SSC CHSL Exam 2023 Tier-II Official Paper (Held On: 02 Nov, 2023 Shift 1). (Previous Year Paper)

Given:

Concentration of wine A = 10%

Concentration of wine B = 20%

Concentration of wine C = 30%

Ratio of mixing = 2 ∶ 3 ∶ x

Resulting concentration = 23%

Formula used:

Weighted average concentration = (C_A × W_A + C_B × W_B + C_C × W_C) / (W_A + W_B + W_C)

Where C_A, C_B, and C_C are concentrations of A, B, and C respectively, and W_A, W_B, and W_C are weights of A, B, and C respectively.

Calculation:

Let weights be 2, 3, and x respectively.

Resulting concentration = (10 × 2 + 20 × 3 + 30 × x) / (2 + 3 + x)

⇒ 23 = (20 + 60 + 30x) / (5 + x)

⇒ 23 × (5 + x) = 80 + 30x

⇒ 115 + 23x = 80 + 30x

⇒ 115 - 80 = 30x - 23x

⇒ 35 = 7x

⇒ x = 5

∴ The value of x is 5.

Given:

A pole stands vertically on the ground with the help of a 12-metre steel wire tied to its top and affixed on the ground. The steel wire makes an angle of 30º with the horizontal ground.

Formula used:

In a right triangle, height (h) = hypotenuse (H) × sin(angle)

Calculation:

Height of the pole (h) = 12 × sin(30º)

⇒ h = 12 × 1/2

⇒ h = 6 meters

∴ The correct answer is option (1).

Given:

A sum of money is divided among A, B, and C in the ratio 4 ∶ 3 ∶ 6. If the share of C is ₹600 more than B, then how much amount will A get more than B?

Formula used:

Let the shares of A, B, and C be 4x, 3x, and 6x respectively.

C - B = ₹600

Calculation:

6x - 3x = 600

⇒ 3x = 600

⇒ x = 200

Share of A = 4x = 4 × 200 = 800

Share of B = 3x = 3 × 200 = 600

Amount A gets more than B = 800 - 600 = 200

∴ The correct answer is option (1).

Given:

A person borrowed some money on simple interest. After 3 years, he returned ⁴/₃ of the money to the lender.

Formula used:

Simple Interest (SI) = P × R × T / 100

Where, P = Principal, R = Rate, T = Time

Calculation:

Let the principal amount be ₹P.

After 3 years, the amount returned = ⁴/₃ P

Simple Interest (SI) = ⁴/₃ P - P

⇒ SI = ¹/₃ P

We know SI = P × R × T / 100

⇒ ¹/₃ P = P × R × 3 / 100

⇒ ¹/₃ = R × 3 / 100

⇒ ¹/₃ = R / 33.33

⇒ R = 33.33 × ¹/₃

⇒ R = $11\frac{1}{9}$ % p.a

∴ The correct answer is option (2).

Given:

 of his journey at the speed of 25 km/h,

of the journey at 40 km/h

Remaining at the speed of 50 km/h.

Formula used:

Average Speed = Total Distance / Total Time

Calculations:

Let the total distance be 100 km.

⇒ 1/4 of the total distance = 100/4 = 25 km

So, time taken to cover 25 km at 25 km/h = 25/25 = 1 hour

⇒ 1/2 of the total distance = 100/2 = 50 km

So, time taken to cover 50 km at 40 km/h = 50/40 = 1.25 hours

⇒ Remaining distance = 100 - (50 + 25) = 100 - 75 = 25 km

So, time taken to cover 25 km at 50 km/h = 25/50 = 0.5 hour

Now,

Average Speed = Total Distance / Total Time

⇒ Average Speed = 100/(1 + 1.25 + 0.5)

⇒ Average Speed = 100/2.75

⇒ Average Speed = 4/0.11 = 400/11

⇒ Average Speed = 36$\frac{4}{11}$ km/h

∴ The correct answer is option (1).

Given:

cot⁴A + cot²A = 1

Formula used:

cot²A + 1 = cosec²A

Calculation:

cot4 A + cot2 A = 1

cot²A (cot²A + 1) = 1

⇒ cot2A.cosec2A = 1

⇒ cot2A = 1/cosec2A

⇒ cot2A = sin²A

⇒ cos²A / sin2A= sin2A

⇒ cos²A = sin2A.sin2A

⇒ cos²A = (1 - cos2A). (1 - cos2A)

⇒ cos²A = 1 - cos2A - cos2A + cos⁴A

⇒ cos4A - 3cos2A + 1 = 0

⇒ cos4A - 3cos2A = -1

∴ The value of cos⁴A - 3cos²A is -1.

Given:

The cost of 4 chairs and 3 tables is ₹2,100 and the cost of 5 chairs and 2 tables is ₹1,750.

Formula used:

Let the cost of one chair be ₹C and the cost of one table be ₹T.

We have two equations:

4C + 3T = 2100

5C + 2T = 1750

Calculation:

First, we can multiply the equations to eliminate T:

4C + 3T = 2100 (Equation 1)

5C + 2T = 1750 (Equation 2)

Multiply Equation 1 by 2:

8C + 6T = 4200

Multiply Equation 2 by 3:

15C + 6T = 5250

Now, subtract the two new equations:

(15C + 6T) - (8C + 6T) = 5250 - 4200

⇒ 7C = 1050

⇒ C = 150

∴ The correct answer is option (3).

Shortcut Trick

Weight of new person = Old Average + (New Total Strength × Increase in Average)

Old Average = 52 kg

New Total Strength = 40 + 1 = 41 people

Increase in Average = 500 g = 0.5 kg

Teacher's weight = 52 + (41 × 0.5) = 52 + 20.5 = 72.5 kg

∴ The correct answer is 72.5 kg.

Alternate Method

Given:

Initial number of students = 40

Initial average weight = 52 kg

Increase in average = 500 g = 0.5 kg

Formula Used:

Total Weight = Average Weight × Total Number of Persons

Calculations:

⇒ Total weight of 40 students = 40 × 52 = 2080 kg

⇒ Total number of people after including teacher = 40 + 1 = 41

⇒ New average weight = 52 + 0.5 = 52.5 kg

⇒ Total weight including teacher = 41 × 52.5 = 2152.5 kg

⇒ Weight of teacher = Total weight with teacher − Total weight of students

⇒ Weight of teacher = 2152.5 − 2080 = 72.5 kg

∴ The correct answer is 72.5 kg.

Additional Information

Basic Average Formula

The average of a set of observations is defined as the Sum of observations ÷ Number of observations.

