SSC CHSL 2022 PYQs

Question 1

Find the area of the triangle whose sides are 5 cm, 12 cm and 13 cm.

Accepted Answer

The sides 5, 12, 13 form a Pythagorean triplet (5² + 12² = 13²), indicating a right-angled triangle. Area = ½ × base × height = ½ × 5 × 12 = 30 cm².

Question 2

The value of‌sin‌⁡4θ‌‌+‌sin‌⁡2θ‌cos‌⁡4θ‌‌+‌cos‌⁡2θ‌is:

Accepted Answer

Apply sum-to-product formulas: sin A + sin B = 2 sin((A+B)/2) cos((A-B)/2) and cos A + cos B = 2 cos((A+B)/2) cos((A-B)/2). Simplify to get tan((A+B)/2), which is tan(3θ).

Question 3

In the given figure, If ∠RPS = 25°, the value of ∠ROS is_______.

Accepted Answer

The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle. So, ∠ROS = 2 * ∠RPS = 2 * 25° = 50°.

Question 4

If x =√10+√11, y =√10-√11, then value of 7x2- 50xy + 7y2= ___________.

Accepted Answer

First, find x+y = 2√10 and xy = (√10)² - (√11)² = 10-11 = -1. Rewrite the expression as 7(x+y)² - 64xy. Substitute the values to get 7(2√10)² - 64(-1) = 7(40) + 64 = 280 + 64 = 344.

Question 5

Find the radius of the circle x2+ y2- 4x + 6y = 12.

Accepted Answer

Rewrite the equation as (x-2)^2 + (y+3)^2 = 12 + 4 + 9 = 25. Comparing with (x-h)^2 + (y-k)^2 = r^2, the radius r is sqrt(25) = 5 cm.

Question 6

40% of Ranita’s income is equal to 56% of Bhaskar’s income. If Ranita’s income was ₹800 more than what it is and Bhaskar’s income was ₹2,000 more than what it is, then the ratio of the incomes of Ranita and Bhaskar would have been 4 ∶ 3. What is the actual combined income of Ranita and Bhaskar?

Accepted Answer

Let Ranita's income be R and Bhaskar's be B. From the first condition, 0.40R = 0.56B, so R = 1.4B. From the second condition, (R+800)/(B+2000) = 4/3. Substitute R=1.4B into the second equation to find B, then R, and finally R+B.

Question 7

P, Q and R are batsmen. The ratio of the runs scored by them in a certain match was P ∶ Q = 16 ∶ 17 and Q ∶ R = 15 ∶ 16. At the end of the match, they scored a total of 956 runs. The number of runs scored by R is (nearest to an integer):

Accepted Answer

Combine ratios P:Q = 16:17 and Q:R = 15:16 to get P:Q:R = 240:255:272. Total parts = 767. R's runs = (272/767) * 956 ≈ 339.

Question 8

Bhanu spends 20% of his monthly salary on rent, 10% on stationery, 14% on transport, 18% on electricity, and the balance of ₹1,520 on remaining items. What is the monthly salary of Bhanu?

Accepted Answer

Total known expenses are 20+10+14+18 = 62%. The remaining 100-62 = 38% of salary is ₹1,520. So, total salary is (1520/38)*100 = ₹4,000.

Question 9

Using 2cosA cosB = cos(A + B) + cos(A – B), find the value of cos75°cos15°.

Accepted Answer

Given 2cosA cosB = cos(A + B) + cos(A – B). So, cosA cosB = 1/2 [cos(A + B) + cos(A – B)]. Substitute A=75°, B=15° to get 1/2 [cos(90°) + cos(60°)] = 1/2 [0 + 1/2] = 1/4.

Question 10

Study the given graph carefully and answer the question that follows.Production of food grains by a state over the years (1000 tonnes)What was the percentage drop in the production of food grains from 2018 to 2019 (consider up to two decimals)?

Accepted Answer

Production in 2018 was 7000 tonnes and in 2019 was 6500 tonnes. Percentage drop = ((7000-6500)/7000) * 100 = (500/7000) * 100 = 7.14%.

