Practice questions
88551 published questions with worked solutions.
- The greatest and the least value of |z_1+z_2|, if z_1=24+7i and |z_2|=6, are respectively
- If n Z, then 2^n (1-i)^ 2n + (1+i)^ 2n 2^n is equal to
- The polynomial x^ 3m +x^ 3n+1 +x^ 3k+2 is exactly divisible by x^2+x+1 if
- If +2 +3 = +2 +3 =0 and + + =n , then 3 +8 3 +27 3 =
- If x^2-2x +1=0, then x^ 2n -2x^n n +1 is equal to
- The curve represented by Im (z^2 )=k, where k is a non-zero real number, is
- For n=6k, k Z, ( 1-i 3 2 )^n+ ( -1-i 3 2 )^n has the value
- If z=re^ i , then |e^ iz | is equal to
- If _ 30^ ( 2|z|^2+2|z|-3 |z|+1 )<-2, then
- Let and be two fixed non-zero complex numbers and z' a variable complex number. If the lines z+ z+1=0 and z+ z-1=0 are mutually...
- The number of real solutions of the equation 6-x x^2-4 =2+ x x+2 , is
- Let , be the roots of x^2+bx+1=0. Then the equation whose roots are - ( + 1 ) and - ( + 1 ), is
- The value of c' for which | ^2- ^2 |= 74, where and are the roots of 2x^2+7x+c=0, is
- The set of possible values of a for which x^2- (a^2-5a+5 )x+ (2a^2-3a-4 )=0 has roots whose sum and product are both less than 1...
- If and are the roots of ax^2+bx+c=0, then
- If the ratio of the roots of the equation x^2+px+q=0 be equal to the ratio of the roots of x^2+lx+m=0, then
- The real roots of |x|^3-3x^2+3|x|-2=0 are
- If the equations ax^2+bx+c=0 and cx^2+bx+a=0, a c have a negative common root, then a-b+c=
- The values of x satisfying |x^2+4x+3 |+(2x+5)=0 are
- The number of real roots of the equation 2x-3 x-1 +1= 6x^2-x-6 x-1 , is