SSC CGL 2024 PYQs

Question 1

Find the average of the prime numbers lying between 50 and 76.

Accepted Answer

The prime numbers between 50 and 76 are 53, 59, 61, 67, 71, 73. Their sum is 384. Dividing by 6 (total count) gives an average of 64.

Question 2

The average of 12 numbers is 48. The average of the first 5 numbers is 45 and the average of next 4 numbers is 52. If the 10thnumber is 10 less than the 11thnumber and is 5 more than the 12thnumber, then the average of the 11thand 12thnumbers is:

Accepted Answer

Calculate the sum of all 12 numbers, then the sum of the first 9. Find the sum of the last three numbers. Set up equations for the 10th, 11th, and 12th numbers based on their relationships and solve for them. Finally, average the 11th and 12th numbers.

Question 3

Let O be the centre of the circle and AB and CD are two parallel chords on the same side of the radius. OP is perpendicular to AB and OQ is perpendicular to CD. If AB = 10 cm, CD = 24 cm and PQ = 7 cm, then the diameter (in cm) of the circle is equal to:

Accepted Answer

Let radius be r. Using Pythagoras theorem, OP = sqrt(r^2 - 5^2) and OQ = sqrt(r^2 - 12^2). Since PQ = OQ - OP = 7, solve for r. Diameter is 2r.

Question 4

The angles of triangle are such that one is average of other two, then the angles are:1)‌π6‌‌π3‌‌π22)‌π3‌‌π3‌‌π23)‌π6‌‌π3‌‌π44)‌π2‌‌π2‌‌π3

Accepted Answer

Let the angles be A, B, C. Given B = (A+C)/2, which means 2B = A+C. Since A+B+C = 180° (or π radians), substitute A+C = 2B into the sum: 2B+B = 180°, so 3B = 180°, B = 60° (or π/3). The only option with π/3 as one angle is option 1.

Question 5

Let 0º < t < 90º. Then which of the followings is true?

Accepted Answer

For angles between 0° and 45°, the value of sin(t) increases from 0 to 1/√2, while cos(t) decreases from 1 to 1/√2. Thus, sin(t) < cos(t) for t < 45°.

Question 6

The concentrations of three acids, A, B, and C, are specified as 20%, 30%, and 40%, respectively. They are blended in a ratio of 3 : 5 : a, yielding a solution with a concentration of 30%. What is the value of 'a'?

Accepted Answer

Use the weighted average formula: (C1V1 + C2V2 + C3V3) / (V1 + V2 + V3) = C_final. Substitute the given values and solve for 'a'. (20*3 + 30*5 + 40*a) / (3+5+a) = 30. This simplifies to 60 + 150 + 40a = 30(8+a), leading to a=3.

Question 7

The interest accrued on a sum of ₹16,000 lent at a simple interest rate of 14% p.a. for the time in those many years, which gives a simple interest of three-fifths of a certain sum at 10% p.a., is:

Accepted Answer

First, find the time (T) using SI = (3/5)P at 10% p.a. This gives T = 6 years. Then, calculate SI for ₹16,000 at 14% for 6 years: (16000 * 14 * 6) / 100 = ₹13,440.

Question 8

In a triangle, ΔABC, the ∠ABC = 90°. If the sin A = 1/2, then cos C is equal to:

Accepted Answer

In a right-angled triangle, angles A and C are complementary (A + C = 90°). Therefore, sin A = cos C. Given sin A = 1/2, so cos C = 1/2.

Question 9

Find the value of the following expression.√‌1+sin‌⁡θ1−sin‌⁡θ

Accepted Answer

Rationalize the expression by multiplying the numerator and denominator by √(1+sinθ). This simplifies to (1+sinθ)/cosθ, which further breaks down into 1/cosθ + sinθ/cosθ, yielding secθ + tanθ.

Question 10

If cosecθ = 5/3, then evaluate (sec²θ - 1) × cot²θ × (1 + cot²θ).

Accepted Answer

Given cosecθ = 5/3. Use identities: sec²θ - 1 = tan²θ and 1 + cot²θ = cosec²θ. The expression simplifies to tan²θ × cot²θ × cosec²θ = 1 × cosec²θ. Substitute cosecθ = 5/3 to get (5/3)² = 25/9.

