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

Exam Date 04/10/2023 

Exam Time 9:00 AM - 11:00 AM 

Section : Quantitative Aptitude  

Q.1 The total surface area of a square-based right pyramid is 1536 m2, of which 37.5% is the area of the base of the pyramid. What is the volume (in m3) of this pyramid?  

1. 3048  

2. 3072  

3. 3144  

4. 3108  

Ans : 2. 3072  

Q.2 If sin A+ sin^2 A = 1$ \sin A+\sin^2A=1$ , then the value of $ \cos^4A+\cos^6A $ is:  

1. cos A  

2. sin A  

3. 1  

4. 0  

Ans : 2. sin A  

Q.3 The radius of a circle is 1.75 cm. What is the circumference of the circle?  

1. 5.5 cm  

2. 11 cm  

3. 9.63 cm  

4. 22 cm  

Ans : 2. 11 cm  

Q.4 Let the HCF of m and n be ‘a’ and let n = ab, LCM of m and n is given by:  

1. bm  

2. am  

3. ab  

4. mn  

Ans : 1. bm  

Q.5 Study the given pie-chart and answer the question that follows. 

The pie-chart shows the number of students (boys and girls) studying in standard 10 of various schools (X. Y, Z in the year 2022). 

What is the difference between the total number of students (boys and girls) in school Y and Z together and the total number of students (boys and girls) in school X and Y together"? 

1. 720  

2. 840  

3. 780  

4. 820  

Ans : 1. 720  

Q.6 The radius of the base of a right circular cone is 5 cm. Its slant height is 13 cm. What is its volume (in $cm^3$, rounded off to 1 decimal place)? (Take $\pi\ =\frac{22}{7}$)  

1. 328.6  

2. 323.4  

3. 314.3  

4. 340.5  

Ans : 3. 314.3  

Q.7 A sum of money was invested at 10% interest per year, compounded half-yearly, for 18 months. If the amount payable on maturity was ₹64,827, what was the sum invested?  

1. ₹55,600  

2. ₹56,000  

3. ₹56,800  

4. ₹56,500  

Ans : 2. ₹56,000  

Q.8 Let C be a circle with centre O and radius 5 cm. Let PQ be a tangent to the circle and A be the point of tangency. Let B be a point on PQ such that the length of AB is 12 cm. If the line joining O and B intersects the circle at R, find the length of BR (in cm).  

1. 2  

2. 13  

3. 6  

4. 8  

Ans : 4. 8  

Q.9 The Value of $ 1 \frac{2}{5}-\left[3 \frac{3}{4} \div\left\{1 \frac{1}{4} \div \frac{1}{2}\left(1 \frac{1}{2} \times 3 \frac{1}{3} \div 1 \frac{1}{3}\right)\right\}\right] $ is :  

1. 3  

2. 0  

3. 2  

4. 1  

Ans : 4. 1  

Q.10 When A alone does a piece of work, he takes 25 days more than the time taken by A and B to do the work together. On the other hand, B alone takes 16 days more than the time taken by A and B to do the work together. How many days will A and B, working together, take to do the work?  

1. 24  

2. 20  

3. 23  

4. 22  

Ans : 2. 20  

Q.11 In what proportion should a grocer mix wheat at ₹12 per kg and ₹25 per kg so as to make a mixture of worth ₹20 per kg?  

1. 8 : 3 

2.  3 : 5 

3. 5 : 8 

4. 5 : 7 

Ans : 3.  

Q.12 Find the mean proportional between 32 and 162.  

1. 99  

2. 65  

3. 72  

4. 97  

Ans : 3. 72  

Q.13 Rakhi purchased a basket, a wallet and a belt. She got discounts of 5%, 8% and 10% on the basket, the wallet and the belt, respectively, on their respective marked prices of ₹80, ₹150 and ₹350. How much amount (in ₹) did she pay in total?  

1. 529  

2. 51  

3. 580  

4. 519  

Ans : 1. 529  

Q.14 In ΔABC, ∠B = 90° and AB : BC = 1 : 2. The value of cos A + tan C is:  

1.  $ \frac{\left(5+\sqrt{5}\right)}{2\sqrt{5}} $ 

2.  $ \frac{\left(1+\sqrt{5}\right)}{2\sqrt{5}} $ 

3. $ \frac{\left(2\sqrt{5}\right)}{2+\sqrt{5}} $ 

4. $ \frac{\left(2\sqrt{5}\right)}{2\sqrt{5}} $ 

Ans : 4.  

Q.15 The product of two numbers is 20000. If their LCM is 800, then what is their HCF?  

1. 25  

2. 30  

3. 35  

4. 20  

Ans : 1. 25  

Q.16 If $ a\ +\frac{1}{a} $ , then the value of $ a^{4\ }+\frac{1}{a^4}\ $ is  

1. 48  

2. 81  

3. 27  

4. 47  

Ans : 4. 47  

Q.17 Study the given graph and answer the question that follows. 

The given graph represents the percentage of books on different subjects that a person has in his library. 

If the total number of books is 60, then what is the ratio of the number of books on subject C 1 to the average number of books per subject? 

1. 3 : 7  

2. 2 : 3  

3. 3 : 5  

4. 2 : 5  

Ans : 4. 2 : 5  

Q.18 Find the value of $ \frac{\cos 37^{\circ}}{\sin 53^{\circ}}-\cos 47^{\circ} \operatorname{cosec} 43^{\circ} $  

1. 0  

2. −1  

3. 2  

4. 1  

Ans : 1. 0  

Q.19 The volume of a sphere is given by 130977 cm ³. Its surface area (in cm ²) is:  

1. 16847  

2. 12474  

3. 17424  

4. 14274  

Ans : 2. 12474  

Q.20 The speed of a boat in standing water is 6 km/h and the speed of the stream is 2.5 km/h. A man rows to a place at a distance of 59.5 kilometres and comes back to the starting point. The total time taken by him is:  

1. 16 hours  

2. 24 hours  

3. 22 hours  

4. 18 hours  

Ans : 2. 24 hours  

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