Inclusion Rule

When a new person joins and the average increases, the new person's value = Old Average + (New Count × Increase).

Exclusion Rule

When a person leaves and the average increases, the left person's value = Old Average − (Remaining Count × Increase).

Unit Conversion

Always ensure all units are the same before calculation. For example, 1 kg = 1000 g, so 500 g = 0.5 kg.

Given:

$(\sqrt[3]{0.08×0.8× p}=0.008 × 0.8 × \sqrt[3]{q})$

Formula used:

$(\sqrt[3]{a} = a^{1/3})$ and basic algebraic rearrangement

Calculation:

$(\sqrt[3]{0.08×0.8× p}=0.008 × 0.8 × \sqrt[3]{q})$

$(\sqrt[3]{0.064 × p}=0.0064 × \sqrt[3]{q})$

$(\sqrt[3]{0.064}×\sqrt[3]{p}=0.0064 × \sqrt[3]{q})$

$(0.4×\sqrt[3]{p}=0.0064 × \sqrt[3]{q})$

$(\sqrt[3]{p}=0.016 × \sqrt[3]{q})$

$(\sqrt[3]{p}/\sqrt[3]{q}=0.016)$

⇒ $(\sqrt[3]{p/q}=0.016)$

⇒$(p/q=(0.016)^3)$

⇒ $(p/q=0.000004096)$

⇒ 84 × 10-9

∴ The value of 84 × 10-9.

Given:

Which of the following statements is NOT true?

Option 1: The area of the triangle with the largest side l always has an area less than (l²)/(2).

Option 2: If the sides of a triangle are in the ratio 13 ∶ 5 ∶ 12, then two of its angles are acute angles.

Option 3: The triangle formed by connecting the midpoints of the sides of a triangle has one-fourth area of the bigger triangle.

Option 4: The area of an isosceles triangle with sides 2a, 2a and 3a is (3√3 × a²)/2.

Formula used:

Heron's formula for the area of a triangle: √[s × (s - a) × (s - b) × (s - c)] where s = (a + b + c) / 2

Calculations:

For option 4:

Sides of the triangle are 2a, 2a, and 3a

s = (2a + 2a + 3a) / 2

⇒ s = 7a / 2

Using Heron's formula:

Area = √[s × (s - 2a) × (s - 2a) × (s - 3a)]

⇒ Area = √[(7a/2) × (7a/2 - 2a) × (7a/2 - 2a) × (7a/2 - 3a)]

⇒ Area = √[(7a/2) × (3a/2) × (3a/2) × (a/2)]

⇒ Area = √[(7a/2) × (3a/2) × (3a/2) × (a/2)]

⇒ Area = √[(7 × 3 × 3 × a⁴) / 16]

⇒ Area = (3√7 × a²) / 4

The given area in option 4 is (3√3 × a²) / 2, which is incorrect.

∴ The correct answer is option (4).

Given:

A's investment = ₹25,000 for 9 months

B's investment = ₹50,000 for 12 months

C's investment = ₹30,000 for 5 months

Total profit = ₹3,900

Formula used:

Share of profit = (Investment × Time) / Total Investment Time

Calculation:

A's share = 25000 × 9 = 225000

B's share = 50000 × 12 = 600000

C's share = 30000 × 5 = 150000

Total = 225000 + 600000 + 150000 = 975000

C's share of profit = (150000 / 975000) × 3900

⇒ C's share of profit = 600

∴ The correct answer is option (2).

Shortcut Trick

Use Multiplying Factor method for successive growth.

Present Population = 1,75,000 × (104/100) × (105/100)

Present Population = 1,750 × 1.04 × 105 = 1,82,000 × 1.05

Present Population = 1,91,100

∴ The correct answer is 1,91,100.

Alternate Method

Given: Initial Population = 1,75,000 | Growth Rate 1 (R₁) = 4% | Growth Rate 2 (R₂) = 5%

Formula Used: Final Value = Initial Value × (1 + R₁/100) × (1 + R₂/100)

⇒ Population after 1^st year = 1,75,000 × (1 + 4/100)

⇒ Population after 1^st year = 1,75,000 × 1.04 = 1,82,000

⇒ Population after 2^nd year (Present) = 1,82,000 × (1 + 5/100)

⇒ Present Population = 1,82,000 × 1.05

⇒ Present Population = 1,91,100

∴ The correct answer is 1,91,100.

Additional Information

Successive Percentage Change

If a value changes by x% and then y%, the net effective change is (x + y + xy/100)%.

Depreciation

If the population decreases, use the formula: Final Value = Initial Value × (1 − R/100)ⁿ.

Population n Years Ago

To find the population n years ago given the current population (P), use: P_ago = P / (1 + R/100)ⁿ.

Given:

A and B together can complete the work in 9 days.

B and C together can complete the work in 18 days.

A, B, and C together can complete the work in 8 days.

Formula used:

Work done per day = 1 / Number of days

Calculation:

Let the total work be 1 unit.

Work done by A and B in 1 day = 1 / 9

Work done by B and C in 1 day = 1 / 18

Work done by A, B, and C in 1 day = 1 / 8

Let the work done by A in 1 day be a, B in 1 day be b, and C in 1 day be c.

Then:

a + b = 1 / 9

b + c = 1 / 18

a + b + c = 1 / 8

Subtract a + b from a + b + c:

c = (1 / 8) - (1 / 9)

c = 1 / 72

Substitute c into b + c:

b + 1 / 72 = 1 / 18

b = (1 / 18) - (1 / 72)

b = 1 / 24

Substitute b into a + b:

a + 1 / 24 = 1 / 9

a = (1 / 9) - (1 / 24)

a = 5 / 72

Work done by A and C in 1 day = a + c

a + c = (5 / 72) + (1 / 72)

a + c = 1 / 12

∴ A and C together will complete the work in 12 days.

Shortcut Trick

Using the identity: (a + 2b)² = (a − 2b)² + 4 × (a × 2b)

Given (a − 2b) = 8 and 2ab = 9, substitute the values:

(a + 2b)² = 8² + 4 × 9 = 64 + 36 = 100

a + 2b = √100 = 10

∴ The correct answer is 10.

Alternate Method

Given:

(a − 2b) = 8

2ab = 9

Formula Used:

We use the algebraic identity relating the square of a sum and the square of a difference:

(x + y)² = (x − y)² + 4xy

Calculations:

Let x = a and y = 2b.