Question 11

Let C be a circle with centre O and P be an external point to C. Let PA and PB be two tangents to C with A and B being the points of tangency, respectively. If PA and PB are inclined to each other at an angle of 60º, then find ∠POA.

Accepted Answer

Tangents from an external point to a circle are equal in length and subtend equal angles at the center. Thus, ∠APO = ∠BPO. Since ∠APB = 60°, ∠APO = 30°. In right triangle ΔOAP, ∠POA = 90° - ∠APO = 90° - 30° = 60°.

Question 12

Ramesh purchased some items from a dealer on 19 November 2019. The bill generated was for ₹5,480. He had also purchased some items on 10 November 2019 having the bill value of ₹9,800. He cleared both the bills this time and paid the total amount in cash. If the dealer gives a scheme of 2% discount on the payments done within 10 days and 5% for the payments made in cash at the time of purchase, then find the amount paid by Ramesh on 19 November 2019.

Accepted Answer

For the ₹5,480 bill (19 Nov), a 5% cash discount applies: 5480 * 0.95 = ₹5206. For the ₹9,800 bill (10 Nov), a 2% discount applies (within 10 days): 9800 * 0.98 = ₹9604. Total paid = 5206 + 9604 = ₹14,810.

Question 13

Simplify‌0.58×0.58×0.58−0.0010.58×0.58+0.058+0.01

Accepted Answer

Recognize the expression as (a³ - b³) / (a² + ab + b²), where a = 0.58 and b = 0.1. This simplifies to (a - b). So, 0.58 - 0.1 = 0.48.

Question 14

A group of 30 students appeared in a test. The average score of 12 students is 62, and that of the rest is 62. What is the average score of the group?

Accepted Answer

If all subgroups have the same average, the overall group average will also be that same value. Here, both parts average 62, so the total average is 62.

Question 15

The distance between the centres of two circles of radii 22 cm and 10 cm is 37 cm. If the points of contact of a direct common tangent to these circles are M and Q, then find the length of the line segment MQ.

Accepted Answer

The length of the direct common tangent is given by the formula: sqrt(d^2 - (R-r)^2). Substitute d=37, R=22, r=10 to get sqrt(37^2 - (22-10)^2) = sqrt(1369 - 144) = sqrt(1225) = 35 cm.

Question 16

At present, A is thrice as old as B. C is 5 years elder than B. The sum of the ages of A, B, C is 75 years. The ratio of the age of B five years ago to the age of A three years from now is:

Accepted Answer

Let B's age be x. A = 3x, C = x+5. Sum: 3x + x + (x+5) = 75 => 5x = 70 => x = 14. B's age 5 years ago = 14-5 = 9. A's age 3 years from now = (3*14)+3 = 42+3 = 45. Ratio = 9:45 = 1:5.

Question 17

Find the gain percentage, given that Priya sold her scooter for ₹42564 gaining‌16th of the selling price.

Accepted Answer

Gain is 1/6th of SP. So, if SP is 6 units, Gain is 1 unit. CP = SP - Gain = 5 units. Gain percentage = (Gain/CP) * 100 = (1/5) * 100 = 20%.

Question 18

Ravi's salary was increased by 50%. After some time, his new salary was also increased by 50%. Find his gain percentage on the salary.

Accepted Answer

Assume initial salary is 100. First increase makes it 150. Second 50% increase on 150 is 75, making total 225. Gain is 125% (225-100).

Question 19

In a rhombus ABCD, O is any interior point such that OA = OC. What is five-ninths of the degree measure of ∠DOB?

Accepted Answer

In a rhombus, diagonals bisect each other at 90 degrees. Since OA=OC, O must lie on the diagonal BD. Thus, ∠DOB is a straight angle, 180°. Five-ninths of 180° is (5/9)*180° = 100°.

Question 20

If 0.4x + 0.16y = 1.7 and 0.3x + 0.12y = 3.4, then which of the following is correct?

Accepted Answer

Compare the ratios of coefficients: a1/a2 = 0.4/0.3 = 4/3, b1/b2 = 0.16/0.12 = 4/3. But c1/c2 = 1.7/3.4 = 1/2. Since a1/a2 = b1/b2 ≠ c1/c2, the system has no solution.