QUADRATIC EQUATIONS, PROGRESSIONS & SERIES
1. The product of the roots of the eqn x2 + 2kx + 2a210gk - 1= 0 is 7 then the root of the eqn are real for K=
a) 1 b) -1 c) 2 d) 3
2. If a,b,c are real all a+ b+ c = 0 then the root of the eqn 4ax2 + 3bx + 2c = 0 are
a) Both real b) Both imaginary c) One real & one imaginary d) None
3. If one root of 3x2 + Px + 3 = 0 is square of the other , then P = a) 1/3 b) 1 c) 3 d) 2/3
4. If one root of i x2-2 (1+ i) x + 2-i = 0 is -i, the other root is a) i b) 2 + i c) 2 - i d) -(2 - i )
5. The integral value of m for which the roots of the eqn mx2 + (2m-1 ) x + ( m-2 ) = 0 are rational are
a) n, n e I b) n+ 1 , n e I c) n( n + 1) , neI d) n ( n - 1 ), neI
6. Ifa,b be the root of a(x2 + p2 ) + apx + bp2x2 = 0 then value of a(a2 + b2) + aa b + ba2b2 is
a) p b) -p c) 0 d) 1
7. If teh eqn x2 - bx / ax -c = n-1 / n+1 has roots equale in magnitude but opposite in sign, then n =
a) a +b /a-b b) a-b/ a+b c) b-a /b+a d) b+a /b-a
8. The number of root of 8 Sec2q - 6 Sec q + 1 then a) 0 b) 1 c) 2 d) infinite
9. If the roots of the eqn x2 + px - q = 0 offer by 1 then a) p2 =4q b) p2 = 4q+1 c) p2 = 4q-1 d) None
10. If a, b are the root of the eqn x2-px + 36 = 0 and a2 +b2 = 9, then p =
a) ±3 b) ±6 c) ±8 d) ±9
11. The value of K for which x2-Kx -21 = 0, x2-3kx + 35 =0 have a common root is
a) 4 b) - 4 c) ±2 d) None
12. If the numbers x,y,z are in AP, and tan x,tan y , tan z are also in AP then x, y, z satisfy
a) x + y = z b) x+ z = y c) y + z = x d) x = y = z
13. In an AP Tm = 1/n , Tn = 1/m then Tmn = a) 1/mn b) 1/m + 1/n c) 1 d) 0
14. If m times mth term of an AP equales n times nth term, the (m + n)th term is a) 1 b) m + n c) 0 d) mn
15. Ratio of the sum of n Am’s between two given number a & b are sum of n Am’s between them is
a) n : m b) m : n c) ( m + n) : ( m-n) d) (m-n ) : ( m + n)
16. The sum of three numbers in GP is 14. If the first two numbers are each increased by 1, and the 3rd
term decreased by 1, the regarding number are in AP , then numbers are
a) 1, 2, 4 b) 2, 4, 8 c) 1, 3, 9 d) 2, 6, 18
17. tn be the nth term of a GP. It 100 S n = 1 t2n = x and 100S n = 1 t2n-1 = y such that x ¹ y then
common ratio is a) x/y b) x/y c) y/x d) None
18. The sum of an infiniti Gp is 4 and second term is 3/4 then
a) a = 7/4 , r = 3/ 7 b) a = 2 , r = 3/8 c) a = 3/2 , r = 1/2 d) a = 3, r = 1/4
19. If x = 1 + a + a2 + -----¥, y = 1 + b + b2 + ------¥ then 1 + ab + a2b2 + -----¥
a) xy/x+ y-1 b) x + y/ x-y c) x2 + y2 /x - y d) None
20. HM of two numbers is 4 and their AM ‘A’ and GM ‘G’ satisfy .The relation 2A + G2 = 27 then nos are
a) 6,3 b) 5, 4 c) 5, -5/2 d) -3 , 1
21. If A1, A2 are two GM’s, G1,G2 are two GM’s and H1, H2 are two HM’s between two nos , then

= a) b) c) d)
22. a,b,c are in AP and a2, b2, c2 are in GP. Ita a) 1/2 Ö2 b) 1/2 Ö3 c) 1/2 -1/Ö3 d) 1/2 -1/Ö2
23. The value of n for which is GM between a & b is a) -1/2 b) -1 c) 0 d) 1/2

24. The sum of the int5egen from 1 to 100 which are not divisible by 3 or 5 is
a) 2498 b)4735 c) 2317 d) 2032
25. Sum of the series 12 + 32 + 52 + ------ ¥
a n(n + 1)(n = 1) b) n(2n-1)(2n + 1) c) (n-1)2 (2n + 1) d) (2n + 1)3
2 3 6 3