29. SSC CGL 2023

Exam Date 25/07/2023

Exam Time 9:00 AM - 10:00 AM

Section : Quantitative Aptitude

Q.1 A group of men decided to do a job in 13 days but 9 men left the work after each day. The work, as a result, got completed in 16 days. How many men were initially in the group? 

1. 360 

2. 330 

3. 380 

4. 378 

Q.2 When two circles of radii r1 and r2 have their centres at a distance d apart, then length of the common transverse tangent is: 

1. $\sqrt{d-{{\left( {{r}_{1}}-{{r}_{2}} \right)}^{2}}}$ 

2. $\sqrt{{{d}^{2}}-{{\left( {{r}_{1}}+{{r}_{2}} \right)}^{2}}}$ 

3. $\sqrt{{{d}^{2}}+{{\left( {{r}_{1}}-{{r}_{2}} \right)}^{2}}}$ 

4. $\sqrt{{{d}^{2}}-{{\left( {{r}_{1}}-{{r}_{2}} \right)}^{2}}}$ 

Q.3 In a division sum, the divisor is 13 times the quotient and 6 times the remainder. If the remainder is 39, then the dividend is: 

1. 4576 

2. 4800 

3. 4251 

4. 4240 

Q.4 A metallic cube has each of its side of length 12 cm. It is melted and recast into three small cubes. Out of these cubes, two have their sides as 6 cm and 8 cm, respectively. The length of each side of the third cube is: 

1. 5 cm 

2. 9 cm 

3. 7 cm 

4. 10 cm 

Q.5 If tan α = 6, then sec α equals to: 

1. $\sqrt{35}$ 

2. $\sqrt{37}$ 

3. $\sqrt{5}$ 

4. $\sqrt{7}$ 

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

1. 5778 

2. 5776 

3. 5774 

4. 4096 

Q.7 The following bar graph shows the sales of books (in thousands) from six branches of a publishing company during two consecutive years 2018 and 2019. 

1. 68.25% 

2. 65.29% 

3. 73.17% 

4. 62.23% 

Q.8 Study the given graph carefully and answer the question that follows. 

The imports in 1977 were approximately how many times that of the year 1976? 

1. 1.11 

2. 1.22 

3. 1.33 

4. 1.44

Q.9 A policeman starts chasing a thief when he was already 600 m ahead. If the policeman is running at a speed of 9 km/h and the thief at 8 km/h, then the thief would be caught at a distance of: 

1. 6.5 km 

2. 6 km 

3. 5 km 

4. 5.4 km 

Q.10 A shopkeeper bought certain number of apples for Rs.3,600. He sold one-fifth of them at a loss of 10%, one-fourth of the remaining apples at a loss of 5%, and two-third of the rest at a profit of 15%. At what price (in Rs.) should he sell the remaining apples to earn a profit of 27% overall? 

1. 1,864 

2. 1,845 

3. 1,548 

4. 1,584 

Q.11 Out of the total toffees, $\frac{1}{10}$ are wasted. 35% of the rest are given to S and $\frac{1}{8}$ of the total are given to N. If the toffees with N are 10 more than the wasted toffees, then how many toffees were given to S? 

1. 150 

2. 135 

3. 110 

4. 126 

Q.12 Raju and Rajat working together take 5 days to complete a piece of work. If Raju alone can do this work in 7 days, how long would Rajat take to complete the same work? 

1. 18 days 

2. 17 days 

3. 16.5 days 

4. 17.5 days 

Q.13 Find the remainder when 88 + 6 is divided by 7. 

1. 2 

2. 3 

3. 1 

4. 0 

Q.14 What value of 'y' will satisfy the following equation? 

$\frac{3y}{1+\frac{1}{1+\frac{y}{1-y}}}=2$ 

1. $\frac{2}{3}$ 

2. $\frac{3}{2}$ 

3. $\frac{4}{5}$ 

4. $\frac{5}{4}$ 

Q.15 Using $\cos ec\left( \alpha +\beta  \right)=\frac{\sec \beta \times \cos ec\alpha \times \cos ec\beta }{\sec \alpha \times \cos ec\beta +\cos ec\alpha \times \sec \beta }$, find the value of cosec75°. 

1. $\sqrt{6}+\sqrt{2}$ 

2. $\frac{\sqrt{6}+\sqrt{2}}{4}$ 

3. $\frac{\sqrt{6}-\sqrt{2}}{4}$ 

4. $\sqrt{6}-\sqrt{2}$ 

Q.16 A field is 150 m long and 80 wide. How many times (rounded off to 1 decimal place) is its perimeter to the length of its diagonal? 

1. 3.1 

2. 2.7 

3. 2.3 

4. 2.5 

Q.17 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 25 women complete it? 

1. 20 

2. 25 

3. 18 

4. 16 

Q.18 Ram has an average score of 65 runs in 19 innings in cricket matches. Find out how many runs are to be scored by him in the 20th innings to raise the average score to 67. 

1. 135 

2. 105 

3. 115 

4. 195 

Q.19 A thief seeing a policeman from a distance of 400 m started running at a speed of 16 km/h. The policeman chased him immediately with a speed of 18 km/h and the thief was caught. What is the distance run by the thief before he was caught by the policeman? 

1. 3220 m 

2. 3230 m 

3. 3200 m 

4. 3240 m 

Q.20 The simple interest on a certain sum at the rate of 12.5% per annum for 6 years is ₹13,500 less than the principal. Find the simple interest. 

1. ₹40,500 

2. ₹54,000 

3. ₹13,500 

4. ₹40,000 

Q.21 In the following figure. there are two circles that touch each other externally. The radius of the first circle with centre P is 25 cm. The radius of the second circle with centre Q is 4 cm. Find the length of their direct common tangent AB. 

1. 20 cm 

2. 21 cm 

3. 18 cm 

4. 22 cm 

Q.22 Applied to a bill for ₹50,000, the difference between a discount of 40% and two successive discounts of 36% and 4%,is : 

1. ₹1,440 

2. ₹875 

3. ₹720 

4. ₹1,250 

Q.23 If x2 – 15x + 1 = 0, what is the value of x4 – 223x2 + 6? 

1. 0 

2. 9 

3. 5 

4. 6 

Q.24 If cot A = 1, sin B = $\frac{1}{\sqrt{2}}$, then find the value of sin(A + B) – cot(A + B). 

1. $\frac{1}{2}$ 

2. 0 

3. 1 

4. $1-\sqrt{2}$ 

Q.25 The following formula is used to calculate which of the following? 

$\frac{\text{Angle of are at centre}}{\text{360 }\!\!{}^\text{o}\!\!\text{ }}\text{ }\!\!\times\!\!\text{  }\!\!\pi\!\!\text{  }\!\!\times\!\!\text{ diameter}$ 

1. Area of an arc 

2. Radius of a circle 

3. Length of a sector 

4. Length of an arc