Engineering

20 Questions

20 Minutes

RRB

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1. What is the maximum value of the sum of the given AP series? 30, 27, 24, 21 ........

2. If the roots of the equations ax2 + 2bx + c = 0 and bx2 - 2 x + b = 0 are real, then

3. If y = x - x2 + x3 - x4 + ....... ( 1/2 < x < 1 ), then

4. If the sides of a triangle are in A.P and the greatest angle of the triangle is double the smallest angle, the ratio of the sides of the triangle is

5. If log (a + c), log (c - a) and log ( a - 2b + c) are in A.P, then

6. The coefficient of x ^{99} in the expansion of (x - 1) (x - 2) (x - 100).......... is

7. The sum of the integers lying between 1 and 100, which are divisible by either 3 or 7, is

8. The number of divisors of 3087, 1547 and 122 are in

9. Five numbers a, b, c, d and e are such that a, b, and c are in A.P; b, c and d are in G.P and c, d and e are in H.P. If a = 2 and e = 18; then the values of b, c and d are

10. If a, b, c and d are in G.P, then (a - c)2 + (c - b)2 + ( b - d )2 - ( d - a )2 is

11. If 1, log3 (3^{x} - 2), 2 log 9 (3^{x}- 8/3 ) are in A.P, then the value of x can be

12. If in an A.P, Sn = n^{2}p and Sm = m^{2}p, where Sr denotes the sum of 'r' terms of the A.P, then Sp is equal to

13. If the sum of the G.P. p, 1, 1/p, 1/p2 ...... is 9/2, then the value of p is

14. a, b, c are distinct positive real numbers, which are in G.P. If a + x, b + x, c + x are in H.P, then the value of x is

15. Let s (n) = sum of all the divisors of the natural number n. Then s (2^{9}.3^{2}) is not divisible by

16. What will be the sum of n common terms of two sequences <2, 13, 24 .....> and <3, 10, 17, 24 .....>?

17. The largest value of the positive integer m for which n^{m} + 1 divides 1 + n + n^{2} + _________ + n^{127}, is

18. If log x a, a^{x/2 } and log b x are in G.P, then x is equal to

19. Sum upto n terms of the series 1 / 1.3 + 2 / 1.3.5 + 3 / 1.3.5.7 + ........ is

20. The sum upto n terms of the series 1 + 2(1 + 2/n) + 3 (1 + 2/n)^{2} + 4 (1 + 2/n)^{23} + ......... is