Practice questions
88551 published questions with worked solutions.
- The values of k for which the equations x^2-kx-21=0 and x^2-3kx+35=0 will have a common roots are
- If x^2+x+1 x^2+2x+1 =A+ B x+1 + C (x+1)^2 , then A-B is equal to
- If x^3 (2x-1)(x+2)(x-3) =A+ B 2x-1 + C x+2 + D x-3 , then A is equal to
- The partial fraction of 3x^3-8x^2+10 (x-1)^4 is
- If 3x (x-a)(x-b) = 2 x-a + 1 x-b , then a:b is equal to
- If x-4 x^2-5x+6 can be expanded in the ascending powers of x, then the coefficient of x^3 is
- If a real valued function f of a real variable x such that 1 (1+x) (1+x^2 ) = A 1+x + f(x) 1+x^2 , then f(x) is equal to
- Let a,b and c be such that 1 (1-x)(1-2x)(1-3x) = a 1-x + b 1-2x + c 1-3x , then a1+ b3+ c5 is equal to
- If x+1 (2x-1)(3x+1) = A 2x-1 + B 3x+1 , then 16A+9B is equal to
- If 3x+2 (x+1) (2x^2+3 ) = A x+1 + Bx+C 2x^2+3 , then A+C-B is equal to
- If is a cube root of unit and is not real, then ^ 3n+1 + ^ 3n+3 + ^ 3n+5 has the value
- If + + = + + =0, then 3 + 3 + 3 equals
- The equation z z+(2-3i)z+(2+3i) z+4=0 represents a circle of radius
- If the real part of z+2 z-1 is 4, then the locus of the point representing z in the complex plane is
- Statement 1: If |z_1|=1, |z_2|=2, |z_3|=3 and |z_1+2z_2+3z_3|=6, then value of |z_2z_3+8z_3z_1+27z_1z_2| is 36 Statement 2:...
- The complex numbers z_1,z_2,z_3 are the vertices of a triangle. Then the complex number z which makes the triangle into a...
- The trigonometric form of z=(1-i 8)^3 (where i= -1 ) is
- If z be the conjugate of the complex number z, then which of the following relations is false?
- If a= 4 3+i 4 3, then the value of ( 1+a 2 )^ 3n is
- The equation of a circle whose radius and centre are r and z_0 respectively, is