Q1. The radii of two circle are 5 cm and 3 cm, the distance between their  center is 24 cm . then the length  of the transverse common tangent  is 

(a) 16 cm

(b) 15 √2 cm

(c) 16 √2 cm

(d) 15cm

Q2. D is a point on the side BC of a triangle ABC such that AD ⊥ BC, E is a point on AD for which AE : ED = 5 : 1. If  ∠BAD =  30° and tan ∠ACB = 6 tan ∠ DBE , then ∠ACB = 

(a) 30°

(b) 45°

(c) 60°

(d) 15°

Q3.  The greatest number of four digits which when divided by 12, 16, and 24 leave remainders 2, 6 and 14 respectively is :

(a) 9974

(b) 9970

(c) 9807

(d) 9998

Q4. 40 litres of a mixture of milk and 8, water contains 10% of water, the water to be added, to make the water content 20% in the new mixture is :

(a) 6 litres

(b) 6.5 litres

(c) 5.5 litres

(d) 5 litres

Q5. A started a business by investing Rs. 36,000. After 4 month B joined him with some investment. At the end of the year, the total profit was divided between then in the ratio of 9 : 7 How much capital was invested by B in the business? 

(a) Rs. 40,000

(b) Rs. 42,000

(c) Rs. 41,000

(d) None of these

Q6. Two pipes A and B can fill a cistern in 74/2 minutes and 45 minutes respectively. Both pipes are opened the cistern will be filled just in half an hour if the pipe B is turned off after 

(a) 15 minutes

(b) 10 minutes

(c) 5 minutes

(d) 9 minutes

Q7.

(a) 1

(b) -1

(c) 2

(d) 0

Q8.

(a) 30°

(b) 90°

(c) 45°

(d) 60°

Q9.

(a) 1

(b) 2

(c) 3

(d) 4

Q10.

(a) 8

(b) 16

(c) 2√15

(d) 2(√5+√3)

Q11. A train travelling at a speed of 55 km/hr travels from place X to place Y in 4 hours. If its speed in increased by 5 km/hr., then the time of journey is reduced by 

(a) 25 minutes

(b) 35 minutes

(c) 20 minutes

(d) 30 minutes

Q12. A train starts from A at 7 a.m. towards B with speed 50 km/h. Another train starts from B at 8 a.m. with speed 60 km/h towards A. Both of them meet at 10 a.m. at C, The ratio of the distance AC to BC is  

(a) 5: 6

(b) 5:4

(c) 6: 5

(d) 4: 5

Q13.

(a) 4

(b) 6

(c) 9

(d) 10

Q14.

(a) 2

(b) 1

(c) – 1

(d) -2

Q15. A sum of money was lent at simple interest at certain rate for 3 years, Had it been lent at 2.5% per annum higher rate, it would have fetched Rs. 540 more. The money lent was: 

(a) Rs. 6400

(b) Rs. 6472

(c) Rs. 6840

(d) Rs. 7200

1. c 2. c 3. a 4. d 5. b 6. d 7. a 8. a 9. d 10. a 11. c 12. b 13. d 14. b 15. d