⇒ (a + 2b)² = (a − 2b)² + 4 × a × 2b

⇒ (a + 2b)² = (a − 2b)² + 4 × (2ab)

Substitute the given values into the equation:

⇒ (a + 2b)² = 8² + 4 × 9

⇒ (a + 2b)² = 64 + 36

⇒ (a + 2b)² = 100

Taking the square root on both sides:

⇒ a + 2b = √100

⇒ a + 2b = 10

∴ The correct answer is 10.

Additional Information

Square of a Sum and Difference

(x + y)² = x² + 2xy + y² and (x − y)² = x² − 2xy + y².

Sum-Difference Square Relation

(x + y)² − (x − y)² = 4xy. This identity helps find one term when the other two are known.

Difference of Two Squares

x² − y² = (x + y)(x − y). This is used for factorizing quadratic expressions.

Shortcut Trick

Successive fraction calculation using percentage conversions:

Total voters × (16/25) × (24/25) × (16/25) = 12,288

⇒ Total voters = 12,288 × (25/16) × (25/24) × (25/16)

⇒ Total voters = 2 × 25 × 25 × 25 = 31,250

∴ The correct answer is 31,250.

Alternate Method

Given:

Percentage of enrolled voters who cast their votes = 64%

Percentage of votes declared invalid = 4% ⇒ Percentage of valid votes = 96%

Votes received by the candidate = 12,288 (which is 64% of valid votes)

Method Used:

We apply the successive percentage calculation to find the original total.

Enrolled Votes (x)

Cast Votes

Valid Votes

12,288 Votes

64% Cast

96% Valid

64% Got

x × 64% × 96% × 64% = 12,288

Calculations:

Let the total number of enrolled voters be x.

⇒ Number of votes cast = 64% of x = (16/25) × x

⇒ Invalid votes = 4% ⇒ Valid votes = 96% of Cast votes = (24/25) × (16/25) × x

⇒ Votes received by the candidate = 64% of Valid votes

⇒ (16/25) × (24/25) × (16/25) × x = 12,288

⇒ x = 12,288 × (25/16) × (25/24) × (25/16)

⇒ x = (12,288 ÷ 16) × 25 × (25/24) × (25/16)

⇒ x = (768 ÷ 24) × 25 × 25 × (25/16)

⇒ x = (32 ÷ 16) × 625 × 25

⇒ x = 2 × 15,625 = 31,250

∴ The correct answer is 31,250.

Additional Information

Election Base Percentage

The total number of voters on the voting list is always considered as the base (100%). All subsequent percentages regarding cast votes are calculated on this base.

Valid vs Invalid Votes

Invalid votes are strictly deducted from the total votes cast. Only the valid votes are considered for determining the winning and losing candidate's share.

Successive Percentage Method

When percentages are applied sequentially, multiply the continuous factors directly: Final Value = Base × P₁% × P₂% × P₃%.

Reverse Calculation Trick

To find the initial base value from the final resultant value, simply multiply the final value by the reciprocals of the fraction equivalents of each percentage.

Given:

Percentage of men = 60%

Percentage of women = 40%

Average age of men = 55 years

Average age of women = 45 years

Formula used:

Weighted average age = (Percentage of men × Average age of men + Percentage of women × Average age of women) / 100

Calculation:

Weighted average age = (60 × 55 + 40 × 45) / 100

⇒ Weighted average age = (3300 + 1800) / 100

⇒ Weighted average age = 5100 / 100

⇒ Weighted average age = 51

∴ The correct answer is option (4).

Given:

Diameter of sphere is increased by 30%

Formula used:

Volume of sphere, V = (4/3) × π × r³

New radius, r_new = r × 1.30

New Volume, V_new = (4/3) × π × (r × 1.30)³

Calculation:

V_new = (4/3) × π × (r × 1.30)³

= (4/3) × π × r³ × 1.30³

= V × 2.197

Percentage increase in volume = (V_new - V) / V × 100%

= (2.197 - 1) × 100%

= 1.197 × 100%

= 119.7%

∴ The percentage increase in the volume is approximately 119.7%.

Given:

x = $\left(\frac{3}{2}\right)^2 × \left(\frac{2}{3}\right)^{-4}$

Formula used:

$\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n$

Calculation:

x = $\left(\frac{3}{2}\right)^2 × \left(\frac{3}{2}\right)^4$

⇒ $\left(\frac{3}{2}\right)^{2+4}$

⇒ $\left(\frac{3}{2}\right)^6$

x^{- 2} = (1/$(\left(\frac{3}{2}\right)^6)^2$)

x^-2 = $((2)/(3))^{12}$

∴ The value of x^-2 is $((2)/(3))^{12}$

Given:

P(A) = (3)/(8)

P(B) = (1)/(2)

P(A ∩ B) = (1)/(4)

Formula used:

P(A̅ ∩ B̅) = 1 - P(A ∪ B)

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Calculation:

P(A ∪ B) = (3)/(8) + (1)/(2) - (1)/(4)

⇒ P(A ∪ B) = (3)/(8) + (4)/(8) - (2)/(8)

⇒ P(A ∪ B) = (5)/(8)

⇒ P(A̅ ∩ B̅) = 1 - (5)/(8)

⇒ P(A̅ ∩ B̅) = (3)/(8)

∴ The correct answer is option (2).

Given:

A dishonest shopkeeper sells rice at a cost price but makes a 25% profit by using faulty weights. He decides to give a discount to attract more customers. What percent of discount should he offer to make a 10% profit?

Formula used:

Let the cost price (CP) be 100 units.

Selling Price (SP) for 25% profit = CP + 25% of CP = 100 + 25 = 125 units

Let the new SP after discount be X units.

To achieve a 10% profit, the new SP should be = CP + 10% of CP = 100 + 10 = 110 units

Discount = SP (without discount) - SP (with discount)

Discount percent = (Discount / SP (without discount)) × 100

Calculations:

SP (without discount) = 125 units

SP (with discount) = 110 units

Discount = 125 - 110 = 15 units

Discount percent = (15 / 125) × 100

⇒ (15 / 125) × 100 = 12%

∴ The correct answer is option (2).

Given:

A number is increased by 25% and then decreased by 16%.

Formula used:

Final value after increase and decrease = Initial value × (1 + Increase%) × (1 - Decrease%)

Calculation:

Let the initial number be 100.

Increased value = 100 × (1 + 0.25) = 100 × 1.25 = 125

Decreased value = 125 × (1 - 0.16) = 125 × 0.84

⇒ Final value = 125 × 0.84 = 105

Percentage change = [(Final value - Initial value) / Initial value] × 100%

⇒ Percentage change = [(105 - 100) / 100] × 100% = 5%

∴ The number increases by 5%

Given:

Data: 21, 15, 16, 48, 6, 15, 44, 16, 6, 5, 15, 16, 21, 6, 15, 43

Formula used:

Mode is the number that appears most frequently in a data set.

