RRC Group D Previous Year Paper 14 (Held On: 25 Oct 2018 Shift 1)

Shortcut Trick

Passing Marks = Marks obtained + Marks by which failed

Passing Marks = 210 + 50 = 260

Given, 65% = 260

1% = 260 ÷ 65 = 4

100% (Total Marks) = 4 × 100 = 400

∴ The correct answer is 400 marks.

Alternate Method

Given:

Passing Percentage = 65%

Marks Obtained = 210

Failing Margin = 50 marks

Formula Used:

Total Marks = (Passing Marks ÷ Passing Percentage) × 100

Calculations:

⇒ Passing Marks = 210 + 50 = 260

⇒ Let Total Marks be 'x'

⇒ 65% of x = 260

⇒ (65 ÷ 100) × x = 260

⇒ x = (260 × 100) ÷ 65

⇒ x = 4 × 100

⇒ x = 400

∴ The correct answer is 400 marks.

Additional Information

Percentage Basics

To find the whole when a part and its percentage are known: Whole = (Part ÷ Percentage) × 100.

Passing Marks Concept

If a student scores 'a' marks and fails by 'b' marks, then Passing Marks = a + b. If a student scores 'a' marks and gets 'b' marks more than passing, then Passing Marks = a − b.

Shortcut Trick

Apply the Alligation method to find the ratio of the number of items:

Ratio of (Smallest 5) to (Remaining others) = (27.5 − 25) : (25 − 21)

Ratio = 2.5 : 4 ⇒ 5 : 8

Since the 5 parts represent the 5 smallest numbers given in the question,

The 8 parts must represent 8 numbers.

Total numbers in the group = 5 + 8 = 13

∴ The correct answer is 13.

Alternate Method

Given:

Number of smallest numbers = 5

Mean of 5 smallest numbers = 21

Mean of remaining numbers = 27.5

Mean of the entire group = 25

Let the total number of numbers in the group be n.

Formula used: Total Sum = Average × Total Count

⇒ Total Sum = (Sum of smallest 5) + (Sum of remaining numbers)

⇒ n × 25 = 5 × 21 + (n − 5) × 27.5

⇒ 25n = 105 + 27.5n − 137.5

⇒ 27.5n − 25n = 137.5 − 105

⇒ 2.5n = 32.5

⇒ n = 32.5 ÷ 2.5

⇒ n = 13

∴ The correct answer is 13.

Additional Information

Weighted Average Principle

When two groups are mixed, the combined mean is given by X_avg = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂). This is essentially the balance point of the two groups.

Deviation Method

The net deviation from the mean is always zero. Total decrease in one group (n₁ × deviation₁) must equal total increase in the other group (n₂ × deviation₂).

Alligation Rule

Quantity of cheaper / Quantity of dearer = (Dearer price − Mean price) / (Mean price − Cheaper price). This is the fastest way to solve mixture and average problems involving two components.

Shortcut Trick

Initial ratio of milk to water is 3 : 2 (Total parts = 5).

Total mixture = 50 liters ⇒ 1 part = 50 ÷ 5 = 10 liters.

Initial quantities: Milk = 3 × 10 = 30 liters, Water = 2 × 10 = 20 liters.

To make the ratio equal (1 : 1), water must match the milk quantity.

Water to be added = 30 liters − 20 liters = 10 liters.

∴ The correct answer is 10 liters.

Alternate Method

Given: Total mixture = 50 liters, Milk : Water = 3 : 2.

Formula: Quantity = (Ratio part ÷ Total parts) × Total quantity.

⇒ Quantity of Milk = (3 ÷ 5) × 50 = 30 liters.

⇒ Quantity of Water = (2 ÷ 5) × 50 = 20 liters.

⇒ Let x liters of water be added to make the ratio equal (1 : 1).

⇒ 30 ÷ (20 + x) = 1 ÷ 1

⇒ 30 = 20 + x

⇒ x = 30 − 20 = 10 liters.

∴ The correct answer is 10 liters.

Additional Information

Ratio Balancing

When one component remains constant (Milk here), multiply the new ratio to match the constant component's parts.

Alligation Rule

Can be used by taking concentration of water: initial (40%) and added (100%) to get final (50%).

Percentage Base

Equal ratio means each component becomes 50% of the total new mixture.

Follow BODMAS rule to solve this question, as per the order given below∶

Step-1∶ Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2∶ Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3∶ Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4∶ Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

$\Rightarrow \left( {\frac{2}{3} \times \frac{1}{6}} \right) + \left( {\frac{2}{3} \times \frac{7}{2}} \right) - \left( {\frac{{13}}{4} \times \frac{4}{3}} \right)$

$\Rightarrow \frac{1}{9} + \frac{7}{3} - \frac{{13}}{3}$

⇒ (1 + 21 – 39)/9

⇒ -17/9

Shortcut Trick

Total Capacity (LCM of 4.8, 7.2, 9.6) = 28.8 units.

Efficiencies: A = +6, B = +4, C = −3.

Let Pipe B work for 't' hours, then Pipe A worked for (16.8 − t) hours. Pipe C worked for all 16.8 hours.

Equation: 6(16.8 − t) + 4t − 3(16.8) = 28.8

100.8 − 6t + 4t − 50.4 = 28.8 ⇒ 50.4 − 2t = 28.8 ⇒ 2t = 21.6 ⇒ t = 10.8 hours.

∴ The correct answer is 10.8 hours.

Alternate Method

Given: Filling time of A = 4.8 hrs, B = 7.2 hrs. Draining time of C = 9.6 hrs. Total time = 16.8 hrs.

⇒ Let Pipe B be on for x hours.

⇒ Then Pipe A was on for (16.8 − x) hours.

⇒ Pipe C remained on for the entire duration of 16.8 hours.

⇒ Work done by (A + C) for first part + Work done by (B + C) for second part = Total Capacity

⇒ (6 − 3) × (16.8 − x) + (4 − 3) × x = 28.8

⇒ 3 × (16.8 − x) + 1 × x = 28.8

⇒ 50.4 − 3x + x = 28.8

⇒ 50.4 − 2x = 28.8

⇒ 2x = 50.4 − 28.8

⇒ 2x = 21.6

⇒ x = 10.8 hours.

∴ The correct answer is 10.8 hours.

Additional Information

Pipes and Cisterns Efficiency

Filling pipes have positive efficiency (+), while draining/outlet pipes have negative efficiency (−).

Total Work Concept

Total Capacity = LCM of individual times. Work Done = Efficiency × Time.

Combined Efficiency

When multiple pipes operate, their net efficiency is the algebraic sum of their individual efficiencies.

