31. SSC CGL 2023 

Exam Date 25/07/2023 

Exam Time 2:30 PM - 3:30 PM 

Section : Quantitative Aptitude 

Q.1 The cube of the sum of two given numbers is 1728, while the product of the two given numbers is 32. Find the positive difference between the cubes of the two given numbers. 

1. 512 

2. 448 

3. 576 

4. 480 

Q.2 The cost price of an article is decreased by 10% and then increased by 20%. If the final price is ₹540, then the original cost price is: 

1. ₹550 

2. ₹650 

3. ₹500 

4. ₹600 

Q.3 The value of $\sqrt{\frac{1+\cos \theta }{1-\cos \theta }}$ is : 

1. cosec θ – cot θ 

2. cosec θ + cot θ 

3. sec θ + tan θ 

4. sec θ – tan θ

Q.4 The pie chart below shows the distribution of female employees working in a company in five different districts (A, B, C, D and E).  

Total number of female employees in five districts = 136000 

What is the total number of female employees working in a company in district C and district D? 

1. 61200 

2. 62290 

3. 62000 

4. 61000 

Q.5 A boat running upstream takes 10 hours to cover a certain distance, while it takes 7 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and that of the water current, respectively? 

1. 17 : 5 

2. 17 : 3 

3. 2 : 17 

4. 3 : 17 

Q.6 If $\left( y+\frac{1}{y} \right)=4$, find the value of $\left( {{y}^{6}}+\frac{1}{{{y}^{6}}} \right)$.  

1. 2706 

2. 2702 

3. 4096 

4. 2704 

Q.7 2 men can finish a work in 6 days and 3 women can finish the same work in 4 days. In how many days will the work be finished by 1 man and 2 women, working together every day? 

1. 4 

2. 6 

3. 9 

4. 8 

Q.8 The following table shows the percentage of population of four states below poverty line and the proportion of males and females below and above poverty line.  

If the total population of State B is 7,200, then what is the number of females below poverty line in that state? 

1. 1,125 

2. 1,250 

3. 1,075 

4. 1,025 

Q.9 What is the area of the sector of a circle of radius 8 cm and formed by an arc of length 12 cm? 

1. 48 cm2 

2. 45 cm2 

3. 47 cm2 

4. 84 cm2 

Q.10 The fourth proportional to 8, 32 and 13 is: 

1. 52 

2. 40 

3. 26 

4. 39 

Q.11 100÷10-[-2+{-9+(3-6 of 2)}]= ________. 

1. −6 

2. 0 

3. 20 

4. 30 

Q.12 What is the value of $5\sqrt{3}$ cos60° tan 30° - 3 cos 0° + 3 cos2 45° + 2 sin2 60°?  

1. 3.5 

2. 2.5 

3. $3\sqrt{2}$ 

4. $2\sqrt{3}$ 

Q.13 If ${{\cos }^{2}}\theta =\frac{3}{4}$. where θ is an acute angle, then the value of sin (θ + 30°) is:  

1. $\frac{\sqrt{3}}{2}$ 

2. $\frac{1}{\sqrt{2}}$ 

3. 1 

4. $\frac{1}{2}$ 

Q.14 Simplify the following expression. 

$\frac{{{x}^{2}}-2x-63}{{{x}^{2}}+14x+49}$ 

1. $\frac{x-7}{x+7}$ 

2. $\frac{x-7}{x-7}$ 

3. $\frac{x-9}{x+7}$ 

4. $\frac{x+9}{x+7}$ 

Q.15 The curved surface area of a solid circular cylinder of height 12 cm is 2640 cm2. What is the volume (in cm3) of the cylinder? (Take $\pi =\frac{22}{7}$) 

1. 42000 

2. 46200 

3. 37900 

4. 55200 

Q.16 The difference between a discount of 40% and two successive discounts of 30% on a certain bill was ₹220. Find the amount of the bill (in ₹). 

1. 1100 

2. 2000 

3. 2200 

4. 1000 

Q.17 Rice worth ₹35 per kilogram and ₹38 per kilogram are mixed with a third variety in the ratio 2 : 1 : 2. If the mixture is worth ₹42 per kilogram, the price of the third variety per kilogram is: 

1. ₹52 

2. ₹54 

3. ₹53 

4. ₹51 

Q.18 The rate of simple interest for which ₹9,000 will amount to ₹10,200 in 4 years is: 

1. $7\frac{1}{3}$% 

2. $5\frac{1}{2}$% 

3. $3\frac{1}{3}$% 

4. $4\frac{2}{3}$% 

Q.19 In the first month, the income of Mohan increases by 30%. In the second month his income decreases by 30%. What will be percentage increase or decrease in the income after two months? 

1. 15% increase 

2. 9% increase 

3. 9% decrease 

4. 15% decrease 

Q.20 What is the remainder when (x17 + 1) is divided by (x + 1)? 

1. x – 1 

2. 0 

3. 1 

4. x 

Q.21 A is 50% more efficient then B. B worked to finish the same work in 20 days. If A and B worked together, then how much time will they take to finish the same work? 

1. 9 days 

2. 7 days 

3. 8 days 

4. 10 days 

Q.22 The effective speed of a boat is 15.2 km/h against the stream and 20.8 km/h along the stream. Find the speed of the stream. 

1. 2.8 km/h 

2. 1.8 km/h 

3. 3 km/h 

4. 18 km/h 

Q.23 Two circles touch each other externally. The radius of the first circle with centre O is 6 cm. The radius of the second circle with centre P is 3 cm. Find the length of their common tangent AB. 

1. $6\sqrt{3}$ cm 

2. $6\sqrt{2}$ cm 

3. $4\sqrt{2}$cm 

4. $3\sqrt{2}$ cm

Q.24 A can complete a piece of work in 14 days, while A and B together can complete it in $3\frac{1}{2}%$ days. How long will B alone take to complete it? 

1. $\frac{3}{14}$ days 

2. 4 days 

3. $\frac{14}{3}$ days 

4. 5 days 

Q.25 If r = 15( sin θ + cos θ) and S = 16( sin θ – cos θ), then the value of $\frac{{{r}^{2}}}{{{15}^{2}}}+\frac{{{s}^{2}}}{{{16}^{2}}}$ is .......... 

1. 4 

2. 2 

3. 8 

4. 6