Calculation:

Count of each number:

21: 2 times

15: 4 times

16: 3 times

48: 1 time

6: 3 times

44: 1 time

5: 1 time

43: 1 time

⇒ The number that appears most frequently is 15, which appears 4 times.

∴ The correct answer is option (3).

Given:

A and B each have a certain number of oranges. A says to B, "If you give me 10 of your oranges, I will have twice the number of oranges left with you." B replies, "If you give me 10 of your oranges, I will have the same number of oranges left with you."

Formula used:

Let A have x oranges and B have y oranges.

From A's statement: x + 10 = 2(y - 10)

From B's statement: y + 10 = x - 10

Calculation:

From A's statement:

⇒ x + 10 = 2y - 20

⇒ x - 2y = -30 … (1)

From B's statement:

⇒ y + 10 = x - 10

⇒ y - x = -20 … (2)

Solving equations (1) and (2):

From (2):

⇒ y = x - 20

Substitute y in (1):

⇒ x - 2(x - 20) = -30

⇒ x - 2x + 40 = -30

⇒ -x + 40 = -30

⇒ -x = -70

⇒ x = 70

∴ The correct answer is option (1).

Given:

Triangles ABC and PQR are congruent.

∠A = ∠P = 90º

BC = 29 cm

PR = 21 cm

Formula used:

In congruent right triangles, corresponding sides are equal.

Calculations:

Since triangles are congruent:

BC = QR (hypotenuse) = 29 cm

AC = PR = 21 cm

Let, AB = PQ = x

Using Pythagoras theorem in ΔABC:

BC² = AC² + AB²

BC = 29 cm

⇒ 29² = AB² + AC²

⇒ AB² = 841 - 441

⇒ AB2 = 400

⇒ AB = √400

⇒ AB = 20 cm

∴ The value of AB is 20 cm.

Given:

Shopkeeper sold goods at half the list price and lost 17%.

Formula used:

Loss percentage: (CP - SP) / CP × 100 = 17%

Selling price at half list price: SP = 0.5 × List Price

Calculations:

(CP - 0.5 × List Price) / CP × 100 = 17

⇒ CP - 0.5 × List Price = 0.17CP

⇒ CP = 0.5 × List Price + 0.17CP

⇒ CP - 0.17CP = 0.5 × List Price

⇒ 0.83CP = 0.5 × List Price

⇒ List Price = 0.83CP / 0.5

⇒ List Price = 1.66CP

If sold at the list price, gain percentage: (List Price - CP) / CP × 100

⇒ (1.66CP - CP) / CP × 100

⇒ 0.66CP / CP × 100

⇒ 66%

∴ The correct answer is 66%.

Given:

The radius and height of a right circular cone are increased by 25%.

Formula used:

Volume of a cone, V = (1/3)πr²h

Calculations:

Let the original radius be r and the original height be h.

Original volume, V₁ = (1/3)πr²h

New radius = r + 0.25r = 1.25r

New height = h + 0.25h = 1.25h

New volume, V₂ = (1/3)π(1.25r)²(1.25h)

⇒ V₂ = (1/3)π(1.5625r²)(1.25h)

⇒ V₂ = (1/3)π(1.953125r²h)

Increase in volume = V₂ - V₁

⇒ Increase in volume = (1/3)π(1.953125r²h) - (1/3)πr²h

⇒ Increase in volume = (1/3)πr²h(1.953125 - 1)

⇒ Increase in volume = (1/3)πr²h(0.953125)

Percentage increase in volume = (Increase in volume / Original volume) × 100

⇒ Percentage increase in volume = (0.953125 / 1) × 100

⇒ Percentage increase in volume = 95.31%

∴ The correct answer is option (1).

Given:

Electric bill = ₹50,000

Formula used:

Single Discount = Initial Amount × (1 - Discount Rate)

Two Successive Discounts = Initial Amount × (1 - First Discount Rate) × (1 - Second Discount Rate)

Calculation:

Single Discount:

Single Discounted Amount = 50000 × (1 - 0.30)

⇒ Single Discounted Amount = 50000 × 0.70

⇒ Single Discounted Amount = ₹35,000

Two Successive Discounts:

First Discounted Amount = 50000 × (1 - 0.26)

⇒ First Discounted Amount = 50000 × 0.74

⇒ First Discounted Amount = ₹37,000

Second Discounted Amount = 37000 × (1 - 0.05)

⇒ Second Discounted Amount = 37000 × 0.95

⇒ Second Discounted Amount = ₹35,150

Difference between the two discounts:

Difference = 35150 - 35000

⇒ Difference = ₹150

∴ The correct answer is option (2).

Formula used:

Mode is the value that appears most frequently in a data set.

Calculation:

 

The mode is the value with the highest frequency.

So, highest frequency (number of patients) = 7

Days of confinement with the highest frequency = 8

Thus, Mode = 8

∴ The correct answer is option (1).

Given:

Diameter of the hemispherical bowl = 21 cm

Formula used:

Volume of a hemisphere = (2/3)πr³

Where, r = radius of the hemisphere

Calculation:

Radius (r) = Diameter / 2 = 21 cm / 2 = 10.5 cm

Volume = (2/3) × (22/7) × (10.5)³

⇒ Volume = (2/3) × (22/7) × 10.5 × 10.5 × 10.5

⇒ Volume = (2/3) × (22/7) × 1157.625

⇒ Volume = (2/3) × 3.14 × 1157.625

⇒ Volume = 2.09333333 × 1157.625

⇒ Volume ≈ 2425.5 cm³

∴ The correct answer is option (4).

Given:

In ΔABC, ∠A = 85º and ∠C = 58º

ΔPQR is similar to ΔABC

Formula used:

In similar triangles, corresponding angles are equal.

Calculation:

We need to find ∠Q in ΔPQR, which corresponds to ∠B in ΔABC.

Since the sum of angles in a triangle is 180º:

∠B = 180º - ∠A - ∠C

⇒ ∠B = 180º - 85º - 58º

⇒ ∠B = 37º

Therefore, the correct answer is option (3).

When the paper is unfolded, we get:

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: All the symbols of the image are moving in clockwise direction along the sides in the subsequent images.

Hence, the correct answer is "Option 2".

The given statement is: Z < Y = J ≥ G ≥ P ≥ C ≥ R

Conclusions:

I. Z ≥ R → False (There is no definite relation; Z < Y = J ≥ G ≥ P ≥ C ≥ R)

II. J = C → False (There is no definite relation; J ≥ G ≥ P ≥ C)

Hence, the correct answer is "Neither conclusion I nor II is true".

