Practice questions
88551 published questions with worked solutions.
- Let the complex number z=x+iy be such that 2z-3i 2z+i is purely imaginary. If x+y^2=0, then y^4+y^2-y is equal to
- Let A= (0,2 ): 1+2i 1-i is purely imaginary . Then the sum of the elements in A is
- If for z= +i , |z+2|=z+4(1+i), then + and are the roots of the equation
- If and are the roots of the equation x^2-x+1=0, then ^ 101 + ^ 107 is equal to
- Let for a a_1 0, f(x)=ax^2+bx+c, g(x)=a_1x^2+b_1x+c_1 and p(x)=f(x)-g(x). If p(x)=0 only for x=-1 and p(-2)=2, then the value of...
- Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up in...
- If both the roots of the quadratic equation x^2-mx+4=0 are real and distinct and they lie in the interval [1,5] then m lies in...
- The number of all possible positive integral values of for which the roots of the quadratic equation, 6x^2-11x+ =0 are rational...
- Consider the quadratic equation (c-5)x^2-2cx+(c-4)=0, c 5. Let S be the set of all integral values of c for which one root of the...
- The value of such that sum of the squares of the roots of the quadratic equation, x^2+(3- )x+2= has the least value is
- If one real root of the quadratic equation 81x^2+kx+256=0 is cube of the other root, then a value of k is
- Let and the roots of the quadratic equation x^2 -x( +1)+ =0 (0< <45^ ), and < . Then _ n=0 ^ ( ^n+ (-1)^n ^n ) is equal to
- If be the ratio of the roots of the quadratic equation in x, 3m^2x^2+m(m-4)x+2=0, then the least value of m for which + 1 =1, is
- The number of integral values of m for which the quadratic expression, (1+2m)x^2-2(1+3m)x+4(1+m), x R, is always positive, is
- If and are the roots of the equation x^2-2x+2=0, then the least value of n for which ( )^n=1 is
- The sum of the solutions of the equation | x-2 |+ x ( x-4 )+2=0, (x>0) is equal to
- If three distinct numbers a,b,c are in G.P. and the equations ax^2+2bx+c=0 and dx^2+2ex+f=0 have a common root, then which one of...
- The number of integral values of m for which the equation (1+m^2 )x^2-2(1+3m)x+(1+8m)=0 has no real root is
- Let p,q R. If 2- 3 is a root of the quadratic equation, x^2+px+q=0, then
- If m is chosen in the quadratic equation (m^2+1 )x^2-3x+ (m^2+1 )^2=0 such that the sum of its roots is greatest, then the...