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
