Mathematics questions
18011 published questions with worked solutions.
- If x, y, z are three real numbers such that x + y + z = 4 and x^2 + y^2 + z^2 = 6, then the exhaustive set of values of x, is
- The number of negative integral solutions of x^2 2^ x+1 + 2^ |x-3|+2 = x^2 2^ |x-3|+4 + 2^ x-1 , is
- The number of solutions of the equation _ x-3 (x^3 - 3x^2 - 4x + 8) = 3, is
- The number of roots of the equation x = | |x||, is
- The number of positive real roots of x^4 - 4x - 1 = 0, is
- The solution set of inequation _ 1/3 (2^ x+2 - 4^x) -2, is
- Let n be an odd positive integer. Then, the number of real roots of the polynomial P_n(x) = 1 + 2x + 3x^2 + + (n+1)x^n, is
- Let n be an odd integer such that the polynomial P_n(x) = 1 + 2x + 3x^2 + + (n+1)x^n has exactly one real root. This real root...
- Let P_n(x) = 1 + 2x + 3x^2 + + (n+1)x^n be a polynomial such that n is even. Then, the number of real roots of P_n(x), is
- If x, y R, then 1 2 (x + y + |x - y|) = x holds iff
- Let a_n = i^ (n+1)^2 , where i = -1 and n = 1, 2, 3, Then the value of a_1 + a_3 + a_5 + + a_ 25 is
- The value of sum _ n=1 ^ 13 (i^n + i^ n+1 ), where i = -1 , equals
- If z = x + iy, z^ 1/3 = a - ib and x a - y b = k(a^2 - b^2), then value of k equals
- The smallest positive integer n for which ( 1+i 1-i )^n = 1, is
- 3 + 2i 1 - 2i will be purely imaginary, if is equal to
- The values of x and y satisfying the equation (1+i)x - 2i 3+i + (2-3i)y + i 3-i = i are
- The real part of (1 - + 2i )^ -1 is
- The number of non-zero integer solutions of the equation |1 - i|^x = 2^x is
- If (1+i)^2 2-i = x + iy, then x + y is equal to
- Let z = 11 - 3i 1 + i . If is a real number such that z - i is real, then the value of is