 molecules) and is expressed in grams per mole (g/mol). Numerically, molecular mass and molar mass are the same.
• Formula Unit Mass: This term is specifically used for ionic compounds (like NaCl or CaCl2) where the constituent particles are ions rather than discrete molecules. It is calculated the same way as molecular mass.
• Significance in Chemistry: Molecular mass is essential for stoichiometry calculations in chemical reactions, allowing scientists to calculate the exact proportions of reactants needed to produce a specific amount of product.
• Example Calculations:
• Carbon Dioxide (CO2): (1 x 12u) + (2 x 16u) = 44u.
• Methane (CH4): (1 x 12u) + (4 x 1u) = 16u.

Important Points

• Standard Reference: The current scale for atomic and molecular masses is based on Carbon-12, adopted by the IUPAC in 1961 to replace older scales based on Oxygen.
• Precision: Molecular mass can be determined with high precision using Mass Spectrometry, which measures the mass-to-charge ratio of ionized molecules.
• Dalton (Da): In biology and biochemistry, the unit Dalton is frequently used interchangeably with the unified atomic mass unit (u) to describe the mass of large organic molecules like proteins and DNA.
• Gram Molecular Mass: This is simply the molecular mass of a substance expressed in grams. For example, the gram molecular mass of Oxygen (O2) is 32g.

The correct answer is Both I and II.

Key Points

• In the realm of Indian Classical Music, specifically the Carnatic tradition, Gitam (also spelled Geetham) is recognized as the simplest type of musical composition. It is designed primarily for students who have moved past basic exercises to understand the melodic structure of a Raga. Hence, statement I is correct.
• A Gitam is characterized by its very simple construction. Unlike more complex forms like Kritis or Varnas, it does not have distinct sections like Pallavi, Anupallavi, and Charana. Instead, it features a continuous and melodious flow of music. Hence, statement II is correct.
• Hence, the correct answer is Both I and II.

Additional Information

• Structural Features of Gitam:
• The term Gitam literally translates to "song." In these compositions, the Sahitya (lyrics) and the Svara (notes) are given equal importance. There are no Sangatis (variations) or complex Gamaka (ornamentations) used, making it easy for beginners to perform.
• It is typically set to Madhyama Kala (medium tempo). The Sahitya often consists of praises for Gods and Goddesses, reflecting the Bhakti (devotional) essence of Indian music.
• Historical Significance:
• Purandara Dasa, widely revered as the Pitamaha (grandfather) of Carnatic music, is credited with standardizing the teaching methodology, which includes the Pillari Gitams.
• The Pillari Gitams are usually the first few songs taught to students and are composed in praise of Lord Ganesha, such as the famous "Sri Gananatha" in Raga Malahari.
• Types of Gitams:
• Samanya Gitam: Also known as Sanchari Gitam, these are ordinary compositions where the Sahitya is religious or philosophical.
• Lakshana Gitam: These are unique because the Sahitya describes the Lakshanas (characteristics) of the Raga itself, including its Arohana (ascending scale), Avarohana (descending scale), and Varjya notes.

Important Points

• Musical Components:
• Tala: Gitams are usually set to simple Suladi Sapta Talas like Rupaka, Triputa, Dhruva, and Matya.
• Language: The lyrics are commonly found in Sanskrit, Kannada, or a specialized musical dialect known as Bhandira Bhasha.
• Pedagogical Role: Learning Gitams is a crucial milestone for a student to grasp the Svarupa (personality) of different Ragas like Kalyani, Sankarabharanam, or Mohanam before advancing to the Varnam stage.

The correct answer is Ministry of Statistics & Programme Implementation.

Key Points

• The EnviStats India 2025: Environment Statistics is a flagship publication released by the National Statistical Office (NSO), which operates under the Ministry of Statistics and Programme Implementation (MoSPI) of the Government of India.
• The report provides comprehensive data and statistics related to the environment, including physical assets, biodiversity, forests, and climate-related indicators within the Indian territory.
• The publication follows the System of Environmental-Economic Accounting (SEEA) framework, which is the international statistical standard for environmental-economic accounting adopted by the United Nations Statistical Commission in 2012.
• It aims to bridge the gap between economic policy and environmental sustainability by providing quantitative data that helps in assessing the impact of economic activities on natural resources.
• The 2025 edition (and its predecessors) serves as a critical resource for monitoring India’s progress towards the Sustainable Development Goals (SDGs), particularly those concerning Clean Water and Sanitation (SDG 6), Climate Action (SDG 13), and Life on Land (SDG 15).