Shortcut Trick

Ratio of Speed = 4 : 6 = 2 : 3

Ratio of Time = 3 : 2 (Since Distance is constant, Time ∝ 1/Speed)

Difference in time units = 3 − 2 = 1 unit

Actual time difference = 9 min (late) + 6 min (early) = 15 minutes = 1/4 hour

Time taken at 4 km/h = 3 units = 3 × 1/4 = 3/4 hours

Distance = Speed × Time = 4 × (3/4) = 3 km

∴ The correct answer is 3 km.

Alternate Method

Given:

Speed₁ (S₁) = 4 km/h (Late by 9 min)

Speed₂ (S₂) = 6 km/h (Early by 6 min)

Formula Used:

Distance = [ (S₁ × S₂) / (S₂ − S₁) ] × [ (Total Time Difference) / 60 ]

Calculations:

⇒ Total Time Difference = Late time + Early time = 9 + 6 = 15 minutes

⇒ Distance = [ (4 × 6) / (6 − 4) ] × [ 15 / 60 ]

⇒ Distance = [ 24 / 2 ] × [ 1 / 4 ]

⇒ Distance = 12 × 1/4

⇒ Distance = 3 km

∴ The correct answer is 3 km.

Additional Information

Time Difference Rule

If both cases are 'Late' or both are 'Early', subtract the times. If one is 'Late' and the other is 'Early', add the times to find the net difference.

Speed-Time Relation

For a constant distance, speed is inversely proportional to time (S₁ / S₂ = T₂ / T₁).

Unit Conversion

To convert Speed from km/h to m/s, multiply by 5/18. To convert minutes to hours, divide by 60.

Shortcut Trick

Product of numbers = HCF × LCM

16 × 100 = 4 × LCM

LCM = 1600 ÷ 4 = 400

∴ The correct answer is 400.

Alternate Method

Given:

First number (a) = 16

Second number (b) = 100

HCF (a, b) = 4

Formula Used:

LCM (a, b) × HCF (a, b) = a × b

Calculations:

⇒ LCM × 4 = 16 × 100

⇒ LCM × 4 = 1600

⇒ LCM = 1600 ÷ 4

⇒ LCM = 400

∴ The correct answer is 400.

Additional Information

HCF (Highest Common Factor)

The greatest number that divides two or more numbers without leaving a remainder.

LCM (Least Common Multiple)

The smallest positive integer that is divisible by both a and b.

Co-prime Numbers

Two numbers are co-prime if their HCF is 1. In this case, LCM is simply the product of the two numbers.

Let x will be added to the difference of 5.42 and 3.56 to get 10

According to the question

⇒ x + 5.42 – 3.56 = 10

⇒ x + 1.86 = 10

⇒ x = 10 – 1.86

⇒ x = 8.14

Shortcut Trick

Sum of angles on a straight line at point Q: x + (x − 60) = 180°

⇒ 2x − 60 = 180° ⇒ 2x = 240° ⇒ x = 120°

Given ∠TUR = x + 50 = 120 + 50 = 170°

Since TU ∥ PS, ∠URS and ∠TUR are alternate interior angles.

∴ ∠URS = ∠TUR = 170°.

∴ The correct answer is 170°.

Alternate Method

Given:

Line TU ∥ PS, points Q and R lie on PS.

∠PQT = x°, ∠RQT = (x − 60)°, and ∠TUR = (x + 50)°.

Formula Used:

1. Sum of angles on a straight line is 180°.
2. Alternate interior angles between parallel lines are equal.

Calculations:

Points P, Q, R, S lie on a straight line.

⇒ ∠PQT + ∠RQT = 180° (Linear pair)

⇒ x + (x − 60) = 180

⇒ 2x − 60 = 180

⇒ 2x = 240

⇒ x = 120

Now, calculate ∠TUR:

⇒ ∠TUR = x + 50 = 120 + 50 = 170°

Since TU ∥ PS and UR is a transversal:

⇒ ∠URS = ∠TUR (Alternate interior angles)

⇒ ∠URS = 170°

∴ The correct answer is 170°.

Additional Information

Parallel Lines and Transversals

When a transversal intersects two parallel lines, alternate interior angles are equal, and consecutive interior angles sum to 180°.

Linear Pair Axiom

If a ray stands on a line, then the sum of the two adjacent angles so formed is 180°.

Corresponding Angles

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

Shortcut Trick

Identify two numbers whose sum is 3 and product is 2.

The factors of 2 are 2 and 1. Checking the sum: 2 + 1 = 3 (Satisfied).

Substitute x = 2 and y = 1 into the expression x³ − y³.

⇒ 2³ − 1³ = 8 − 1 = 7.

∴ The correct answer is 7.

Alternate Method

Given: x + y = 3 and xy = 2

Formula Used: (x − y)² = (x + y)² − 4xy and x³ − y³ = (x − y)(x² + xy + y²)

⇒ First, find (x − y):

⇒ (x − y)² = 3² − 4(2) = 9 − 8 = 1

⇒ x − y = √1 = 1 (Taking positive difference for the options provided)

⇒ Next, find (x² + y²):

⇒ x² + y² = (x + y)² − 2xy = 3² − 2(2) = 9 − 4 = 5

⇒ Now, substitute values into the difference of cubes formula:

⇒ x³ − y³ = (x − y)(x² + y² + xy)

⇒ x³ − y³ = 1 × (5 + 2) = 1 × 7 = 7

∴ The correct answer is 7.

Additional Information

Difference of Cubes

The formula is a³ − b³ = (a − b)(a² + ab + b²). It is also written as (a − b)³ + 3ab(a − b).

Sum of Cubes

The formula is a³ + b³ = (a + b)(a² − ab + b²) or (a + b)³ − 3ab(a + b).

Square Relationship

The identity relating sum and difference is (a − b)² = (a + b)² − 4ab.

Shortcut Trick

Identify prime numbers between 1 and 12: 2, 3, 5, 7, 11.

Since all these numbers are prime, their LCM is simply their product.

LCM = 2 × 3 × 5 × 7 × 11

LCM = 10 × 21 × 11 = 210 × 11 = 2310.

∴ The correct answer is 2310.

Alternate Method

Given: Numbers are prime numbers between 1 and 12.

Formula Used: LCM of prime numbers = Product of the numbers.

⇒ Prime numbers between 1 and 12 are 2, 3, 5, 7, and 11.

⇒ LCM(2, 3, 5, 7, 11) = 2 × 3 × 5 × 7 × 11

⇒ 6 × 5 × 7 × 11

⇒ 30 × 77

⇒ 2310

∴ The correct answer is 2310.

