Mathematics questions
18011 published questions with worked solutions.
- The value of _ k=1 ^6 ( 2 k 7-i 2 k 7 ) is
- The locus of z satisfying the inequality _ 1/3 |z+1|> _ 1/3 |z-1| is
- If x= ( 1+i 2 ), (where i= -1 ), then the expression 2x^4-2x^2+x+3 equals
- If the points z_1,z_2,z_3 are the vertices of an equilateral triangle in the complex plane, then the value of z_1^2+z_2^2+z_3^2...
- If z^2+z|z|+|z|^2=0, then the locus of z is
- Given that the equation z^2+(p+iq)z+r+is=0, where p,q,r,s are real and non-zero has real roots, then
- If z_1 and z_2 be complex numbers such that z_1 z_2 and |z_1|=|z_2|. If z_1 has positive real part and z_2 has negative imaginary...
- If ( 1) is a cube root of unity and (1+ )^7=A+B , then A and B are respectively
- If ( +i )( 2 +i 2 ) ( n +i n )=1, then the value of is
- If z_1,z_2,z_3 be three complex numbers such that |z_1+1| 1, |z_2+2| 2 and |z_3+4| 4, then the maximum value of |z_1|+|z_2|+|z_3|...
- The real part of (1- +2i )^ -1 is
- If 1, , ^2 are the cube roots of unity, then = vmatrix 1& ^n& ^ 2n ^n& ^ 2n &1 ^ 2n &1& ^n vmatrix is equal to
- The closest distance of the origin from a curve given as a z+ az+|a|^2=0 is
- For all x', x^2+2ax+(10-3a)>0, then the interval in which a' lies, is
- Statement 1: The greatest integral value of for which (2 -1)x^2-4x+(2 -1)=0 has real roots, is 2. Statement 2: For real roots of...
- Statement 1: If a+b+c=0 and a,b,c are rational, then the roots of the equation (b+c-a)x^2+(c+a-b)x+(a+b-c)=0 are rational....
- If a<b<c<d, then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are
- If the roots of the equation x^2+px+q=0 are and and roots of the equation x^2-xr+s=0 are ^4, ^4, then the roots of the equation...
- If at least one root of the equation x^3+ax^2+bx+c=0 remains unchanged, when a,b and c are decreased by one, then which one of...
- Statement 1: Let f(x) be quadratic expression such that f(0)+f(1)=0. If -2 is one of the root of f(x)=0, then other root is 35....