According to the given information,

Here, we can see that the code for 'L' is 1.

Hence, the correct answer is "1".

The logic followed here is,

Hence, the correct answer is "UYTWU".

The meaningful English words that can be made using B, E, O and R using each letter only once in each word are shown below,

1. BORE (Verb): To make someone feel weary and uninterested by talking too much about something tedious.

2. ROBE (Noun): A long, loose outer garment typically worn on formal or ceremonial occasions.

3. BOER (Noun): A white person in South Africa who is related to the Dutch people who went to live there in the 17^th century.

Hence, the correct answer is "Three".

The logic followed here is,

Hence, the correct answer is "ZMPUA".

The logic followed here is:

Logic: The letter turns 90° in clockwise direction and number of sides of the polygon decreases by 1 in the second image of the pair.

Similarly,

Hence, the correct answer is "Option 3".

The logic followed here is,

Hence, the correct answer is "204".

The logic followed here is:

Logic: Second number = First number + Third number

(4, 12, 8)

→ 12 = 4 + 8

(2, 7, 5)

→ 7 = 2 + 5

Now, let's check each option,

1) 7, 2, 1

→ 2 ≠ 7 + 1

2) 3, 6, 5

→ 6 ≠ 3 + 5

3) 9, 4, 7

→ 4 ≠ 9 + 7

4) 1, 4, 3

→ 4 = 1 + 3 ⇒ Follows the logic.

Hence, the correct answer is "1, 4, 3".

The meaningful words that can be formed using second, third, sixth and seventh letters of the word ‘CRACKER’ (when counted from left to right) using each letter only once in each word is shown below,

1. REAR → (Noun) The back part of something, especially a building or vehicle.

2. RARE → (Adjective) Not common; infrequent.

Hence, the correct answer is "Two".

Given equation: 292 ÷ 2 - 15 + 164 × 4 = ?

After interchanging the signs, the equation we get: 292 × 2 + 15 - 164 ÷ 4 = ?

→ 292 × 2 + 15 - 164 ÷ 4 = ?

→ 292 × 2 + 15 - 41 =?

→ 584 + 15 - 41 =?

→ 599 - 41 =?

→ 558 =?

Hence, the correct answer is "558".

The logic followed here is:

1. Hospital - doctors: This pair represents a place (hospital) and the professionals (doctors) who work there.

2. School - teachers: This pair represents a place (school) and the professionals (teachers) who work there.

3. Theatre - movies: This pair represents a place (theatre) and the main activity (movies) that takes place there.

4. Restaurant - chefs: This pair represents a place (restaurant) and the professionals (chefs) who work there.

Here, we can see that Option 3 doesn't belong to the group.

Hence, the correct answer is "Theatre - movies".

The given statement is: G < H > K ≤ S ≥ L = M < Q

Conclusions:

I. G > L → False (There is no definite relation; G < H > K ≤ S ≥ L)

II. H = Q → False (There is definite relation; H > K ≤ S ≥ L = M < Q)

Hence, the correct answer is "Neither conclusion I nor II is true".

The logic followed here is,

Logic: Both words of the pair are antonyms.

Docile: Defiant

→ Docile means obedient or easily managed. Defiant means boldly resisting or challenging authority.

→ Both are antonyms.

Placid: Turbulent

→ Placid means calm and peaceful. Turbulent means characterized by conflict, disorder, or confusion; not calm or controlled.

→ Both are antonyms.

Now, let's check each option,

1) Relinquish: Surrender

→ These words are synonyms, not antonyms.

2) Zenith: Nadir

→ These words are antonyms. Zenith means the highest point, while nadir means the lowest point.

3) Optimal: Ideal

→ These words are synonyms, not antonyms.

4) Scrumptious: Delicious

→ These words are synonyms, not antonyms.

Hence, the correct answer is "Zenith: Nadir".

According to the given information,

1)  Sunita is ranked 10^th from the top.

2. Sunita is 18^th from the bottom in her class.

On combining, we get:

Number of students in the class = (9 + 1 + 17) = 27

Hence, the correct answer is "27".

According to the given information,

Here, we can see that the code for 'D' is £.

Hence, the correct answer is "£".

The given statement is: Suresh has started practicing critical reasoning after hearing about Ramesh’s incredible result in the competitive exam.

Inference:

I) Ramesh has scored most of the marks in critical reasoning → False (It is possible that Ramesh’s overall incredible result inspired Suresh, but there is no direct indication that Ramesh scored most of his marks specifically in critical reasoning).

II) Most of the questions in the exam constitute of critical reasoning questions → False (The statement does not provide any information about the composition of the exam questions).

Hence, the correct answer is "Neither (I) nor (II) can be inferred".

The meaningful four-letter English words that can be formed using T, U, K and S using each letter only once in each word is,

TUSK → A long, pointed tooth, especially one which sticks out of the mouth of animals such as elephants or walruses.

Hence, the correct answer is "One".

The least possible venn diagram is shown below,

Conclusions:

I. Some C’s are A’s → True (Some A’s are B’s and all the B’s are C’s implies that some A's which are B are also C).

II. Some B’s are J’s → False (Some J’s are A and some A’s are B implies that some B’s can be J. This is possible but not definite).

Hence, the correct answer is "Only Conclusion I follows".

The logic followed here is,

Hence, the correct answer is "EMXRO".

Alternate Method 

X and R are only present in EMXRO, hence option(3) is the correct answer.

The given statement is: The eligibility for admission to the course is a minimum of 80% marks in the 10^th standard board exams. However, students who have appeared for the 10^th standard board exams this year can also apply.

Inference:

I. No 11^th standard students can apply for the course → False (11^th standard students can apply for the course if they fulfill the eligibility of 80% marks in the 10^th standard board exams).

II. Students who have appeared for 10^th standard exams will get admission only if they score 80% or more in their exam → True (students who have appeared for the 10^th standard board exams this year can apply, they will get admission only if they meet the minimum marks requirement of 80%).

Hence, the correct answer is "Only (II) can be inferred".

Given equation: 313 ÷ 4 - 2107 × 7 + 24 = ?

After interchanging the signs, the equation we get: 313 × 4 + 2107 ÷ 7 - 24 = ? 

→ 313 × 4 + 2107 ÷ 7 - 24 = ? 

→ 313 × 4 + 301 - 24 = ?

→ 1252 + 301 - 24 = ?

→ 1553 - 24 = ?

→ 1529 =?

Hence, the correct answer is "1529".