Additional Information

Prime Numbers

Numbers that have exactly two factors: 1 and the number itself. Note that 1 is neither prime nor composite.

LCM of Co-prime Numbers

The Least Common Multiple (LCM) of any set of prime or co-prime numbers is always equal to their product.

HCF of Prime Numbers

The Highest Common Factor (HCF) of any set of distinct prime numbers is always 1.

Shortcut Trick

Efficiency ratio Type 1 : Type 2 = 2.5 : 1 = 5 : 2

Total Work = 12 × 5 × 10 = 600 units

Efficiency of (6 Type 1 + 10 Type 2) = (6 × 5) + (10 × 2) = 30 + 20 = 50 units/day

Required days = 600 ÷ 50 = 12 days

∴ The correct answer is 12 days.

Alternate Method

⇒ Efficiency of Type 1 worker (E₁) = 2.5 × Efficiency of Type 2 worker (E₂)

⇒ Total work = 12 × E₁ × 10 days = 120 E₁

⇒ Substitute E₁ = 2.5 E₂: Total work = 120 × 2.5 E₂ = 300 E₂

⇒ Efficiency of 6 Type 1 and 10 Type 2 = 6E₁ + 10E₂

⇒ Combined Efficiency = 6(2.5 E₂) + 10E₂ = 15 E₂ + 10 E₂ = 25 E₂

⇒ Time taken = Total Work ÷ Combined Efficiency = 300 E₂ ÷ 25 E₂ = 12 days

∴ The correct answer is 12 days.

Additional Information

Chain Rule Formula

The relationship between men, days, and work is given by (M₁ × D₁ × E₁) / W₁ = (M₂ × D₂ × E₂) / W₂.

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete a task. If efficiency ratio is a:b, time ratio is b:a.

Total Work Concept

Total work is always constant for a specific task and is calculated as the product of the number of workers, their efficiency, and the time spent.

Follow BODMAS rule to solve this question, as per the order given below∶

Step-1∶ Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2∶ Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3∶ Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4∶ Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

$\left( {\frac{5}{8} + \frac{3}{4}} \right)of\frac{4}{{11}} \div \frac{3}{{16}} - \frac{1}{2} \times \frac{3}{4} = ?$

⇒ 11/8 × 4/11 ÷ 3/16 – 3/8

⇒ 1/2 ÷ 3/16 – 3/8

⇒ 1/2 × 16/3 – 3/8

⇒ 8/3 – 3/8

⇒ (64 – 9)/24

⇒ 55/24

$\Rightarrow 2\frac{7}{{24}}$

Shortcut Trick

To find the largest size of square tiles, calculate the HCF of the dimensions.

Dimensions in cm: 525 cm and 455 cm.

HCF(525, 455): Difference = 525 − 455 = 70.

Factors of 70 are 70, 35, 14, 10... Since 35 divides both 525 and 455, HCF = 35.

∴ The correct answer is 35 cm.

Alternate Method

Given: Length = 5.25 m, Breadth = 4.55 m.

Formula Used: Side of largest square tile = HCF(Length, Breadth).

⇒ Length = 5.25 × 100 = 525 cm

⇒ Breadth = 4.55 × 100 = 455 cm

⇒ Prime factors of 525 = 3 × 5 × 5 × 7 = 3 × 5² × 7

⇒ Prime factors of 455 = 5 × 7 × 13

⇒ Common factors = 5 × 7

⇒ HCF = 35 cm

∴ The correct answer is 35 cm.

Additional Information

Highest Common Factor (HCF)

HCF is the greatest number that divides two or more numbers without leaving a remainder. It is also known as GCD (Greatest Common Divisor).

Number of Tiles Formula

Number of tiles = (Area of Floor) ÷ (Area of one tile) = (L × B) ÷ (Side × Side).

Least Common Multiple (LCM)

The smallest common multiple of two or more numbers. Relationship: Product of two numbers = HCF × LCM.

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

⇒ Average Speed = 400 ÷ 20

⇒ Average Speed = 20 ms⁻¹

∴ The correct answer is 20 ms⁻¹.

Alternate Method

Given:

Distance covered by the athlete = 400 m

Time taken = 20 s

Formula Used:

Average Speed = Total Distance / Total Time

Calculations:

⇒ Average Speed = 400 m ÷ 20 s

⇒ Average Speed = 20 ms⁻¹

∴ The correct answer is 20 ms⁻¹.

Additional Information

Unit Conversion

To convert speed from m/s to km/h, multiply by 18/5. To convert km/h to m/s, multiply by 5/18.

Average Speed Formula

For two equal distances covered at speeds x and y, the average speed is given by (2xy) / (x + y).

Relative Speed

When two objects move in the same direction, relative speed is the difference (S₁ − S₂); in opposite directions, it is the sum (S₁ + S₂).

Shortcut Trick

To find the minimum number of sections, the number of students per section must be the HCF of students in each grade.

HCF(215, 258, 301): Differences are 258 − 215 = 43 and 301 − 258 = 43. ∴ HCF = 43.

Total sections = (215 ÷ 43) + (258 ÷ 43) + (301 ÷ 43)

Total sections = 5 + 6 + 7 = 18.

∴ The correct answer is 18 sections.

Alternate Method

Given: Number of students in Grade 4 = 215, Grade 5 = 258, Grade 6 = 301.

Formula Used: Minimum sections = Total students ÷ HCF of students in each grade.

⇒ Prime factorization: 215 = 5 × 43

⇒ Prime factorization: 258 = 2 × 3 × 43

⇒ Prime factorization: 301 = 7 × 43

⇒ HCF (Students per section) = 43

⇒ Sections in Grade 4 = 215 ÷ 43 = 5

⇒ Sections in Grade 5 = 258 ÷ 43 = 6

⇒ Sections in Grade 6 = 301 ÷ 43 = 7

⇒ Total sections = 5 + 6 + 7 = 18

∴ The correct answer is 18 sections.

Additional Information

Highest Common Factor (HCF)

HCF is the largest positive integer that divides each of the integers without a remainder. It is also known as GCD (Greatest Common Divisor).

Optimization Rule

To minimize the number of groups/sections, we must maximize the size of each group by taking the HCF of the given quantities.

HCF Property

The HCF of a set of numbers is always less than or equal to the smallest difference between any two numbers in the set.

Shortcut Trick

Effective Compound Interest rate for 3 years at 10% = 33.1%.

Since the Principal and Amount are same for both, total Simple Interest rate must also be 33.1%.

