KVPY Government Jobs Exams

Let P be an m × m matrix such that P2 = P. Then (1 + P^)n equals

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KVPY Other Question

Suppose n is a natural number such that| i + 2i2 + 3i3 + ... + nin |=18 2 , where i is the square root of – 1.
Then n is Consider the cubic equation x^3 + ax^2 + bx + c = 0, where a, b, c are real numbers. Which of the following
statements is correct ?
(A) If a^2 – 2b < 0, then the equation has one real and two imaginary roots
(B) If a^2 – 2b ≥ 0, then the equation has all real roots
(C) If a^2 – 2b > 0, then the equation has all real and distinct roots
(D) If 4a^3 – 27b^2 > 0, then the equation has real and distinct roots