The logic followed here is,

Hence, the correct answer is "30".

The logic followed here is,

Logic: The images are placed diagonally.

Let's check,

A) 

 ⇒ Follows the logic.

B) 

 ⇒ Follows the logic.

C) 

 ⇒ Follows the logic.

D) 

 ⇒ Doesn't follows the logic.

E) 

 ⇒ Follows the logic.

Hence, the correct answer is "D".

The mirror image of the given figure is shown below,

Hence, the correct answer is "Option 2".

The logic followed here is,

Logic: Second number = First number × 4 

Let's check each option,

1) 25, 100

→ 100 = 25 × 4 

2) 13, 52

→ 52 = 13 × 4 

3. 41, 164

→ 164 = 41 × 4 

4. 33, 152

→ 152 ≠ 33 × 4 ⇒ Doesn't follows the logic.

Hence, the correct answer is "33, 152".

The logic followed here is,

Logic: Second number = First number × 3

Now, let's check each option,

1) 38-114

→ 114 = 38 × 3

2) 41-123

→ 123 = 41 × 3

3) 25-75

→ 75 = 25 × 3

4) 33-97

→ 97 ≠ 33 × 3 ⇒ Doesn't follows the logic.

Hence, the correct answer is "33-97".

The logic followed here is,

Logic: Third number = (First number + Second number) + 10

(3, 5, 18)

→ 18 = 3 + 5 + 10

(2, 3, 15)

→ 15 = 2 + 3 + 10

Let's check each option,

1) 1, 5, 11

→ 11 ≠ 1 + 5 + 10

2) 1, 2, 13

→ 13 = 1 + 2 + 10 ⇒ Follows the logic.

3) 5, 2, 10

→ 10 ≠ 5 + 2 + 10

4) 5, 6, 11

→ 11 ≠ 5 + 6 + 10

Here, we can see that only Option 2 follows the logic. 

Hence, the correct answer is "1, 2, 13".

According to the given information,

1) L sits third to the right of M.

2) Only two people sit between K and L.

3) I sits to the immediate right of K.

4) Only three people sit between I and J.

Here, we can see that there are twelve people.

Hence, the correct answer is "Twelve".

The correct answer is: Option 3.

Key Points

• The word "Superindednt" is incorrectly spelt. The correct spelling is "Superintendent". (अधीक्षक)
• Example: The superintendent of the school ensured that all safety protocols were followed.
• "Superintendent" refers to a person who manages or superintends an organization or activity. (अधीक्षक)
• Example: The superintendent of the police department held a press conference today.

Therefore, the correct answer is: Option 3.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Inconspicuous (अप्रमुख): Not clearly visible or attracting attention.
• Example: She tried to remain as inconspicuous as possible in the crowded room.
• Susceptibility (संवेदनशीलता): The state of being likely to be influenced or harmed by a particular thing.
• Example: His susceptibility to colds is due to his weak immune system.
• Extemporise (तात्कालिक): Compose, perform, or produce something such as music or a speech without preparation; improvise.
• Example: The actor had to extemporise his lines when he forgot the script.

The correct answer is ‘2’ i.e. An apple is being eaten by him.

Key Points

• To convert an active voice sentence into passive voice, the object of the active sentence becomes the subject of the passive sentence, and the subject of the active sentence becomes the agent (introduced by the preposition 'by').
• In the given active voice sentence 'He is eating an apple,' 'He' is the subject, and 'an apple' is the object.
• The passive voice construction will restructure it as 'An apple is being eaten by him.' This maintains the present continuous tense and correctly places the focus on the action being performed on the object.
• The other options do not correctly convert the sentence into passive voice:
• Option 1: 'He has been eating an apple.' - Incorrect as it is not in passive voice.
• Option 3: 'An apple was eaten by him.' - Incorrect tense; past simple instead of present continuous.
• Option 4: 'He was eating an apple.' - Incorrect as it is not in passive voice.

 

Hence, the correct answer is option 2.

Passive voice sentence: An apple is being eaten by him.

Additional Information

• Understanding the difference between active and passive voice helps in constructing sentences accurately:
• Example: Active: She is writing a letter.

Passive: A letter is being written by her.

The correct answer is: Option 4 i.e. "If you play with fire, you’ll get burned".

Key Points

• The idiom "If you play with fire, you’ll get burned" means that if you take unnecessary risks, you will encounter negative consequences. (अगर आप आग से खेलते हैं, तो आप जल जाएंगे)
• Example: If you keep driving so recklessly, one day you’ll have an accident. Remember, if you play with fire, you’ll get burned.

Therefore, the correct answer is: Option 4.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• If you can’t beat ’em, join ’em (अगर आप उन्हें हरा नहीं सकते, तो उनके साथ शामिल हो जाएं): If you can’t defeat your opponents, it’s better to be on their side.
• Example: After years of competing against the big company, we decided, if you can’t beat ’em, join ’em, and merged with them.
• If it ain’t broke, don’t fix it (अगर यह टूटा नहीं है, तो इसे ठीक मत करो): Don’t try to improve something that already works well.
• Example: The old software is still running smoothly on our computers. If it ain’t broke, don’t fix it.
• If you want something done right, you have to do it yourself (अगर आप चाहते हैं कि कुछ सही हो, तो आपको इसे खुद करना होगा): To ensure something is done correctly, you need to do it yourself.
• Example: I always end up redoing the work done by others. If you want something done right, you have to do it yourself.

The correct answer is: Option 2.

Key Points

• The word "Insomnia" refers to the inability to obtain adequate sleep. (अनिद्रा)
• Example: She has been suffering from insomnia for several months and finds it hard to stay alert during the day.
• "Pyromania" is a compulsion to set things on fire. (आग लगाने का जुनून)
• Example: The man was diagnosed with pyromania after he admitted to setting multiple fires in the neighborhood.

Therefore, the correct answer is: Option 2.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Pyromania (आग लगाने का जुनून): A compulsion to set things on fire.
• Example: The man was diagnosed with pyromania after he admitted to setting multiple fires in the neighborhood.
• Andromania (पुरुषों के प्रति अत्यधिक आकर्षण): An excessive liking for or preoccupation with men.
• Example: Her andromania led her to obsess over every male celebrity she encountered.
• Mythomania (झूठ बोलने की आदत): An abnormal or pathological tendency to lie or exaggerate.
• Example: The politician's mythomania made it difficult for people to trust anything he said.

The correct answer is ‘4’ i.e. the World Cup.