Total SI % = Rate × Time ⇒ 3 × x = 33.1%

x = 33.1 ÷ 3 = 11.033...

∴ The correct answer is 11.03%.

Alternate Method

Given:

Principal (P) = ₹100 | Time (T) = 3 years | CI Rate = 10% | SI Rate = x%

Formula Used:

Amount in CI = P(1 + R/100)^T

Amount in SI = P + (P × R × T)/100

Calculations:

⇒ Amount (Dilip) = 100(1 + 10/100)³

⇒ Amount (Dilip) = 100(1.1)³

⇒ Amount (Dilip) = 100 × 1.331 = ₹133.1

⇒ Amount (Haru) = 100 + (100 × x × 3)/100

⇒ Amount (Haru) = 100 + 3x

Since both received the same amount:

⇒ 133.1 = 100 + 3x

⇒ 3x = 133.1 − 100

⇒ 3x = 33.1

⇒ x = 33.1 ÷ 3 = 11.0333...

∴ The correct answer is 11.03%.

Additional Information

Effective Rate of Compound Interest

For a rate R over 3 years, the effective rate is [3R + 3R²/100 + R³/10000]%.

SI and CI Relationship

For the 1st year, SI and CI are always equal if interest is compounded annually. From the 2nd year onwards, CI > SI because of interest on interest.

Difference for 3 Years

The difference between CI and SI for 3 years is given by P(R/100)² × (3 + R/100).

Shortcut Trick

Given sinA = 12/13, this represents a Pythagorean triplet (5, 12, 13) where Perpendicular = 12, Hypotenuse = 13, and Base = 5.

Value of secA = H/B = 13/5 and cosecA = H/P = 13/12.

Sum = 13/5 + 13/12 = 13 × (12 + 5) / (5 × 12) = 13 × 17 / 60 = 221/60.

∴ The correct answer is 221/60.

Alternate Method

A B C P=12 B=5 H=13

Given: sinA = 12/13

Formula Used: sinA = P/H, cosA = B/H, secA = 1/cosA, cosecA = 1/sinA

⇒ Perpendicular (P) = 12, Hypotenuse (H) = 13

⇒ Base (B) = √(H² − P²) = √(13² − 12²) = √(169 − 144) = √25 = 5

⇒ secA = H/B = 13/5

⇒ cosecA = H/P = 13/12

⇒ secA + cosecA = (13/5) + (13/12)

⇒ (13 × 12 + 13 × 5) / (5 × 12) = (156 + 65) / 60 = 221/60

∴ The correct answer is 221/60.

Additional Information

Trigonometric Identities

Fundamental identities include sin²A + cos²A = 1, 1 + tan²A = sec²A, and 1 + cot²A = cosec²A.

Pythagorean Triplets

Common triplets used in exams are (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), and (9, 40, 41).

Reciprocal Relations

sinA = 1/cosecA, cosA = 1/secA, and tanA = 1/cotA.

Shortcut Trick

Total time taken = 23 days. Ratul left 7 days before, so Praful worked alone for the last 7 days.

Together they worked for 23 − 7 = 16 days. Remaining work for both = 18 − 16 = 2 days of joint work.

This 2 days of work for (R+P) was finished by Praful alone in 7 days ⇒ (R+P) × 2 = P × 7.

Efficiency Ratio (R+P) : P = 7 : 2. Total work = 7 × 18 = 126 units.

Time taken by Praful = 126 ÷ 2 = 63 days.

∴ The correct answer is 63 days.

Alternate Method

Given: Total work duration = 23 days. Ratul left 7 days before completion.

⇒ (Ratul + Praful) worked for (23 − 7) = 16 days.

⇒ Praful worked alone for the last 7 days.

⇒ Work done in 16 days by both + Work done in 7 days by Praful = Total Work

⇒ 16 × (W/18) + 7 × (Efficiency of Praful) = W

⇒ 16W/18 + 7 × (E_P) = W

⇒ 8W/9 + 7 × (E_P) = W

⇒ 7 × (E_P) = W − 8W/9

⇒ 7 × (E_P) = W/9

⇒ E_P = W/63

⇒ Time taken by Praful = Work ÷ Efficiency = W ÷ (W/63) = 63 days.

∴ The correct answer is 63 days.

Additional Information

Work Equality Principle

Total Work = Efficiency × Time. If work is constant, Efficiency is inversely proportional to Time.

Leaving Before Completion

When a person leaves 'n' days before completion, their share of work for those 'n' days must be completed by the remaining persons.

Combined Efficiency

If A and B work together, their combined efficiency is E_A + E_B. If B works alone, efficiency is only E_B.

Shortcut Trick

To find the 3^rd shift employees, we need the Total employees and the values for the other two shifts.

From 1 & 2: Shift 1 = 1/4 × 500 = 125 employees.

From 3: Shift 2 = 2 × Shift 1 = 2 × 125 = 250 employees.

Remaining: Shift 3 = 500 − (125 + 250) = 125 employees.

All three statements are required to determine the exact count.

∴ The correct answer is Statements 1, 2 and 3 together are sufficient.

Alternate Method

Given:

Total employees (from Statement 1) = 500

Shift 1 (from Statement 2) = 1/4 of Total

Shift 2 (from Statement 3) = 2 × Shift 1

Calculations:

⇒ Number of employees in Shift 1 = 1/4 × 500

⇒ Shift 1 = 125

⇒ Number of employees in Shift 2 = 2 × 125

⇒ Shift 2 = 250

⇒ Number of employees in Shift 3 = Total − (Shift 1 + Shift 2)

⇒ Shift 3 = 500 − (125 + 250)

⇒ Shift 3 = 500 − 375 = 125

To reach this specific number, data from all three statements was utilized.

∴ The correct answer is Statements 1, 2 and 3 together are sufficient.

Additional Information

Data Sufficiency Logic

In Data Sufficiency, you must check if the provided statements can lead to a unique answer. You do not always need to find the final numerical value, just confirm that the variables can be solved.

Fraction to Total Relationship

If parts of a whole are given as fractions (e.g., 1/4), the sum of all parts (Shift 1 + Shift 2 + Shift 3) must equal 1 (or the Total Count).

Ratio Method

If Shift 1 is 1 unit, then Shift 2 is 2 units. Together they are 3 units out of 4 (since Shift 1 is 1/4). This implies Shift 3 is the remaining 1 unit.

Shortcut Trick

Retailer cost price = Selling price to customer ÷ (1 + Profit% of retailer)

Retailer CP = 270 ÷ 1.08

Retailer CP = 27000 ÷ 108 = 250

The 10% wholesaler profit is redundant as we already have the retailer's selling price and profit percentage.

