Practice questions
88551 published questions with worked solutions.
- Let Z_1=(8+i) +(7+4i) and Z_2=(1+8i) +(4+7i) are two complex numbers. If Z_1 Z_2=a+ib where a,b R. If M is the greatest value of...
- Let 1,w,w^2 be the cube root of unity. The least possible degree of a polynomial with real coefficients having roots 2w,(2+3w),...
- If is the imaginary cube root of unity, then find the number of pairs of integers (a,b) such that |a +b|=1
- If [ 1+ +i +i(1+ ) ]^4= n +i n , then n is
- If |z+2-i|=5 and maximum value of |3z+9-7i| is M then the value of M/4 is
- If x= - ^2-2, then the value of x^4+3x^3+2x^2-11x-6 is (where is cube root of unity)
- The complex number z satisfies z+|z|=2+8i. The value of (|z|-8) is
- Number of positive integers x for which f(x)=x^3-8x^2+20x-13 is a prime number is
- Let and be the solutions of the quadratic equation x^2-1154x+1=0, then the value of [4] + [4] is equal to
- f:R R, f(x)= 3x^2+mx+n x^2+1 . If the range of this function is [-4,3], then find the value of |m+n| is
- Suppose a,b,c I such that greatest common divisor of x^2+ax+b and x^2+bx+c is (x+1) and the least common multiple of x^2+ax+b and...
- If the cubic 2x^3-9x^2+12x+k=0 has two equal roots, then maximum value of |k| is
- Suppose a,b,c are the roots of the cubic x^3-x^2-2=0. Then the value of a^3+b^3+c^3 is
- If a,b,c are non-zero real numbers, then the minimum value of the expression ( (a^4+3a^2+1 ) (b^4+5b^2+1 ) (c^4+7c^2+1 )...
- If the equation 2x^2+4xy+7y^2-12x-2y+t=0 where t' is a parameter has exactly one real solution of the form (x,y). Then the sum of...
- Let _1, _1 are the roots of x^2-6x+p=0 and _2, _2 are the roots of x^2-54x+q=0. If _1, _1, _2, _2, from an increasing G.P., then...
- Let a,b and c be distinct non zero real numbers such that 1-a^3 a= 1-b^3 b= 1-c^3 c. The value of (a^3+b^3+c^3 ), is
- The function f(x)=ax^3+bx^2+cx+d has three positive roots. If the sum of the roots of f(x) is 4, the largest possible integral...
- Given and are the roots of the quadratic equation x^2-4x+k=0 (k 0). If , ^2+ ^2 , ^3+ ^3 are in geometric progression, then the...
- Let P(x)= 53-6x-9x^2 and Q(y)=-4y^2+4y+ 13 2. If there exist unique pair of real numbers (x,y) such that P(x)Q(y)=20, then the...