Q1. A tyre has 2 punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat?
Q2. A and B together can do a piece of work in 12 days which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days. C finishes it in 13 days. In how many days B could finish the work?
(a) 48 days
(b) 24 days
(c) 16 days
(d) 12 days
Q3. Three circles of radius a, b, c touch each other externally. The area of the triangle formed by joining their centres is
Q4. If a metallic cone of radius 30 cm and height 45 cm is melted and recast into inetallic spheres of radius 5 cm, find the number of spheres.
Q5. Chords AB and CD of a circle intersect at E and are perpendicular to each other. Segments AE, EB and ED are of lengths 2 cm, 6 cm and 3 cm respectively. Then the length of the diameter of the circle in cm is
Q6. For every set of 19 kites sold, a vendor gives 1 kite extra, free of cost. In order to give a discount of 10%, the number of extra kites he should give in a sale of 27 kites to the nearest integer is
Q7. A ruby stone was bought for Rs. 1600 at Jaipur. A sum of Rs. 2400 was spent on making a ring with the ruby stone. It was advertised for sale at Bombay for Rs. 7800. If a discount of 10% was given, then the % profit made was
Q8. The area of a circle is proportional to the square of its radius. A small circle of radius 3 cm is drawn within a larger circle of radius 5 cm. Find the ratio of the area of the annular zone to the area of the larger circle. (Area of the annular zone is the difference between the area of the larger circle and that of the smaller circle).
(a) 9 : 16
(b) 9 : 25
(c) 16 : 25
(d) 16 : 27
Q9. The average age of Ram and his two children is 17 years and the average age of Ram’s wife and the same children is 16 years. If the age of Ram is 33 years, the age of his wife is (in years):
Q10. One side of a square is increased by 30%. To maintain the same area, the other side will have to be decreased by
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