∴ The correct answer is Rs. 250.

Alternate Method

Given:

Selling Price (SP) of the book for the retailer = Rs. 270

Profit percentage of the retailer = 8%

Profit percentage of the wholesaler = 10%

Formula Used:

Cost Price (CP) = [Selling Price (SP) × 100] ÷ [100 + Profit%]

Calculations:

⇒ Let the cost price of the book to the retailer be Rs. x.

⇒ The retailer sells it at a profit of 8%.

⇒ SP = x × (100 + 8) ÷ 100

⇒ 270 = x × 108 ÷ 100

⇒ x = (270 × 100) ÷ 108

⇒ x = 27000 ÷ 108

⇒ x = Rs. 250

∴ The correct answer is Rs. 250.

Additional Information

Successive Profit Calculation

When profit is applied successively, the final selling price is CP × (1 + r₁/100) × (1 + r₂/100).

Cost Price and Selling Price Relationship

If there is a profit, SP = CP + Profit. If there is a loss, SP = CP − Loss.

Profit Percentage

Profit% = (Profit ÷ Cost Price) × 100. Always calculate profit/loss on the Cost Price unless stated otherwise.

Shortcut Trick When two articles are sold at the same Selling Price (SP), one at a gain of x% and another at a loss of x%, there is always an overall loss. Overall loss percentage = x2 ÷ 100. Given x = 20%, Overall loss % = (20 × 20) ÷ 100 = 400 ÷ 100 = 4%. ∴ The correct answer is 4% loss.

Alternate Method Given: Selling Price (SP) of each power bank = 2960, Gain = 20%, Loss = 20%. Formulas: CP = SP × 100 ÷ (100 + P%) | CP = SP × 100 ÷ (100 − L%) | Loss% = (Total CP − Total SP) ÷ Total CP × 100.

⇒ CP of first power bank = 2960 × 100 ÷ 120 = 2466.67 ⇒ CP of second power bank = 2960 × 100 ÷ 80 = 3700 ⇒ Total CP = 2466.67 + 3700 = 6166.67 | Total SP = 2960 + 2960 = 5920 ⇒ Loss = 6166.67 − 5920 = 246.67 ⇒ Loss% = (246.67 ÷ 6166.67) × 100 = 4% ∴ The correct answer is 4% loss.

Additional Information Two articles with same Selling Price If two items are sold at the same price, one at x% profit and other at x% loss, the net result is always a loss of (x/10)2 %. Cost Price and Selling Price When Profit occurs, SP > CP. When Loss occurs, CP > SP. Profit or Loss is always calculated on the Cost Price (CP) unless stated otherwise.

Shortcut Trick

Let the age of Keong 12 years ago be 1 unit.

Ryu age 12 years ago = 2.25 units.

Difference in age = 2.25 − 1 = 1.25 units.

Given Age Difference is always constant = 25 years.

⇒ 1.25 units = 25 → 1 unit = 20 years.

Ryu age 12 years ago = 2.25 × 20 = 45 years.

Current age of Ryu = 45 + 12 = 57 years.

∴ The correct answer is 57 years.

Alternate Method

Given:

Age difference between Ryu and Keong = 25 years.

12 years ago, Ryu was 2.25 times as old as Keong.

Calculations:

Let current age of Ryu be R and Keong be K.

⇒ R − K = 25 --- (i)

12 years ago, Ryu age = (R − 12) and Keong age = (K − 12).

⇒ (R − 12) = 2.25 × (K − 12)

⇒ R − 12 = 2.25K − 27

⇒ R − 2.25K = −15 --- (ii)

Substitute R = K + 25 in (ii):

⇒ (K + 25) − 2.25K = −15

⇒ −1.25K = −40

⇒ K = 40 / 1.25 = 32 years.

⇒ R = K + 25 = 32 + 25 = 57 years.

∴ The correct answer is 57 years.

Additional Information

Constant Age Difference

The difference between the ages of two people remains constant regardless of how many years pass.

Ratio Method for Ages

If the ratio of ages is given for two different time periods, equate the parts of difference to the actual years to solve quickly.

Total production of all type of grains of state A = 15 + 10 + 10 = 35

Total production of all type of grains of state B = 5 + 20 + 15 = 40

Total production of all type of grains of state C = 25 + 15 + 10 = 50

Total production of all type of grains of state D = 15 + 25 + 5 = 45

State A produces the minimum grains.

Square root of 5184

⇒ √5184 = √2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 = 2 × 2 × 2 × 3 × 3 = 72

Shortcut Trick

Directly substitute the standard trigonometric values.

sin 45° = 1/√2

sin 30° = 1/2

Ratio = (1/√2) ÷ (1/2) = 2/√2 = √2

∴ The correct answer is √2.

Alternate Method

Given: Expression = sin 45° / sin 30°

Formula Used: Standard trigonometric ratios for specific angles.

⇒ sin 45° = 1/√2

⇒ sin 30° = 1/2

⇒ Value = (1/√2) / (1/2)

⇒ Value = (1/√2) × 2

⇒ Value = 2/√2

⇒ Value = √2

∴ The correct answer is √2.

Additional Information

Trigonometric Table Values

Values for sin θ: sin 0° = 0, sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, sin 90° = 1.

Reciprocal Relations

The cosecant function is the reciprocal of sine: cosec θ = 1 / sin θ.

Rationalization

To simplify 2/√2, multiply numerator and denominator by √2 to get (2√2)/2 = √2.

Shortcut Trick

Let Nipa's current age be x years.

Hari = x + 5 and Damini = 2 × (x + 5).

In 5 years: Damini + 5 = 3 × (Nipa + 5).

2x + 10 + 5 = 3x + 15 ⇒ x = 0.

Hari's age = 0 + 5 = 5 years.

∴ The correct answer is 5 years.

Alternate Method

Given: Damini = 2 × Hari; Hari = Nipa + 5.

Calculations:

⇒ Let Nipa's present age = x

⇒ Hari's present age = x + 5

⇒ Damini's present age = 2(x + 5) = 2x + 10

⇒ After 5 years, Damini's age = (2x + 10) + 5 = 2x + 15

⇒ After 5 years, Nipa's age = x + 5

⇒ According to the condition: (2x + 15) = 3(x + 5)

⇒ 2x + 15 = 3x + 15

⇒ x = 0

⇒ Hari's age now = 0 + 5 = 5

∴ The correct answer is 5 years.

Additional Information

Age Ratio Problems

When the difference in ages remains constant, the ratio method or linear equations are best for solving age-related word problems.

