DIRECTIONS for question: Answer the questions independently of each other. (1312-1 p) 1. If the numbers obtained by using all the digits 1, 2, 3, 4, 5 and 6, without repetition, are listed in the increasing order of their magnitude, the 313th number will be

2. Spending र422, Ranjit bought 35 pens from among three varieties of pens - A, B, C. If each pen of varieties A, B, and C costs र10, र8, and र15 respectively, and Ranjit bought the maximum possible pens of variety C, find the total number of pens of varieties A and B that he bought.

(1) 23
(2) 20
(3) 15
(4) 19 (Your Answer: 2)

3. A swimming pool is connected with three pipes to fill it. The times taken by the first, second and third pipes, individually, to fill the pool form an increasing arithmetic progression in that order. If the time taken to fill the pool by the second pipe alone is 10 hours and the time taken by the first and third pipes together to fill the pool is 1.8 hours, then the first and second pipes together can fill the pool in

(1) 21/3 hours
(2) 12/5 hours
(3) 12/3 hours
(4) None of these (Your Answer: 4)

4. If the sum of the 4th and the 20th terms of an arithmetic progression equals the sum of the 6th, 12th and 16th terms, which term of the progression is necessarily zero?

5. Raju covered a distance of 490 km at a constant speed. Had he covered this distance at a speed which was 21 kmph more, he would have taken three hours less for the journey. Find the speed (in kmph) at which he covered the distance.

(1) 49
(2) 70
(3) 87.5
(4) 770 (Your Answer: 1)

6. In the figure below, PQRS is a square. An isosceles triangle is removed from each corner of the square (as shown) so that a rectangle ABCD remains. If diagonal AC measures 24 cm, find the area of the shaded region.