**Find solutions for all the questions at the end of each set:**

### Set A

1. If the number 72a47b is completely divisible by 45 but not by 10, then find ‘a’?

(a) 3

(b) 2

(c) 5

(d) 0

2. The value of -12 + 22 – 32 +42 – 52………………+2002 is

(a) 20100 (b) 12010

(c) 24010 (d) None of these

3. The compound interest on a certain sum for 2 years is Rs.1100 and the simple interest is Rs.1000. If this sum is invested such that the simple interest is Rs.400 and the number of years is equal to rate percent per annum, find the new rate percent.

(a) 10% (b) 20 %

(c) 4 % (d) 5%

4. The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is—

(a) 1 (b) 2

(c) 3 (d) None of these

5. The percentage increases of population for three consecutive years in a country are 10%, 25% and 10% respectively. What is the total percentage increase for the three years?

(a) 51.25 % (b) 25 .25%

(c) 30.25% (d) 61%

6. If sec(7θ+28°)=cosec(30°-3θ), then find θ?

(a) 8° (b) 5°

(c) 6° (d) 9°

7. Find the value of cos 240 + cos550 + cos1250 + cos1560

(a) 0 (b) 2

(c) 3 (d) 1

8. Find the value of (sin5 + cos85)/ (sin5 – cos85)

(a) 1 (b) 0

(c) ∞ (d) None of these

9. A copper wire is bent in the form of an equilateral triangle and has area 121Ö3 cm2 if the same wire is bent into the form of a circle, the area ( in cm2) enclosed by the wire is ( Take )

(a) 364.5 (b) 693.5

(c) 346.5 (d) 639.5

10. A road which is 7 m wide surrounds a circular track whose circumference is 352 m. Find the area of the road.

(a) 2618 m2 (b) 2520m2

(c) 2025m2 (d) None of these

ANSWER KEY:

1. B

2. A

3. C

4. B

5. A

6. A

7. A

8. C

9. C

10.A

**Find solutions for all the questions at the end of each set:**

### Set B

1. The least positive integer that should be added to 875321 × 875319 so that the product is a perfect square is:

(a) 1

(b) 875321

(c) 875319

(d) 4

2. Two pipe M and N can fill a tank in 8 (1/3) min and 12 (1/2) min respectively and an outlet pipe can drain 162 litre water in 1 minute. If tank is full, all the three pipes are opened then tank will be empty in 4 minute then capacity of tank will be –

(a) 916 litre

(b) 300 litre

(c) 360 litre

(d) None of these

3. A reduction of 20% in the price of sugar enables Mr. Bhadra to buy an extra 5 kg of it for Rs. 320. The original rate of sugar was:

(a) Rs. 12 per kg

(b) Rs. 15 per kg

(c) Rs. 16 per kg

(d) Rs. 20 per kg

4. In a particular type of alloy the ratio of lead to tin is 5 : 6. Find the amount of lead should be added to 12.1 kg of this material to make the ratio 1 : 1.

(a) 1.1 kg

(b) 1 kg

(c) 0.9 kg

(d) 1.5 kg

5. A person sells his T.V. at 25% profit of the cost price. If he sells his T.V. at 25% of the selling price then his profit is increased by (5% of C.P. + Rs. 80) find the cost price of T.V.

(a) Rs. 6400

(b) Rs. 8000

(c) Rs.6320

(d) Rs.7500

6. A man walks from M at 7: 00 A.M. and reaches at N at 10:00 A.M. The another walks from N at 7:00 A.M. and reaches at M at 01:00 PM. Then at what time they meet together?

(a) 9: 20 AM

(b) 9:40 AM

(c) 9:00 AM

(d) None of these

7. A man borrows Rs. 3000 at 10% compound rate of interest. At the end of each year he pays back Rs. 1000. How much amount should he pay at the end of the third year to clear all his dues?

(a) Rs. 1530

(b) Rs.1683

(c) Rs.1663

(d) Rs.1563

8. In a zoo, there are rabbits and pigeons. If heads are counted there are 200 and if legs are counted, there are 580. How many pigeons are there?

(a) 90

(b) 110

(c) 120

(d) 80

9. A cubic metre of copper weighing 9002 kilogram is rolled into a square bar 9 metres long. An exact cube is cut off from the bar. How much does it weight?

(a) 334 kg

(b) 336 kg

(c) 313.3 kg

(d) Data insufficient

10. A man sets out to cycle from Delhi to Rohtak and at the same time another man starts from Rohtak to Delhi. After passing each other, they complete their journey in 4 hours and 9 hours respectively. At what speed does the second man cycle if the first cycle at 18 km per hour?

(a) 12 km/hr

(b) 9 km/hr

(c) 27 km/hr

(d) 15 km/hr

ANSWERS KEY:

1- (a)

(875321*875319+a) is a perfect square

so,

(875320+1)(875320-1)+a =(875320)^2-1+a

so, a-1 = 0 => a = 1

2- (c)

3- (c)

New rate of sugar = 320*20/100*1/5 = Rs. 64/5

so, original rate of sugar = Rs.(64/5 * 5/4) = 16 per kg.

4- (a)

Lead : Tin

5 : 6 = 1

so, make the ratio into 1 : 1

lead should be added = 1/11

so, lead should added = 1/11*12.1 = 1.1 kg

5- (a)

let cost price = Rs. x

selling price = 5/4x

A.T.Q

(1/4x)+(1/20X)+80 = (5/4x)*1/4

x = 6400

Cost price = Rs. 6400

6- (c)

7- (b)

8- (b)

9- (a)

10- (a)

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