Additional Information

• Ministry of Statistics & Programme Implementation (MoSPI):
• This Ministry was created as an independent entity on 15^th October 1999 following the merger of the Department of Statistics and the Department of Programme Implementation.
• The National Statistical Office (NSO) under this ministry is responsible for the conduct of large-scale sample surveys and the compilation of national accounts, including the Gross Domestic Product (GDP).
• System of Environmental-Economic Accounting (SEEA):
• The SEEA framework integrates economic and environmental data to provide a multipurpose information system for understanding the interactions between the economy and the environment.
• It facilitates the calculation of Green GDP, which adjusts the traditional GDP by accounting for environmental degradation and resource depletion.
• Other Ministries and their Roles:
• The Ministry of Environment, Forest and Climate Change (MoEFCC) is the nodal agency for the planning, promotion, and coordination of India's environmental and forestry programs; however, the statistical compilation for EnviStats is handled by MoSPI.
• The Ministry of Home Affairs is primarily responsible for internal security, border management, and the Census of India (via the Registrar General).
• The Ministry of Social Justice and Empowerment focuses on the welfare and empowerment of marginalized sections of society, such as Scheduled Castes, OBCs, and persons with disabilities.
• Significance of EnviStats:
• The report includes detailed accounts of land cover, water use, and solid waste management across different Indian states and Union Territories.
• By providing time-series data, it allows researchers to track long-term environmental trends and the efficiency of government conservation schemes like Namami Gange or the National Afforestation Programme.

Important Points

• Global Context: India is one of the few countries that have actively implemented the SEEA framework to produce Environmental Accounts, aligning its domestic statistical practices with global benchmarks set by the United Nations.
• Data Sources: The MoSPI collaborates with several technical agencies like the Forest Survey of India (FSI), Central Pollution Control Board (CPCB), and Central Ground Water Board (CGWB) to collect primary data for these statistical volumes.
• Scope: EnviStats India is typically released in two volumes: Volume I focuses on Environmental Statistics (based on the FDES 2013 framework), while Volume II focuses on Environmental Accounts.

The correct answer is '3' i.e. Have a whale of a time .

Key Points

• The idiom "Have a whale of a time" means to enjoy oneself very much or have a great time.
• It is often used in informal contexts to describe a fun or exciting experience.
• None of the other options (1, 2, or 4) convey this meaning, making option 3 the correct choice.

Correct sentence: We had a whale of a time at the party last night.

Additional Information

• Idioms and their meanings:
• Have a nick of a time: Not a commonly used idiom or phrase.
• Have a click of a time: Not a recognized idiom in English.
• Have a shell of a time: Doesn't carry the intended meaning of enjoying oneself.
• Using idioms: Idioms are phrases that have figurative meanings, and they are often tied to cultural or linguistic contexts.

The correct answer is '3' i.e. Fascination .

Key Points

• The word Fascination refers to the state of being fascinated or attracted to something strongly.
• The correct spelling of the word is Fascination.
• Option 1 (Fasination) and Option 2 (Fascinacion) are incorrect because they are misspelled versions of the word.

Correct word: Fascination

Additional Information

• Root Word: The word originates from the Latin root "fascinare," meaning to captivate or bewitch.
• Usage in a Sentence: Her fascination with astronomy led her to pursue a career in space science.

The correct answer is '2' i.e. kleptomania .

Key Points

• The word kleptomenia in the sentence is misspelled.
• The correct spelling of the word is kleptomania, which refers to a psychological disorder causing an uncontrollable urge to steal items.
• Option 2, kleptomania, is the correct replacement for the misspelled word.
• Options 1 (Kleptominia) and 3 (klaptomania) are incorrect spellings.
• Option 4 (No replacement required) is incorrect because the spelling in the sentence needs correction.

Correct sentence: The doctor diagnosed her with kleptomania, a disorder that caused her to steal compulsively.

Additional Information

• Kleptomania: A mental health disorder characterized by repeated inability to resist urges to steal things not needed for personal use or monetary value.
• It is classified as an impulse control disorder in psychiatry.
• It is important to use the correct spelling to convey the intended meaning clearly.