MCQ (Previous Year Questions) - Complex Numbers (Competition Level 2) - JEE MCQ

The set of all real numbers x for which x² – |x + 2| + x > 0, is       [JEE 2002 (Scr.), 3]

If x² + (a – b)x + (1 – a – b) = 0 where a, b ∈ R then find the values of `a' for which equation has unequal real roots for all values of `b'.                 [JEE 2003 (Mains), 4]

 (a) If one root of the equation x² + px + q = 0 is the square of the other, then       [JEE 2004 (Scr.)]

(A) p³+q²–q(3p+1)=0 (B) p³+q² + q(1+3p)=0 (C) p³+q²+q(3p_1)=0 (D) p³+q²+q(1–3p)=0

(b) If x² + 2ax + 10 _ 3a > 0 for all x Î R, then

(A) –5 < a < 2 (B) a < –5 (C) a > 5 (D) 2 < a < 5

If |z1| = 4, |z2| = 4, then |z1 + z2 + 3 + 4i| is less than​

 (a) Let a, b, c be the sides of a triangle. No two of them are equal and λ ∈ R. If the roots of the equation x² + 2(a + b + c)x + 3λ(ab + bc + ca) = 0 are real, then                   [JEE 2006, 3 + 6]

(A) l <  (B) l >  (C) l <  (D) l < 

(b) If roots of the equation x² –10cx –11d = 0 are a, b and those of x² – 10ax – 11b = 0 are c, d, then find the values of a + b + c + d. (a, b, c and d are distinct numbers)

(a) Let a, b be the roots of the equation

x² – px + r = 0 and a/2, 2b be the roots of the equation x² – qx + r = 0. Then the value of `r' is

   [JEE 2007, 3 + 6]

(A) (p – q)(2q – p) (B) (q – p)(2p – q) (C) (q – 2p)(2q – p) (D) (2p – q)(2q – p)

(b) Let f(x) = 

Match the expressions / statements in Column I with expressions / statements in Column II.

Column–I Column–II

(A) If –1 < x < 1, then f(x) satisfies (P) 0 < f(x) < 1

(B) If 1 < x < 2, the f(x) satisfies (Q) f(x) < 0

(C) If 3 < x < 5, then f(x) satisfies (R) f(x) > 0

(D) If x > 5, then f(x) satisfies (S) f(x) < 1

 Let a, b, c, p, q be real numbers. Suppose a, b are the roots of the equation x² + 2px + q = 0 and a, 1/b are the roots of the equation ax² + 2bx + c = 0, where b² Ï {_1, 0, 1} [JEE 2008, 3]

statement–1 : (p² – q)(b² – ac) ³ 0

statement–2 : b ¹ pa or c ¹ qa

 Let p and q are real numbers such that p ¹ q, p³ ¹ q and p³ ¹ _q. If a and b are two non zero complex number satisfies a + b = –p and a³ + b³ = q then quadratic equation whose roots are  and , is

 Let a and b be the roots of x² – 6x – 2 = 0, with a > b. If a_n = aⁿ – bⁿ for n > 1, then the value of  is

 A value of b for which the equations x² + bx – 1 = 0, x² + x + b = 0, have one root in common is