Question 11

16 men can paint 15 walls in 45 days. In how many days can 20 men paint 20 walls?

Accepted Answer

Use the formula M1*D1/W1 = M2*D2/W2. Substitute the given values: 16*45/15 = 20*D2/20. Simplify to find D2 = 48 days.

Question 12

Find the greatest among the following options.

Accepted Answer

Convert all options to decimals: 0.62, 2/3 ≈ 0.666..., 0.57, 4/5 = 0.8. Comparing these values, 0.8 is the greatest.

Question 13

The value of tan 48°. tan 23°. tan 42°. tan 67° is

Accepted Answer

Use the identity tan(90°-θ) = cot θ. Pair tan 48° with tan 42° (cot 48°) and tan 23° with tan 67° (cot 23°). Since tan θ * cot θ = 1, the product simplifies to 1*1 = 1.

Question 14

Calculate the area of the quadrilateral formed with the vertices (-3, 2), (5, 4),(7, -6) and (-5, -4).

Accepted Answer

Use the shoelace formula: 1/2 |(x1y2 + x2y3 + x3y4 + x4y1) - (y1x2 + y2x3 + y3x4 + y4x1)|. Substitute the coordinates and calculate to get 80 square units.

Question 15

Study the given table and answer the question that follows.The table shows quanity of various food items used by a restaurant during four months of a year (in kg).Food ItemJuneJulyAugustSeptemberRice180200240300Wheat420400380350Sugar200210230240Pulses250310320280Vegetables300320390370The quantity of wheat used in the month of July is what percentage of the total quantity of food items used in June ?

Accepted Answer

Total food in June = 180+420+200+250+300 = 1350 kg. Wheat in July = 400 kg. Percentage = (400/1350) * 100 = 4000/135 = 29.629...% which is 29 17/27%.

Question 16

The distance between stations A and B is 778 kilometres. A train travels from station A to station B at a uniform speed of 84 km/h and then returns to station A at a uniform speed of 56 km/h. What is the train's average speed (in km/h) throughout the journey?

Accepted Answer

Average speed for equal distances is 2ab/(a+b). Substitute a=84 and b=56: 2*84*56 / (84+56) = 9408 / 140 = 67.2 km/h.

Question 17

Two grandparents, two parents, and three grandchildren make up a family. The average present age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the present age of the family (in years)?

Accepted Answer

Calculate total age for each group: Grandparents (2*67=134), Parents (2*35=70), Grandchildren (3*6=18). Sum these totals (134+70+18=222) and divide by total family members (2+2+3=7) to get 222/7 = 31.71 or 31 5/7.

Question 18

The pie chart shows the percentage-wise break up of students in terms of specialisation in Engineering.Total number of students = 8000What is the ratio of the total number of students having either Networking or Graphics as their specialisations to the number of students having C programming as their specialisation?

Accepted Answer

Networking + Graphics = 19% + 12% = 31%. C Programming = 17%. The ratio is 31:17. The total number of students (8000) is not needed for this ratio calculation.

Question 19

Ifx4+(‌1x4)=322, then what is the value ofx3−(‌1x3)?

Accepted Answer

From x⁴ + 1/x⁴ = 322, find x² + 1/x² = 18, then x - 1/x = 4. Finally, use the identity a³ - b³ = (a - b)(a² + ab + b²) to get x³ - 1/x³ = (x - 1/x)(x² + 1/x² + 1) = 4(18 + 1) = 4 × 19 = 76.

Question 20

If x2= b - ax and x3(x3+ c) = d, then which of the following can be the values of c and d?

Accepted Answer

From x² = b - ax, we get x² + ax = b. Cube both sides: (x² + ax)³ = b³. Expand using (A+B)³ formula to find x⁶ + a³x³ + 3ax(x² + ax) = b³. Substitute x² + ax = b to get x⁶ + a³x³ + 3abx³ = b³. Rearrange to x³(x³ + a³ + 3ab) = b³. Comparing with x³(x³ + c) = d, we find c = a³ + 3ab and d = b³.