Key Points

• The phrase 'an World Cup' is incorrect because 'World Cup' is a proper noun and should be preceded by 'the' instead of 'an'.
• 'An' is used before words that begin with a vowel sound, while 'the' is used before specific items or proper nouns.
• The corrected sentence will be: "Those players who chose not to play in the league were banned from playing in the World Cup."
• The other underlined parts of the sentence are correct and do not require modification:
• Option 2: 'play in a league' is acceptable but 'the league' is contextually more appropriate.
• Option 3: 'play in league' is grammatically incorrect.

 

Hence, the correct answer is option 4.

Correct sentence: Those players who chose not to play in the league were banned from playing in the World Cup.

Additional Information

• Articles ('a,' 'an,' 'the') must be used correctly to ensure grammatical accuracy and clarity in sentences:
• Example: I saw an elephant.

I saw the elephant that you mentioned earlier.

The correct answer is ‘4’ i.e. No error.

Key Points

• All parts of the sentence are grammatically correct.
• The phrase 'like you and he' is correct because 'like' is used as a comparison to two subjects, and 'he' is the correct pronoun form to use as part of the compound subject 'you and he'.
• 'Sincere students like you and he' is a grammatically sound construction because it maintains parallel structure and the proper case for pronouns when used as subjects.

 

Hence, the correct answer is option 4.

Correct sentence: Sincere students like you and he should study regularly to pass the examination.

Additional Information

• Maintaining the correct form of pronouns and their cases in compound structures ensures that sentences are both grammatically correct and clear:
• Example: You and she are going to the market.

The coach congratulated him and her for their performance.

The option that expresses the given sentence in passive voice is ‘4’ i.e. The tournament was won by the team after weeks of hard work and commitment.

Key Points

• The sentence "The team won the tournament after weeks of hard work and commitment" is in active voice. In passive voice, the object of the action (the tournament) becomes the subject of the sentence.
• Option 4 correctly changes the sentence to passive voice: "The tournament was won by the team after weeks of hard work and commitment."
• The other options are incorrect:
• Option 1: Incorrect tense - 'had been won' is past perfect, not simple past.
• Option 2: Incorrect form - 'was winning' is not appropriate for this context.
• Option 3: Incorrect continuous tense - 'was being won' does not fit the context.

 

Hence, the correct answer is option 4.

The appropriate option to make the following sentence grammatically correct is ‘1’ i.e. contains.

Key Points

• In the phrase "Neither of the biscuits," the word 'neither' is considered singular. Therefore, a singular verb should follow it.
• Option 1 correctly uses the singular verb "contains" to match the singular subject "neither."
• The other options are incorrect:
• Option 2: 'are contained' is incorrect because it uses a plural verb and is in passive voice, which does not fit the context.
• Option 3: 'contain' is incorrect because it uses a plural verb.
• Option 4: 'is contain' is grammatically incorrect.

 

Hence, the correct answer is option 1.

The correct answer is: Option 3.

Key Points

• The word "Epitaph" refers to a phrase or words written in memory of a person who has died. (शिलालेख)
• Example: The epitaph on her tombstone read, "Beloved mother and wife."
• "Epigram" is a brief, interesting, memorable, and sometimes surprising or satirical statement. (सूक्ति)
• Example: Oscar Wilde was known for his witty epigrams.
• Hence, the word that best describes a phrase or words written in memory of a person who has died is "Epitaph".

Therefore, the correct answer is: Option 3.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Epigram (सूक्ति): A brief, interesting, memorable, and sometimes surprising or satirical statement.
• Example: Oscar Wilde's epigrams are still widely quoted today.
• Tombstone (समाधि): A large, flat inscribed stone standing or laid over a grave.
• Example: The tombstone was engraved with her name and dates of birth and death.
• Calligraphy (सुलेख): Decorative handwriting or handwritten lettering.
• Example: She practiced calligraphy to create beautiful wedding invitations.

The correct option that makes the sentence grammatically accurate is ‘2’ i.e. This lesser known heritage building is as much beautiful as the Red Fort.

Key Points

• In the original sentence, the phrase "so beautiful as" is incorrect. The correct comparative structure for emphasis should be "as much beautiful as."
• Option 2 uses the correct comparative structure "as much beautiful as" and makes the sentence grammatically accurate.
• The other options are incorrect:
• Option 1: Incorrect structure - "very much beautiful as" is grammatically incorrect.
• Option 3: Incorrect structure - "as beautiful as" does not emphasize "much" as intended.
• Option 4: Incorrect word usage - "less known" is incorrect and "much beautiful than" is also incorrect.

 

Hence, the correct answer is option 2.

The correct option that rectifies the error in the sentence is ‘2’ i.e. the laws pertaining.

Key Points

• The original sentence erroneously uses "a laws" which is incorrect since "a" is used for singular nouns and "laws" is plural.
• Option 2 corrects this error by changing "a laws" to "the laws," which is grammatically correct.
• The other options do not rectify the error:
• Option 3: the migration - This option changes a part of the sentence that is already correct and does not address the actual error.
• Option 4: an home minister - This option introduces a grammatical error because "an" should be "a" before "home minister."

 

Hence, the correct answer is option 2.

The correct option that can substitute the underlined segment in the sentence is ‘1’ i.e. call around.

Key Points

• The original sentence uses "call out," which typically means to shout or speak loudly to attract attention and is not the most appropriate verb for contacting multiple places by phone.
• Option 1, "call around," is the correct phrase meaning to contact various people or places, which fits the context of the sentence.
• The other options are incorrect:
• Option 3: call off - This means to cancel something and does not fit the context of the sentence.
• Option 4: call on - This typically means to visit someone or request for someone to do something, which is not suitable in this context.

 

Hence, the correct answer is option 1.

The correct spelling to fill in the blank is ‘1’ i.e. contemplating.

Key Points

• The correct spelling of the word meaning to think about or consider something carefully is "contemplating."
• The other options have incorrect spellings:
• Option 2: cuntempltaing - Incorrect spelling.
• Option 3: cuntemplating - Incorrect spelling.
• Option 4: contempltaing - Incorrect spelling.

 

Hence, the correct answer is option 1.

The most appropriate tense form to fill in the blank is ‘1’ i.e. are moving.

Key Points

• The subject "Mohnish and Ravi" is plural, so the verb form should be "are" instead of "is" or "has."
• Option 1, "are moving," is the correct present continuous form for a planned future action involving a plural subject.
• The other options are incorrect:
• Option 2: has moving - Incorrect as "has" is not used with "moving" for plural subjects.
• Option 3: is moving - Incorrect because it does not agree with the plural subject.
• Option 4: has move - Incorrect as "has" is not followed by the base form "move" and does not agree with the plural subject.

