**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