Wow qns

QUADRATIC EQUATION
**SINGLE OPTION CORRECT :-
Q.1 The set of values of parameter m for which the equation (m2 – 1)x2 – (m + 2)x + 1 = 0 has exactly one of its
roots lying in ] – 1, 1 [ , is
(A) (– 1, 2] (B) (– 1, 1)  (1, 2) (C) (– 1, 2) (D) [– 1, 2]

Q.2 A monic quadratic trinomial P(x) is such that P(x) = 0 and PPP( x ) = 0 have a common root, then
(A) P(0) · P(1) > 0 (B) P(0) · P(1) < 0 (C) P(0) · P(1) = 0 (D) none
Q.3 Let  are the roots of the cubic equation a0x3 +3a1x2 + 3a2x + a3 = 0 (a0 0).
Then the value of ( – )2 + ( – )2 + ( – )2 equals
18(a 22  a 0 a1 ) 18(a 22  a 0a1 ) 18(a 02  a1a 2 ) 18(a12  a 0a 2 )
(A) (B) (C) (D)
a 02 a 02 a 02 a 02

Q.4 Let k1, k2 (k1 < k2) be two values of k for which the expression x2 – y2 + kx + 1 can be factorised into
two real linear factors, then (k2 – k1) is equal to
(A) 2 (B) – 2 (C) 0 (D) 4
Q.5 If all the roots (zeros) of the polynomial f(x) = x5 + ax4 + bx3 + cx2 + dx – 420 are integers larger than 1, then
f(4) equals
(A) 0 (B) –6 (C) 12 (D) –12
x 2  3x  c 1
Q.6 If maximum and minimum values of y = 2 are 7 and respectively then c is equal to
x  3x  c 7
(A) 3 (B) 4 (C) 5 (D) 6
Q.7 The set of real value(s) of p for which the equation, 2x + 3 + 2x  3 = px + 6 has more than two
solutions is :
(A) (0, 4] (B) ( 4, 4) (C) R  {4, - 4, 0} (D) {0}
Q.8 If x2 + Px + 1 is a factor of the expression ax3 + bx + c then
(A) a2 + c2 = – ab (B) a2 – c2 = – ab (C) a2 – c2 = ab (D) none of these
Q.9 The number of solutions to the system of equations :- y2 – xy – | x | y + x | x | = 0 and x2 + y2 = 1 is
(A) 1 (B) 2 (C) 3 (D) 4
Q.10 Number of integral values of parameter 'c' for which the inequality
 2 7
1 + log2  2 x  2 x   > log2(cx2 + c), holds good  x  R, is
 2
(A) 0 (B) 2 (C) 7 (D) infinite

Q.11 Number of real values of x satisfying the equation :- x 2  6 x  9 + x 2  6 x  6 = 1 is
(A) 0 (B) 1 (C) 2 (D) more than 2
Q.12 If roots of equation x3 – px2 – r = 0 are tan , tan  and tan  then value of sec2 · sec2 · sec2 is
(A) p2 + r2 + 2rp + 1 (B) p2 + r2 – 2rp + 1 (C) p2 – r2 – 2rp + 1 (D) None
Q.13 Let f (x) = x2 + ax + b. Maximum and the minimum values of f (x) are 3 and 2 respectively for 0  x  2;
then the possible ordered pair(s) of (a, b) is/are
(A) (–2, 3) (B) (– 3/2, 2) (C) (– 5/2, 3) (D) (– 5/2, 2)



Prepared by Gaurav Sir