 

Hence, the correct answer is option 1.

The sentence that has the correct use of words and spellings is ‘1’.

Key Points

• Option 1 uses all words correctly spelled and in their proper forms:
• intricate: correct spelling, meaning very complicated or detailed.
• multifaceted: correct spelling, meaning having many aspects or sides.
• captivated: correct spelling, meaning attracted and held the interest of.
• pondering: correct spelling, meaning thinking deeply about.
• The other options contain misspellings:
• Option 2: multifacted (should be multifaceted), paundering (should be pondering).
• Option 3: intricete (should be intricate), multifacted (should be multifaceted).
• Option 4: intrcate (should be intricate).

 

Hence, the correct answer is option 1.

The most appropriate homonym to fill in the blanks of the given sentences is ‘2’ i.e. scale.

Key Points

• Scale is the correct homonym because it fits both sentences contextually:
• A. I use a scale to weigh my ingredients while cooking.
• B. The mountaineer is going to scale the rocky hills.
• The other options do not fit both sentences appropriately:
• Option 1: climb - Does not fit sentence A.
• Option 3: horn - Does not fit either sentence.
• Option 4: crawl - Does not fit sentence A.

Hence, the correct answer is option 2.

The correct answer is: Option 1.

Key Points

• The word "Fatalist" means a person who believes that all events are predetermined and therefore inevitable. (भाग्यवादी)
• Example: As a fatalist, he believed that no matter what he did, the outcome of his life was already decided.

Therefore, the correct answer is: Option 1.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Flirt (फ्लर्ट): Someone who behaves as though they are attracted to someone, but does not have serious intentions.
• Example: He is known to be a flirt at parties, always charming everyone he meets.
• Superstitious (अंधविश्वासी): Having or showing a belief in superstitions.
• Example: She is superstitious and avoids walking under ladders.
• Fatal (घातक): Something causing death.
• Example: The accident was fatal, leading to multiple casualties.

The correct answer is: Option 4.

Key Points

• The idiom "Two heads are better than one" means that it is easier to solve a problem when two people work together rather than one person working alone. (दो सिर एक से बेहतर हैं)
• Example: When they couldn't fix the car by themselves, they decided to call a mechanic because two heads are better than one.
• "I was unable to solve the geometry question myself. So, I have asked my teacher to help me out." indicates a situation where seeking help from another person is beneficial. (मैं खुद ज्यामिति का प्रश्न हल करने में असमर्थ था। इसलिए, मैंने अपने शिक्षक से मेरी मदद करने के लिए कहा।)
• Example: He couldn't figure out the puzzle alone, so he asked his friend for help because two heads are better than one.

Therefore, the correct answer is: Option 4.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Two wrongs don’t make a right (दो गलत एक सही नहीं बनाते): Doing something wrong in response to a wrong action is not justified.
• Example: He stole your lunch, but stealing his in return is not the solution because two wrongs don’t make a right.
• You can’t always get what you want (आप हमेशा वह नहीं पा सकते जो आप चाहते हैं): It is not possible to achieve everything one desires.
• Example: She wanted to go on vacation, but due to financial constraints, she realized that you can’t always get what you want.
• When the going gets tough, the tough get going (जब हालात कठिन हो जाते हैं, तो मजबूत लोग आगे बढ़ते हैं): Strong people don’t give up when faced with challenges; they work harder.
• Example: Despite the setbacks, the team continued to push forward because when the going gets tough, the tough get going.

The segment that contains an error in the sentence is ‘4’ i.e. look after the matter.

Key Points

• Look after means to take care of, which doesn’t fit the context. The correct term should be look into, meaning to investigate or examine.
• The correct sentence should be: "The committee requested the Chief Investigator to personally look into the matter."
• The other segments do not contain any errors:
• Option 1: the Chief Investigator - correct.
• Option 2: The committee requested - correct.
• Option 3: to personally - correct.

Hence, the segment with the error is ‘4’ look after the matter.

The option that will improve the given sentence by using the most appropriate pronoun is ‘3’ i.e. "Pradeep, who is a teacher, also works as a content writer."

Key Points

• The correct relative pronoun to refer to a person who performs an action is who.
• "Pradeep, who is a teacher, also works as a content writer."
• The other options do not fit correctly:
• Option 1: which - used for things, not people.
• Option 2: whose - indicates possession.
• Option 4: that - used for things or as a restrictive clause indicator, not suitable here.

Hence, the correct answer is option 3.

The option that expresses the given sentence in indirect speech is ‘4’ i.e. "Rakesh exclaimed that it was a beautiful house."

Key Points

• When converting direct speech into indirect speech, exclamatory sentences need to be changed properly by using words like "exclaimed". The correct answer does this appropriately:
• "Rakesh exclaimed that it was a beautiful house."
• The other options do not correctly convey the original sentence:
• Option 1: Rakesh told that it had been a beautiful house – Incorrect tense and reporting verb.
• Option 2: Rakesh exclaimed with sorrow that it was a beautiful house – “With sorrow” is incorrect; the original exclamation is of surprise or admiration, not sorrow.
• Option 3: Rakesh exclaimed with surprise that it was must be beautiful house – The phrase “must be” is not necessary and grammatically incorrect here.

Hence, the correct answer is option 4.

The correct answer is: Modest.

Key Points

• The word "humble" means having or showing a modest or low estimate of one's importance. (विनम्र)
• Example: Despite his success, he remained a humble person who always credited his team.
• "Modest" refers to having a moderate view of one's own value or abilities; not boastful. (मध्यम, विनम्र)
• Example: She gave a modest reply when asked about her achievements, emphasizing the team's efforts instead.

Therefore, the correct answer is: Modest.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Beautiful (सुंदर): Pleasing the senses or mind aesthetically.
• Example: The garden is filled with beautiful flowers in the spring.
• Keen (उत्सुक): Having or showing eagerness or enthusiasm.
• Example: He is very keen to learn new languages.
• Amusing (मनोरंजक): Causing laughter or providing entertainment.
• Example: The comedian's performance was very amusing.

The most appropriate option to fill in the blank is ‘3’ i.e. "is learning."

Key Points

• Since the phrase "to play the violin now" indicates an action currently taking place, the present continuous tense is most appropriate:
• "Stanley is learning to play the violin now, with an amateur instructor."
• The other options do not fit the context of "now":
• Option 1: had learnt - past perfect tense, indicates a completed action in the past.
• Option 2: will learn - future tense, indicates an action that will happen.
• Option 4: was learning - past continuous tense, indicates an action that was happening in the past.

Hence, the correct answer is option 3.