23. SSC CGL 2023 

Exam Date 21/07/2023 

Exam Time 11:45 AM - 12:45 PM 

Section : Quantitative Aptitude

Q.1 The value of secx - cosx= ? 

1. secx cosx 

2. tanx cosx 

3. tanx sinx 

4. secx tanx 

Q.2 The distance between two towns is covered in 7 hours and 30 minutes at the speed of 72 km/h. The time saved if the speed is increased by 25% is: 

1. 1 hour 50 minutes 

2. 1 hour 20 minutes 

3. 1 hour 30 minutes 

4. 1 hour 36 minutes 

Q.3 What is the value of $\left( \frac{1}{a}-\frac{1}{b}-\frac{1}{c} \right)$ if, $\frac{2a-5}{a}-\frac{4b-5}{b}+\frac{6c+5}{c}=0$?  

1. $-\frac{8}{5}$ 

2. $\frac{2}{5}$ 

3. $-\frac{12}{5}$ 

4. $\frac{4}{5}$ 

Q.4 To earn a 12% profit, a shopkeeper sells a television for ₹22,400. What should be the selling price (in ₹) of the television if he wants a double profit? 

1. 24,600 

2. 24,800 

3. 24,000 

4. 25,000 

Q.5 AB = 28 cm and CD = 22 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 4 cm. The radius of the circle is _________. (Consider up to two decimals) 

1. 15.82 cm 

2. 14.82 cm 

3. 15.20 cm 

4. 13.20 cm 

Q.6 An inlet pipe can fill an empty tank in $4\frac{1}{2}$hours while an outlet pipe drains a completely filled tank in $7\frac{1}{5}$% hours. The tank is initially empty, and the two pipes are alternately opened for an hour each, till the tank is completely filled, starting with the inlet pipe. In how many hours will the tank be completely filled? 

1. 24 

2. $20\frac{1}{4}$ 

3. $20\frac{3}{4}$ 

4. $22\frac{3}{8}$ 

Q.7 If $\left( x-\frac{1}{x} \right)=2\sqrt{2}$, what is the value of $\left( {{x}^{6}}-\frac{1}{{{x}^{6}}} \right)$? 

1. 1000 

2. 970 

3. 1030 

4. 960 

Q.8 What is the value of (27x3 + 58x2y + 3lxy2 + 8y3), when x = 5 and y = –7? 

1. 1926 

2. –1924 

3. –1926 

4. 1924 

Q.9 The value of (32)2 + 3 × 3 ÷ 3 – 3 is: 

1. 92 

2. 22 

3. 23 

4. 30 

Q.10 The following bar diagram shows the number of students who opted for the different subjects in the year 2020 and 2021. 

1. 21.18% 

2. 22.34% 

3. 24.31% 

4. 23.14% 

Q.11 If ∆ABC is right angled at B, AB = 12 cm and ∠CAB = 60°, determine the length of BC. 

1. $12\sqrt{3}$ cm 

2. $24\sqrt{3}$ cm 

3. 12 cm 

4. $12\sqrt{2}$ cm 

Q.12 The sides of two similar triangles are in the ratio 5:7. The areas of these triangles are in the ratio: 

1. 25 :49 

2. 36 :49 

3. 35 :49 

4. 15 :49 

Q.13 The chart shows the population of seven districts of National Capital Territory of Delhi. 

If the total population of the seven districts is 150 crore, find the total population of A and D. 

1. 46 Crore 

2. 45 Crore 

3. 42 Crore 

4. 40 Crore 

Q.14 Amit can complete a piece of work in 5 hours; Jeevan and Paul together can complete it in 4 hours, while Amit and Paul together can complete it in 3 hours. Approximately, how many hours will Jeevan alone take to complete the work (rounded off to the nearest integer)? 

1. 8 

2. 5 

3. 9 

4. 6 

Q.15 Two pipes S1 and S2 alone can fill an empty tank in 15 hours and 20 hours respectively. Pipe S3 alone can empty that completely filled tank in 40 hours. Firstly both pipes S1 and S2 are opened and after 2 hour pipe S3 is also opened. In how much time tank will be completely filled after S3 is opened? 

1. 92/11 hours 

2. 90/17 hours 

3. 89/12 hours 

4. 90/13 hours 

Q.16 Three successive discounts of 25% each on the marked price of an item are together equivalent to a single discount (correct up to 2 decimal places) of: 

1. 56.45% 

2. 60.25% 

3. 62.35% 

4. 57.81% 

Q.17 Rice worth ₹126 per kg and ₹135 per kg are mixed with a third variety in the ratio of 1 :1 : 2. If the mixture is worth ₹153 per kg, then the price of the third variety per kg (in ₹) is: 

1. 182.5 

2. 133.5 

3. 175.5 

4. 195.5 

Q.18 A works 5.4 times as fast as B, and A takes 22 days less than B to complete the job when each works alone. Calculate the number of days taken to complete the same job if A and B work together. 

1. $4\frac{5}{32}$ 

2. $4\frac{3}{16}$ 

3. $4\frac{7}{32}$ 

4. $4\frac{1}{4}$ 

Q.19 The perimeter of an isosceles triangle is 100 cm. If the base is 36 cm, then find its semi perimeter (in centimetres). 

1. 64 

2. 45 

3. 60 

4. 50 

Q.20 While baking a cake for 15 people, Jaya used 2.4 kg of flour. How much flour will she need to bake a similar cake for 36 people? 

1. 5.88 kg 

2. 5.76 kg 

3. 6.00 kg 

4. 5.60 kg 

Q.21 Find the value of $\sqrt{\frac{1-\sin 3\theta }{1+\sin 3\theta }}$ . 

1. (sec3θ – tan3θ)2 

2. (sec3θ – tan3θ) 

3. sec3θ – tan3θ 

4. (sec3θ – tan3θ)3 

Q.22 A policeman chasing a thief is 0.5 km behind the thief. The speed of thief is 80% of the speed of the policeman and policeman catches him in 12 minutes. What is the speed of the thief (in km/h)? 

1. 15 

2. 7.5 

3. 10 

4. 12.5 

Q.23 The value of tan 25°tan 35°tan 45° tan 55° tan 65° is: 

1. $\sqrt{3}$ 

2. 2 

3. 0 

4. 1 

Q.24 Simplify : 

$264-\left[ 142-\left\{ 75+\left( 38-\left( \frac{5}{4}+\frac{11}{4} \right) \right) \right\} \right]$ 

1. 230 

2. 231 

3. 234 

4. 232 

Q.25 A person borrowed some money on simple interest. After 4 years, he returned $\frac{9}{5}$ of the money to the lender. What was the rate of interest? 

1. 25% p.a. 

2. 15% p.a. 

3. 10% p.a. 

4. 20% p.a.