Future and Past Ages

If current age is x, then age n years later is x + n, and age n years ago was x − n.

Here, we get the series

0 + 1 = 1;

1 + 1 = 2;

2 + 3 = 5;

5 + 8 = 13;

13 + 8 = 21

21 + 13 = 34

Hence, the correct answer is 21.

According to the given information,

According to the Pythagores theorem,

(GD)² = GX² + XD²

GD² = 6² + 9²

GD = $\sqrt {81{\rm{}} + {\rm{}}36}$

GD = $\sqrt {117}$

GD = $3\sqrt {13}$ Km

Hence, shortest distance between G and D is $3\sqrt {13} ;Km$.

Fermentation process is used to make Beer.

Similarly,

Decomposition methos is used to make vermicompost.

Hence, the correct answer is Vermicompost.

From the given information,

As per the diagram, she is the cousin of Neha.

Hence, the correct answer is ‘Cousin’.

A – Basketball

B – Football

C – Volleyball

Based on the diagram, the players who play only one game are,

13 + 12 + 10 = 35

Hence, 35 is the correct answer.

The pattern followed here is,

Hence, 30V is the correct answer.

The statement does not suggests anything about a damaged fuel tank.

Therefore, a leak cannot be assumed.

Thus, assumption 1 is not implicit.

Since the fuel guage is indicating a shortage of petrol, it can be safely assumed that the chauffeur needs to locate a petrol pump which made him worry. Thus, assumption 2 is implicit.

Hence, only assumption 2 is implicit.

MP, MLC and MLA are political positions whereas the Registrar is not.

Hence, the odd one among the given options is the Registrar.

Alternate solution:

MP, MLC and MLA are acronyms but The Registrar is not.

Note:

An acronym is a word (such as NATO, radar, or laser) formed from the initial letter or letters of the words in a phrase.

Hence the odd one among the given options is The Registrar.

The given statement talks about saving the city from air pollution.

Vehicles are one of the main sources of air pollution.

Therefore, restricting the use of personal vehicles and using public transport is a great step in this direction. Hence, argument I is strong.

Inconvenience caused to some people cannot be considered as a strong reason to reject the idea of using public transport which has more benefits than disadvantages.

Thus, argument II is not strong.

Hence, only argument I is strong.

Here, the year is 2020 = 2000 + 19 (as 2020 is running year).

Number of odd days in 2000 = 0

In 19, there are 4 leap years and 15 ordinary years.

So, no. of odd days in 4 leap year = 8 as in one leap year there are 2 odd days.

no. of odd days in 15 ordinary years = 15, as there is 1 odd day in one year.

no. of odd days in march = 3 + 1 = 4

no. of odd days in date (30) = 4 weeks and 2 odd days

Total odd days = 2 + 8 + 15 + 4 = 29 i.e. 4 weeks and 1 odd day

And according to the days code = 1 odd day means Monday.

Hence, the correct answer is Monday.

It is given that there were no major breakthrough in the study of nuclear science after 1975.

This implies that there were breakthroughs before 1975. But the scientists in the period before 1975 could not have had better infrastructure than those after 1975.

Hence even if they were not given better infrastructure they could have made breakthrough like those scientists before 1975.

Therefore, statement 1 alone is not sufficient to answer the question.

A country’s development requires its scientists to succeed and develop in its research initiatives, thus it is the fundamental duty of the scientists to contribute in the country’s growth process.

Moreover, research is a never-ending process.

Though statement 2 says that the scientists believed the research done by the west is sufficient for country X’s development, it does not say that they stopped doing research in the study of nuclear science altogether.

Thus, we cannot be certain that this was the reason, no breakthrough was achieved after 1975 as the reason itself is vague.

Therefore, statement 2 alone is not sufficient to answer the question.

Also, statements 1 and 2 do not form a complementary pair.

Therefore, option 4 (either 1 or 2 alone is sufficient) is ruled out.

Statements 1 and 2 together fail to answer the question due to the vagueness of statement 2.

Hence, both 1 and 2 together are not sufficient to answer the question.

The least possible Venn diagram for the given statements is as follows,

Conclusions :

1. X is not strong = True (as X is man and no men are strong).
2. All men are X = False (X = men, hence, only some men can be X)

Hence, only conclusion 1 follows.

As per the venn diagram, 4 people only know all three languages.

Hence, 4 is the correct answer.

Given: L and M are brothers.

Statement 1: L is 5 years old now.

Hence, statement 1 is insufficient to answer the question.

Statement 2: M is older to L by a year.

Hence, statement 2 is insufficient to answer the question.

By combining statement 1 and 2,

L = 5;

M = L + 1 = 5 + 1 = 6

So, the sum of the age = 5 + 6 = 11 and after 5 years, sum of their ages will be 11 + 5 = 16

Hence, both statements 1 and 2 together are sufficient.

The pattern followed here is:

Letter:

P + 1 → Q

Q + 2 → S

S + 3 → V

V + 4 → Z

Number:

12 + 2 = 14

14 + 4 = 18

18 + 6 = 24

24 + 8 = 32

Hence, the next term in the series is 32Z.

Here in all figures except figure C, 2 stars are connected with one line

Whereas in figure C, no line is connected between the edge of the side of the star.

Hence, figure C is odd one out.

Chalk is used to write on board,

Similarly,

Pencil is used to write on paper.

Hence, the correct answer is paper.

From first image to second image, a new figure is added just above the given figure without any other changes in the original figure.

Similarly,

From third image to fourth image, the same pattern will be repeated.

Hence, figure B is the correct answer.

The given figure is similar to figure B

Hence, the correct answer is figure B.

Increase in the price of fruits need not mean that fruits are being rarely produced.

Thus, we cannot conclude that fruits are becoming rare.

Hence conclusion I does not follow.

Similarly, rise in the prices of fruits need not affect people’s ability of eating them.

Therefore, conclusion II does not follow.

Hence, neither conclusion I nor conclusion II follows.

In all figures except figure A, half portion of each the figure is shaded.

Hence, figure A is odd one out.

The pattern followed here is,

Hence, ‘TTTTXBBBB’ is the correct answer.

Hence, the water image of the given figure is figure B.

The four parts obtained in question figure A are placed in such a manner in B that their pointed corners are facing each other.

Hence, figure A is correct answer.

In the given figure,

Number of row is = 3

And number of column = 3

($\frac{{n\left( {n; + ;1} \right)}}{2}$)² = n = 3

(3 × 4 / 2)² = 6² = 36

Hence, total 36 rectangles are present.

Shortcut Trick

Given figure:

Total rectangles = 6 × 6 = 36

Hence, the correct answer is "36".

