Practice questions
88551 published questions with worked solutions.
- If and are the roots of x^2-5x+16=0 and ^2+ ^2, 2 are the roots of x^2+ax+b=0, then find the value of a+b.
- Find the product of the roots of the equation 4^x-3 (2^ x+3 )+128=0.
- Find the smallest prime number x such that it satisfies 2^ _ 2 (x-1) >x+5.
- If one of the roots of the equation 6x^2+kx+6=0, k>0, is square of the other, then find the value of k.
- If and are the roots of x^2-5x+4=0, then find the value of ^3 2 cosec ^2 ( 12 ^ -1 )+ ^3 2 ^2 ( 12 ^ -1 ).
- Find the value of such that the sum of the squares of the roots of x^2+(4- )x+3= has the least value.
- If the roots of the equation 12x^2+mx+5=0 are in the ratio 3:2, then find the value of m^2.
- If the roots of the quadratic equation x^2-6x+ _2 =0 are real, then find the maximum value of .
- Find the largest integral value of m for which the quadratic expression y=x^2+(2m+4)x+7m+8 is positive for all x R.
- If one of the roots of the equation px^2-6x+q=0, where p and q are real numbers, is 32+ 72i, then find the value of |p-q|.
- Let z be a complex number satisfying the equation 2|z-1|+i+z=0. Find the number of such complex numbers.
- Let z_1,z_2,z_3 be the roots of the equation x^3+bx^2+cx+d=0, b,c,d R. If z_1=1, z_2=1+Ai (A 0, A R), then evaluate d+c-b.
- A complex number z satisfies ( z z-i )= 3 and |z|=|z-i|, then evaluate [ Re (2z-i) ] where [ ,] represents the greatest integer...
- If is a complex cube root of unity, then evaluate | + ^ ( 15+ 9 50 + 81 500 + 729 5000 + ) |.
- If z=x+iy and x^2+y^2=36 and the range of |x|-|y| is [a,b], then evaluate b^2-a^2.
- Two points A and B in Argand plane represent z and z_1=2 (z+ 3+i ) respectively. If A moves on a circle with centre at origin and...
- Side AB of a square joins z_1=-1 and z_2=3i, and the vertices C(z_3) and z_4 lie in the second quadrant of Argand plane. Evaluate...
- If and are roots of x^2-4x+8=0 and ^ 24 + ^ 24 =2^k( p +i p ), then evaluate k+p.
- If z is a complex number such that |z| 3, then find the minimum value of |z+ 34 |.
- If Re [(1+i)^ -i ]=e^ p (m n), then evaluate pmn.