Sub Inspector in Delhi Police and Central Armed Police Forces Examination 2023 Paper I 

Exam Date 04/10/2023 

Exam Time 4:00 PM - 6:00 PM 

Section : Quantitative Aptitude  

Q.1 Two mixtures A and B have the following compositions:  

Mixture A has copper and tin in a ratio of 1:2  

Mixture B has copper and tin in a ratio of 1:3  

If equal quantities of mixtures A and B are used for producing mixture C, then find the ratio of copper and tin in mixture C.  

1. 2 : 5 

2. 1 : 5 

3. 7 : 17 

4.  7 : 12 

Ans : 3.  

Q.2 If the volume of a sphere is 38808 cm³, then its surface area is:  

1. 5554 cm²  

2. 5574 cm²  

3. 5564 cm²  

4. 5544 cm²  

Ans : 4. 5544 cm2  

Q.3 The area of a rhombus having one side measuring 17 cm and one diagonal measuring 16 cm is:  

1. 280 cm²  

2. 180 cm²  

3. 240 cm²  

4. 210 cm²  

Ans : 3. 240 cm2  

Q.4 By selling 42 m of cloth, Vijay gains the selling price of 7 m of cloth. Find the profit percentage.  

1. 15%  

2. 30%  

3. 20%  

4. 25%  

Ans : 3. 20%  

Q.5 Ramesh gives fifteen per cent additional discount along with a discount of 25% on the marked price of a sofa set. If the selling price of the sofa set is ₹12,750, then find the marked price of the sofa set.  

1. ₹20,000  

2. ₹23,000  

3. ₹22,000  

4. ₹24,000  

Ans : 1. ₹20,000  

Q.6 Two pipes can fill a cistern in 12 hours and 16 hours, respectively. The pipes are opened simultaneously and it is found that due to leakage at the bottom, it takes 90 minutes more to fill the cistern. How much time will the leakage take to empty the completely filled tank?  

1. $ \ 36\ \frac{29}{49} $ 

2. $ \ 38\ \frac{10}{49} $ 

3. $ \ 39\ \frac{13}{49} $ 

4. $ \ 37\ \frac{15}{49} $ 

Ans : 2.  

Q.7 A sum of money amounts to ₹1,200 in 2 years and becomes ₹1,260 in 3 years at compound interest, when interest is compounded annually. What is the rate of compound interest per annum?  

1. 5%  

2. 3%  

3. 4%  

4. 6%  

Ans : 1. 5%  

Q.8 Find the least value of 16cosec²2θ + 25sin²θ.  

1. 40  

2. 42  

3. 35  

4. 38  

Ans : 1. 40  

Q.9 In a megastore. the following data reveals the units purchased during the years. 

What is the percentage growth in total units purchased (of all the three products) from 2015 to 2020? 

1. 21.68 percent  

2. 22.75 percent  

3. 26.23 percent  

4. 25.76 percent  

Ans : 3. 26.23 percent  

Q.10 If cos A = 1/11, then find the value of cot A.  

1. $ \frac{2\sqrt{30}}{11}$ 

2. $ 2\sqrt{30} $ 

3. $ \frac{1}{2\sqrt{30}} $ 

4. $ \frac{11}{2\sqrt{30}} $ 

Ans : 3.  

Q.11 The following bar graph shows the milk production (in million tons) details for 4 years for three brands (P, Q, R): 

What was the average production of milk (in million tons) per year over the period of 4 years? 

1. 90  

2. 50  

3. 30  

4. 70  

Ans : 1. 90  

Q.12 If cosec A + cot A = 3, 0 ≤ A ≤ 90° , then find the value of cos A.  

1. 3/4 

2. 2/5 

3. 3/5 

4. 4/5 

Ans : 4.  

Q.13 36 equally efficient workers can paint 25 identical walls in 48 days. In how many days can 45 such workers paint 60 such walls?  

1. 92.36  

2. 92.16  

3. 91.96  

4. 91.16  

Ans : 2. 92.16  

Q.14 Which of the following numbers leaves the remainder equal to the highest common factor of 6, 8 and 9, when divided by 6, 8 and 9?  

1. 291  

2. 575  

3. 506  

4. 433  

Ans : 4. 433  

Q.15 Simplify the given expression.  

$ \left(1+x\right)^3+\left(1-x\right)^3\ +\ \left(-2\right)^3\ $ 

1. 6(1-x²)  

2. - 3(1-x²)  

3. - 6(1-x²)  

4. 3(1-x²)  

Ans : 3. - 6(1-x2)  

Q.16 if $ 1\ \frac{1}{3}\ \div\frac{2}{5}\times\frac{x}{5}\ =\ 1\ \frac{1}{4}\times\frac{2}{3}\div\frac{1}{6} $ , then the value of x is : 

1. 5.5  

2. 7.5  

3. 7.0  

4. 15  

Ans : 2. 7.5  

Q.17 The average weight of 49 students is 53 kg. When a new student is admitted to the class, the average decreases by 500 g. Find the weight of the new student.  

1. 48 kg  

2. 18 kg  

3. 28 kg  

4. 38 kg  

Ans : 3. 28 kg  

Q.18 In an election between two candidates, the difference between the candidates who won and lost was 2,500 votes. The candidate who won got 75% of the votes, and there were no invalid votes. The total number of votes polled of the losing candidate was:  

1. 1875  

2. 5000  

3. 1250  

4. 3750  

Ans : 3. 1250  

Q.19 In an election between two candidates,30% of the electorate did not cast their votes. 20% of the votes polled were found invalid. The winning candidate got 64% of the valid votes and won by a majority of 3136 votes. Find the number of voters enrolled in the voter list.  

1. 20000  

2. 25000  

3. 24000  

4. 30000  

Ans : 1. 20000  

Q.20 Find the mean proportion of x³y and xy³.  

1. x²y²  

2. x³y³  

3. xy  

4. x4y4  

Ans : 1. x2y2  

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