Alternate MethodThe number of rectangles in the given figure is-

Hence, the correct answer is "36".

Key Points

• A rectangle is a quadrilateral with four right angles. Thus, all the angles in a rectangle are equal (360°/ 4 = 90°). Moreover, the opposite sides of a rectangle are parallel and equal, and diagonals bisect each other.
• A square is a special type of rectangle because it possesses all the properties of a rectangle. Similar to a rectangle, a square has: interior angles which measure 90∘ each. opposite sides that are parallel and equal.

Important Points 

All the rectangles are quadrilateral.

All the squares are rectangles.

Except ‘Jami Ul-Alfar Mosque’, all are Indian historical places,

Whereas Jami Ul-Alfar Mosque is in Colombo, Shrilanka.

Hence, ‘Jami Ul-Alfar Mosque’ is the odd one out.

Here, in all figures, except figure D, all geometrical shapes are the overlapping on each other.

Hence, figure D is odd one out.

The purpose behind the given notice is to remind the speeding rule for the highway.

It would be safe to assume that the underlying thought behind using the notice was that people will not ignore the information and follow the guideline.

Hence only assumption 2 follows.

Relation between the first and second figures:

The second figure is the mirror image of the first figure.

Similarly,

The fourth figure will be the mirror image of the third figure.

Hence, figure D is the correct answer.

The correct answer is Option 1, Every ore is mineral but every mineral is not an ore.

• In the modern periodic table, there are 118 elements out of which 93 falls in the category of metals, 18 non-metals, and 7 metalloids.
• Metals are extracted from ore and minerals contain both metals as well as non-metals.
• For example, aluminium exists in two mineral forms that are clay and Bauxite. But aluminium is mainly extracted from bauxite which contains 70% aluminium oxide, i.e Bauxite is an ore of aluminium whereas clay is not an ore.
• Hence, every ore is a mineral but every mineral is not an ore.

The correct answer is option 3, Decreases.

Key Points

CONCEPT:

• Velocity: The rate of change of displacement of a body is called the velocity of that body.
• Velocity is a vector quantity that has both magnitudes as well as direction.
• Acceleration: The rate of change of velocity is called as the acceleration of the body.
• Acceleration is also a vector quantity.
• Retardation/Negative acceleration: When the acceleration of the body is in the opposite direction of the velocity is called deceleration.
• It is a negative acceleration of the body.

EXPLANATION:

• The direction of acceleration is determined by the general principle that if an object is slowing down, the acceleration is in the opposite direction of the motion.
• Hence, with negative acceleration, the velocity of a body decreases.
• The negative sign of acceleration shows that the velocity of the body is decreasing per unit of time.

The correct answer is option 4, i.e 10⁹

CONCEPT:

• Pico-metre = 10-12 metre
• Angstrom = 10-10 metre
• Nanometre = 10-9 metre =  1 meter = 10⁹ nm
• Kilometre = 103 metre

EXPLANATION:

Here meter is converted to nanometer - 

1 m = ________ nm

So the correct answer is 1m = 10⁹ nm

The correct answer is option 1, i.e Vijaywada.

• 6,117 Kuchipudi dancers set a new Guinness World Record by performing together in a single event at the Vijayawada district of Andhra Pradesh.
• The performance was of 12 minutes named "Jayamu Jayamu".

The correct answer is option 2, i.e Soumitra Chatterjee.

• France's highest civilian award, Legion d'Honneur was given to Soumitra Chatterjee in January 2018.
• Soumitra Chatterjee is a veteran actor, poet, reciter from Kolkata, India.
• Some international award to Indians in 2019:

The correct answer is option 2, i.e 2.0 C

CONCEPT:

• Electric potential (V): The amount of work done to move a unit charge from a reference point (or infinity) to a specific point in an electric field without producing an acceleration is called electric potential at that point.

${\rm{Electric;potential;}}\left( {\rm{V}} \right) = \frac{{{\rm{Work;done;}}\left( {\rm{W}} \right)}}{{{\rm{Charge;}}\left( {\rm{q}} \right)}}$

• Electrostatic Potential Energy: The amount of work done to move a charged particle from infinity to a point in an electric field is known as the potential energy of that charged particle.

CALCULATION:

Given that:

Work done (W) = 20 J

Potential difference (V) = 10 V

Since Work done (W) = Charge (q) × Potential Difference (V)

⇒ Charge (q) = W/V

⇒ q = 20/10 = 2 coulomb(C)

The correct answer is option 2, i.e 315 W.

⇒ Given, the mass of the body, m = 50 kg. h is the height, t is the time. g is the accelaration due to gravity which is aproximated to 10 m/s2 

⇒ h = 45 × 14 = 630 cm = 6.30 m

⇒ t = 10 s, g = 10 ms-2

⇒ Potential Energy = mgh = 50 × 10 × 6.30 = 3150 J. (where J is the unit of energy/work which is joules)

⇒ Power = PE / time = Energy / time = 3150 / 10 = 315 watt.  (watt is the unit of power which is different from units)

Option 2 is correct.

• Bhakti movement started in India in the 7th and 12th centuries A.D. The followers of the Bhakti movement had no religion and they strongly opposed the idol worship and caste division.
• Bhakti movement was based on the fact the relationship between man and God is through love and worship rather than performing any ritual or religious ceremonies.

The correct answer is option 3, i.e Bhuvneshwar Kumar.

• Indian fast bowler Bhuvneshwar Kumar became the first Indian bowler to take 5 wicket haul in all three formats.
• He took 5 wickets in T-20 against South Africa in Wanderers.
• The five bowlers to have picked up five-wickets hauls in all three formats are the following:

The correct answer is option 1, i.e Ductility.

• The ability of metals to be drawn into thin wires is called ductility.
• Gold is the most ductile metal.
• A wire of about 2 km length can be drawn from one gram of gold.
• It is because of their malleability and ductility that metals can be given different shapes according to our needs.

Ductility:

• Ductility is the property of the material that enables it to be drawn out or elongated to an appreciable extent before rupture occurs.
• The percentage elongation or percentage reduction in the area before the rupture of a test specimen is the measure of ductility. Normally if the percentage elongation exceeds 15% the material is ductile and if it is less than 5% the material is brittle.
• Lead, copper, aluminium, mild steel are typical ductile materials.

Source: NCERT (Chapter - Metal and Non-Metal) please go through page no. 38

• Ductility- Ability of metals to be drawn into thin wires.
• Sonorous-  Ability of metals to produce sound when beaten hard on its surface.
• Malleability- Ability of metals to be beaten into thin sheets.

