32. SSC CGL 2023 

Exam Date 25/07/2023 

Exam Time 5:15 PM - 6:15 PM

Section : Quantitative Aptitude 

Q.1 Simplify the expression $\frac{{{s}^{2}}+{{t}^{2}}+2st-{{u}^{2}}}{{{s}^{2}}-{{t}^{2}}-2tu-{{u}^{2}}}$, provided (3 + t + u) $\ne $0. 

1. $\frac{s-t-u}{s+t-u}$ 

2. $\frac{s+t+u}{s-t+u}$ 

3. $\frac{s+t-u}{s-t-u}$ 

4. $\frac{s-t+u}{s+t+u}$ 

Q.2 The length of the longest diagonal of a cube is $7\sqrt{3}$ cm. Find its volume (in cm3). 

1. 49 $\sqrt{3}$ 

2. 343 $\sqrt{3}$ 

3. 343 

4. 334 

Q.3 A circle of radius 4 cm is drawn inscribed in a right angle triangle ABC, right angled at C. If AC = 12 cm, then the value of CB is: 

1. 12 cm 

2. 16 cm 

3. 8 cm 

4. 20 cm 

Q.4 Simplify the expression $\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}$, where x = 2 and y = 3. 

1. $2\sqrt{6}-5$ 

2. $2\sqrt{6}-6$ 

3. $5-2\sqrt{6}$ 

4. $\sqrt{6}-5$ 

Q.5 S deposits a total of ₹50,000 in two accounts which give 8% and 12% simple interest annually, respectively. After one year, he gets a total ₹5,200. How much money does he deposit in the account with a 12% interest rate? 

1. ₹20,000 

2. ₹32,000 

3. ₹25,000 

4. ₹30,000 

Q.6 A cuboid with sides 4, 6 and 8 units is covered with paper. The paper is removed and a square is made from it. What is the side (in units) of the square? 

1. 12.24 

2. 16.62 

3. 14.42 

4. 12.62 

Q.7 Tarun owned a plot of land having an area that was 10% more than the area of the plot owned by Basab, while the area of the plot of land owned by Nakul was 40% more than the area of the plot owned by Tarun. If the area of the plot owned by Nakul was 2695 square feet, what was the area (in square feet) of the plot owned by Basab? 

1. 1800 

2. 1750 

3. 1740 

4. 1780 

Q.8 The marked price of a microwave oven is ₹15,990 and it is sold for ₹12,792. What is the rate of discount offered? 

1. 24% 

2. 21% 

3. 20% 

4. 25% 

Q.9 In the figure given below. PQ is the diameter of the circle with centre 0. If ∠QOR = 100° then the measure of ∠PSR is:  

1. 40° 

2. 100° 

3. 160° 

4. 80° 

Q.10 A thief steals an item and escapes, running at a speed of 15 km/h. A policeman arrives at the spot of the crime after 4 minutes and immediately starts chasing the thief. 16 minutes after the policeman started to chase the thief; there is still a gap of 200 m between the two. At what distance from the spot of the crime will the policeman catch up the thief and what is the speed (in km/h) of the policeman? 

1. 6.5 km; 19.5 

2. 5 km; 15 

3. 5.5 km; 16.5 

4. 6 km; 18

Q.11 Study the given table and answer the question that follows. 

The table represents the expenditure of a company (in thousand rupees) per annum over the given year. 

What is the average amount of salary per year. which the company has to pay during these four years? 

1. ₹2,00,000 

2. ₹2,75,000 

3. ₹3,00,000 

4. ₹2,80,000 

Q.12 If(a + b — c) = 20, and a2 + b2 + c2 = 152, find the value of a3 + b3 — c3 + 3abc. 

1. 640 

2. 480 

3. 720 

4. 560 

Q.13 A group of college students had decided to complete a project in 10 days. As 2 students dropped out every day, the project got completed at the end of the 15th day. The number of students at the beginning of the project was: 

1. 45 

2. 42 

3. 35 

4. 40 

Q.14 20 women and 15 men together can complete a work in 6 days. It takes 150 days for a single woman to complete the work. In how many days can a single man complete the work? 

1. 450 

2. 350 

3. 225 

4. 210 

Q.15 4 men, working together, can finish a work in 18 days. How many more men are required to finish the same work in 12 days? 

1. 2 

2. 3 

3. 6 

4. 4 

Q.16 If cos(40° + x) = sin 30°, then the value of x is: 

1. 20° 

2. 19° 

3. 23° 

4. 22° 

Q.17 A 40-litre mixture contains 25% alcohol and 75% water. If 10 litres of water are added to the mixture, the percentage of alcohol in the new mixture is: 

1. 18% 

2. 20% 

3. 27% 

4. 25% 

Q.18 Having started from the same point and at the same time, two runners – P and Q – are running around a circular track of length 500 m in opposite directions with the speeds of 6 m/s and 10 m/s, respectively. If they exchange their speeds after meeting for the first time, who will reach the starting point first? 

1. P 

2. Q 

3. Both P and Q will reach at the same time 

4. No one of the P and Q 

Q.19 - 7p - [3q - {8p - (4q - 10p)}] = ? 

1. 11p - 7q 

2. 12p - 9q 

3. 9p - 12q 

4. 7p - 11q 

Q.20 The following bar chart shows the vends of foreign direct investment (FDI) into India from all over the world. 

What was the average of India’s FDI over the years 1992 - 1997? 

1. 15.7 

2. 15.2 

3. 15.6 

4. 15.5 

Q.21 The mean proportional of (a + b) (a — b)3, (a + b)3 (a — b) is: 

1. (a+b)2 (a-b) 

2. a2-b2 

3. (a+b)2 (a-b)2 

4. (a+b) (a-b)2 

Q.22 Which of the following numbers is divisible by 44? 

1. 27048 

2. 32802 

3. 93472 

4. 54736 

Q.23 A shopkeeper purchased 1600 mangos at the rate of ₹120 per dozen. Out of these, he sold 900 mangoes at ₹15 per mango and the remaining mangoes at ₹14 per mango. His gain percentage is: 

1. 48.765% 

2. 38.265% 

3. 45.625% 

4. 35.625% 

Q.24 In the following figure, the circles with centres B and D have radii 4 cm and x cm, respectively. AC is a tangent to both the circles. Find the value of x. 

1. 7 

2. 5 

3. 6 

4. 3 

Q.25 Find (1 / sinθ) – sinθ. 

1. Cosθ cotθ 

2. cosθ cosecθ 

3. cosθ tanθ 

4. cosθ secθ