SSC CHSL 2022 PYQs

Question 1

The speed of a train is 108 km/h. The distance covered by the train in 11 seconds will be:

Accepted Answer

Convert speed from km/h to m/s by multiplying by 5/18. So, 108 * (5/18) = 30 m/s. Then, distance = speed * time = 30 m/s * 11 s = 330 m.

Question 2

The average age of a man and his son is 56 years. The ratio of their ages is 11 : 5. What is the son's age?

Accepted Answer

Total age is 56 * 2 = 112 years. The ratio 11:5 means total 16 parts. Son's age is (5/16) * 112 = 35 years.

Question 3

Which of the following can be a rationalising factor of (√2+√3+√5) ?

Accepted Answer

To rationalize (√2+√3+√5), group it as ((√2+√3)+√5). Multiply by ((√2+√3)-√5) to get (√2+√3)²-5 = 2+3+2√6-5 = 2√6. Then multiply by √6 to make it rational.

Question 4

The fourth proportional to 14, 21, 28 is:

Accepted Answer

For four proportional numbers a, b, c, d, the relation is a/b = c/d. Substitute the given values: 14/21 = 28/d. Solve for d to get 42.

Question 5

A shopkeeper claims that he is selling sugar at Rs.27/kg which cost him Rs.30/kg, but he gives 750 grams instead of 1000 grams. What is his profit or loss percentage?

Accepted Answer

The shopkeeper sells 750g for Rs. 27, which cost him Rs. 30 * (750/1000) = Rs. 22.5. Profit is 27 - 22.5 = Rs. 4.5. Profit percentage = (4.5/22.5) * 100 = 20%.

Question 6

The following pie chart shows the different coloured dresses worn by 60 students in a college party. Study the pie chart and answer the question that follows.The number of students who wore a cement-colored dresses (a sector which represents 20%) is:

Accepted Answer

To find the number of students, calculate 20% of the total 60 students. This is (20/100) * 60 = 12 students.

Question 7

On a sum of money, when invested for 2 years, compound interest and simple interest are ₹300 and ₹250, respectively. For both simple and compound interests the rate of interest per annum is the same, and for compound interest, interest is compounded annually. Find the rate of interest per annum.

Accepted Answer

The difference between CI and SI for 2 years is the interest on the first year's simple interest. SI for 1 year is 250/2 = 125. The difference (300-250=50) is 50. Rate = (50/125)*100 = 40%.

Question 8

The value of sin 2θ (tan θ + cot θ) is:

Accepted Answer

Rewrite tan θ and cot θ in terms of sin θ and cos θ. Simplify the expression using sin 2θ = 2 sin θ cos θ. The terms cancel out, resulting in 2.

Question 9

Which of the following numbers is divisible by 15?

Accepted Answer

A number is divisible by 15 if it is divisible by both 3 and 5. Check options for divisibility by 5 (ends in 0 or 5) and then by 3 (sum of digits divisible by 3). Option 2 satisfies both.

Question 10

The difference between the simple interest and compound interest on ₹1,000 for 1 year at 20% per annum, compounded half-yearly, is:

Accepted Answer

Calculate SI for 1 year at 20%. For CI, adjust rate to 10% and time to 2 half-years. Compute CI, then find the difference between CI and SI.

Question 11

Simplify [7‌12÷ {1‌14-‌12(2‌12-‌14−‌1¯6)}] ÷ (‌12of 8‌13).

Accepted Answer

First, simplify the expression within the innermost bracket using BODMAS. Then, proceed outwards, performing division, multiplication, subtraction, and finally the last division to get 43.2.

Question 12

If triangles ABC and PQR are both isosceles with AB = AC and PQ = PR, respectively. If also AB = PQ and BC = QR and angle B = 50°, then what is the measure of angle R?

Accepted Answer

Given AB=AC and PQ=PR, both triangles are isosceles. With AB=PQ and BC=QR, by SSS congruence, triangle ABC is congruent to triangle PQR. Thus, corresponding angles are equal, so angle R = angle C. Since angle B = 50° and AB=AC, angle C also equals 50°. Therefore, angle R = 50°.

Question 13

The base of a 12 cm-high wooden solid cone has a circumference of 44 cm. Find its volume.(useπ‌227)

Accepted Answer

First, find the radius from the circumference (2πr = 44, so r = 7 cm). Then, use the cone volume formula (1/3πr²h) with h = 12 cm to get 616 cm³.

Question 14

Study the given graph and answer the question that follows.The graph shows the number of appeared candidates and passed candidates ( in hundreds) in a test from six different institutions.From which institution is the difference between the appeared candidates and passed candidates the maximum?

Accepted Answer

Calculate the difference between appeared and passed candidates for each institution. Institution D has the largest difference (700 - 300 = 400), making it the correct answer.

Question 15

What is the fourth proportional to 16, 24, 8?

Accepted Answer

For numbers a, b, c, the fourth proportional d is found by a/b = c/d. Substitute 16/24 = 8/d, which simplifies to d = (24 * 8) / 16 = 12.

Question 16

After spending 20% of his salary on grocery and 30% of the remainder on monthly house rent, a man is left with Rs 8,400. What is his monthly salary?

Accepted Answer

Let salary be S. After 20% on grocery, 0.8S remains. Then 30% of remainder (0.8S) is spent, leaving 70% of 0.8S. So, 0.7 * 0.8S = 8400. Thus, 0.56S = 8400, so S = 15000.

Question 17

Two trains having lengths of 230 m and 240 m are 130 m apart. They start moving towards each other on parallel tracks, at speeds of 160 km/h and 200 km/h, respectively. In how much time will the trains cross each other?

Accepted Answer

Total distance to cover is sum of lengths plus initial gap (230+240+130 = 600m). Relative speed is sum of speeds (160+200 = 360 km/h). Convert speed to m/s (360 * 5/18 = 100 m/s). Time = Distance/Speed = 600/100 = 6 seconds.

Question 18

If cosec2θ + cot2θ =‌13, where 0 ≤ θ ≤‌π‌2, then the value of cosec4θ - cot4θ is:

Accepted Answer

Use the identity a² - b² = (a - b)(a + b). So, cosec⁴θ - cot⁴θ = (cosec²θ - cot²θ)(cosec²θ + cot²θ). Since cosec²θ - cot²θ = 1, the expression simplifies to 1 * 13 = 13.

Question 19

Find the greatest possible value of (a + b) for which the 8-digit number 143b203a is divisible by 15.

Accepted Answer

For a number to be divisible by 15, it must be divisible by both 3 and 5. Divisibility by 5 means 'a' must be 0 or 5. Divisibility by 3 means the sum of digits (13 + a + b) must be a multiple of 3. To maximize (a+b), choose a=5. Then 18+b must be a multiple of 3, so b can be 9. Thus, a+b = 5+9 = 14.

Question 20

Study the given table and answer the question that follows.The following table gives the month-wise number of different types of scooters produced by a company during the first six months of 1992.Months→Typesof scooters↓JANUARYFEBRUARYMARCHAPRILMAYJUNEX252518402015Y252750453020Z252715253020T25262503035TOTAL10010510811011090In which two of the six given months was the total number of scooters produced by the company, of all types taken together, equal?

Accepted Answer

Locate the 'TOTAL' row in the table. Identify months with identical total production figures. April and May both show a total of 110 scooters.