The correct answer is option 3, i.e Both A and B are true.

• The speed of sound depends on the properties of the medium through which it travels.
• The speed of sound in a medium depends on the temperature, density of the medium. The speed of sound decreases when we go from solid to the gaseous state.
• In any medium, as we increase the temperature the speed of sound increases.
• Speed of sound in different media at 25 ºC.

The correct answer is option 2, i.e Father

• The sex of children is decided by the X or Y chromosome inherited from the father.
• A male has XY chromosomes and a female has XX chromosomes.
• If a sperm carrying X chromosome from the father gets combined with the X chromosome from female, then the combination will be XX and the child will be a baby girl.
• If a sperm carrying Y chromosome from the male gets combined with the X chromosome from female, then the combination will be XY, and the child will be a baby boy.

The correct answer is option 1, i.e Deepak Mishra.

• Deepak Mishra was the chief justice of India in the year 2018.
• He was appointed as the 45th chief justice of India from 28 August 2017 to 2 October 2018.
• He also served as chief justice Patna and Delhi High courts.
• Sharad Arvind Bobde became the 47th chief justice of India on 18th November 2019.

The correct answer is option 3, i.e Arun Jaitley.

• Union Finance Minister Arun Jaitely introduced the Economic Survey for the year 2017 in the parliament of India.
• Amitabh Kant - Former CEO of NITI Aayog
• Piyush Goyal - Union Railway Minister.
• Currently, Parameswaran Iyer is the CEO of NITI Aayog appointed in June 2022.

Option 3 is correct

• Arunima Sinha is a former Volley Ballplayer and first Indian physically challenged lady to scale Mt. Everest.
• Kiran Mazumdar Shaw was the first Indian woman to reach a net worth of One billion dollars.
• Harshini Kanhekar is the first firefighter who graduated from National Fire Service College (NFSC) in Nagpur .

Option 4 is correct

CONCEPT:

• Electric potential (V): The amount of work done to move a unit charge from a reference point (or infinity) to a specific point in an electric field without producing an acceleration is called electric potential at that point.

${\rm{Electric;potential;}}\left( {\rm{V}} \right) = \frac{{{\rm{Work;done;}}\left( {\rm{W}} \right)}}{{{\rm{Charge;}}\left( {\rm{q}} \right)}}$

• Electrostatic Potential Energy: The amount of work done to move a charged particle from infinity to a point in an electric field is known as the potential energy of that charged particle.

CALCULATION:

Given that:

Electric charge (q) = 5 C

Potential difference (V) = 16 V

Work done (W) = charge (q) × potential difference (V)

Work done (W) = 5 × 16 = 80 J

Option 2 is correct

• Muscular tissue is not a connective tissue.
• Connective tissues support and bind other tissues of the body together.
• Adipose tissue, cartilage, ligament are examples of connective tissues.

The correct answer is option 4, i.e Nirmala Sitharaman.

• On December 29, 2017, Union Defence Minister Nirmala Sitharaman launched a new start-up incubation centre called 'Centre for Entrepreneurship Opportunities and Learning' in Mangaluru.
• Rs. 1.5 crore allocated from her MPLAD (Member of Parliament's Local Area Development) scheme for the development of CEOL.
• Union Cabinet Ministers of India at present:

The correct answer is option 3 i.e Volley Ball

Option 4 is correct

• Qutub-ud-din Aibak started the construction of Qutub Minar and built the basement.
• Iltutmish built three more storeys of it.
• The last two storeys were built by Feroz Shah Tughlaq. But according to the given options, option, 4 will be the best suitable.

Option 2 is correct

• The radius of curvature of the mirror is equal to the twice of the focal length i.e R=2f
• The distance from the pole to the focal point is known as focal length and it is approximately half of the Radius of curvature.

Option 4 is correct.

• Adrenalin is a hormone secreted by adrenal glands in the human body which controls the blood pressure, immune system and metabolism of the body.
• Auxin is a plant hormone which promotes uniform flowering and also induces parthenocarpy(formation of seedless fruits without fertilisation).
• Abscisic acid is a plant hormone which controls the process of germination of seeds and buds.
• Cytokinin is a plant hormone which suppresses the apical dominance of plants.

The correct answer is option 3, i.e Hydrogen.

• Hydrogen is also a gas like halogens, and exists as a diatomic molecule and forms covalent compounds the same as halogens, unlike alkali metals.
• Therefore, hydrogen can form positive ion as in HCL and also negative ion as in NaOH.
• Hence, the position of hydrogen was not fixed in Mendeleev's periodic table.

The correct answer is option 4, i.e Carbon.

• Carbon forms the maximum number of compounds in the periodic table.
• Since carbon has the property of tetra valency and catenation so they can form a maximum number of compounds.
• Carbon exists in several allotropic forms. Graphite and diamond are examples of allotropes of carbon that have different properties.
• The atomic number of carbon= 6. It lies in the 14th group in the periodic table.

The correct option is 2, i.e more kinetic energy.

• In liquids, a small fraction of particles at the surface has more Kinetic energy. Hence these particles are able to break away the forces of attraction from other particles and gets converted into vapour.
• This phenomenon is known as evaporation and a phase change occurs where liquid gets concerted to gas.

The correct option is 1, i.e Rafael Nadal.

• Rafael Nadal won 2017 Madrid open title.
• Nadal won his 5th Madrid open title by defeating Dominic Thiem of Austria.
• Rafael Nadal belongs to Spain.
• The capital of Spain is Madrid.
• Winners of Grand slam of 2019 are following

The correct option is 3, i.e Finance.

• PMJJBY, Pradhan Mantri Jeevan Jyoti Beema Yojana was announced by union finance minister Arun Jaitely in 2015.
• This scheme covers the life insurance worth 2 lakhs for both natural and accidental deaths.
• People of age between 18-50 years having Aadhar card linked with their bank account are applicable for this scheme.

Important schemes of Indian Government:

The correct answer is option 2, i.e Both path 1 and 2.

• Work Done by gravity depends on the difference in vertical heights of the initial and final positions of the object and not along the path on which the object is moved. Hence displacement is a point function and not a path function.
• In both figures, the block is raised from A to B by taking two different paths.
• Given height is AB= h. So in both the situation the work is done on the object is mgh.

The correct answer is option 3 i.e Uttar Pradesh.

Key Points

• Taj Mahal is situated in Agra, Uttar Pradesh.
• It was built by Mughal emperor Shah Jahan between 1631 and 1648.

​

The current answer is option 3, i.e Bhartruhari Mahtab.