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

Exam Date 04/10/2023 

Exam Time 12:30 PM - 2:30 PM 

Section : Quantitative Aptitude  

Q.1 Find the value of $ \sqrt{\frac{\left(1-\tan\ A\right)}{1+\tan\ A}} $ 

1. $ \sqrt{\frac{\left(1+\sin\ 2\ A\right)}{\cos\ 2\ A}} $ 

2. $ \sqrt{\frac{\left(1-\sin\ 2\ A\right)}{\cos\ 2\ A}} $ 

3. $ \sqrt{\frac{\left(1+\sin\ A\right)}{\cos\ A}} $ 

4. $\sqrt{\frac{\left(1-\sin\ A\right)}{\cos\ A}} $ 

Ans : 2.  

Q.2 If the diameter of a sphere is reduced to its half, then the volume would be:  

1. Increased by 1/4 of the former volume 

2. reduced by 1/4 of the former volume 

3. increased by 1/8of the former volume 

4. reduced by 1/8 of the former volume  

Ans : 4.  

Q.3 The HCF of 3888 and 3969 is:  

1. 81  

2. 73  

3. 83  

4. 71  

Ans : 1. 81  

Q.4 Which is the smallest natural number that is exactly divisible by each of 96, 108 and 144?  

1. 864  

2. 2592  

3. 1296  

4. 1728  

Ans : 1. 864  

Q.5 Find the HCF of 240, 280 and 560.  

1. 30  

2. 10  

3. 20  

4. 40  

Ans : 4. 40  

Q.6 The following table shows the number of mobile phones sold by four different stores in four different years.  

Find the difference between the number of mobile phones sold by store Q in 2013 and store S in 2015.  

1. 12  

2. 7  

3. 10  

4. 8  

Ans : 2. 7  

Q.7 The table below shows the production of jute fabric (in lakh metre) by two Companies P and Q during 2001 to 2005.  

In which year/years, did Company Q produce more fabric than Company P?  

1. 2002  

2. 2005  

3. 2003, 2005  

4. 2002, 2005  

Ans : 4. 2002, 2005  

Q.8 A car, during its entire journey of 5 hours, travels the first 45 minutes at a certain speed, the next 75 minutes at a speed of 85 km/h, and the last 3 hours at a speed of 70 km/h. During its entire journey, the average speed of the car is found to be 73 km/h. What is the speed (in km/h) of the car during the first 45 minutes?  

1. 65  

2. 68  

3. 62  

4. 72  

Ans : 1. 65  

Q.9 Peter invested a certain sum of money in a scheme paying 10% simple interest per annum, while Rachel invested half of the sum that Peter invested in a scheme paying 10% interest per annum compounded annually. Also, while Peter invested for 2 years, Rachel invested for 3 years. If the difference in the interest earned by Peter and Rachel was ₹897, what was the sum that Rachel had invested?  

1. ₹13,000  

2. ₹12,900  

3. ₹13,100  

4. ₹12,960  

Ans : 1. ₹13,000  

Q.10 The price of almonds is increased by 10%. By what percentage should the consumption be decreased so that the expenditure remains the same?  

1.   $ 9\ \frac{1}{11}\% $ 

2. $ 5\ \frac{3}{11}\% $ 

3. $ 8\ \frac{1}{11}\% $ 

4. $ 10\ \frac{3}{11}\% $ 

Ans : 1.  

Q.11 A vendor marked the selling price of a table at ₹5,670 after adding 35% profit to its cost price. Since the sale was very low at this price level, he decided to sell the table with 12% profit. Find the new selling price (in ₹).  

1. 4,810  

2. 4,750  

3. 4,704  

4. 4,608  

Ans : 3. 4,704  

Q.12 The time taken to travel the same distance by three cars is in the ratio of 12:15:10. What is the ratio of the speeds of the three cars?  

1. 4 : 5 : 6 

2. 4 : 6 : 5 

3. 5 : 4 : 6 

4. 5 : 6 : 4 

Ans : 3.  

Q.13 Find the area of a triangle whose length of two sides are 4 cm and 5 cm and the angle between them is 45°.  

1. 4√ 2 cm² 

2. 7√ 2 cm² 

3. 5√ 2 cm² 

4. 6√ 2 cm² 

Ans : 3.  

Q.14 If a shopkeeper allows a discount of 10% to his customers and still gains 30%, then the marked price of an article which costs ₹450 is:  

1. ₹700  

2. ₹650  

3. ₹500  

4. ₹750  

Ans : 2. ₹650  

Q.15 The fourth proportional to 0.3, 0.8 and 0.108 is:  

1. 0.144  

2. 0.124  

3. 0.288  

4. 0.482  

Ans : 3. 0.288  

Q.16 Simplify the given expression.  

$ \frac{(3.254 \times 3.254 \times 3.254)-(0.746 \times 0.746 \times 0.746)}{(3.254 \times 3.254)+(0.746 \times 0.746)+(3.254 \times 0.746)} $ 

1. 3.156  

2. 4.508  

3. 2.146  

4. 2.508  

Ans : 4. 2.508  

Q.17 The price of a land passing through three hands rises on the whole by 65%. The first and second sellers earned 20% and 25% profit, respectively. Find the profit percentage earned by the third seller.  

1. 10% 

2. 20% 

3. 25% 

4. 15% 

Ans : 1.  

Q.18 Study the given table and answer the question that follows. 

Tire table shows the number of people who responded to a survey about their favourite style of music. 

What percentage of the total sample indicated that Rock is their favourite style of music (rounded off to 2 decimal places)? 

1. 27.36%  

2. 18.25%  

3. 29.65%  

4. 22.35%  

Ans : 1. 27.36%  

Q.19 The following table shows the percentage population of four towns below poverty line and the proportion of males and females: 

if the total population of town C is 8000 then what is the number of females above the poverty line in state C? 

1. 2000  

2. 2200  

3. 2400  

4. 2600  

Ans : 3. 2400  

Q.20 The Value of $ \frac{(157 \times 157)+(157 \times 133)+(133 \times 133)}{(157 \times 157 \times 157)-(133 \times 133 \times 133)} $  

1. 1/24 

2. 24 

3. 290 

4. 1/290 

Ans : 1.  

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