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Black Advanced Problems in Mathematics

Exam: Black Advanced Problems in Mathematics
Subject: Mathematics
Chapter: Quadratic Equation

Black Advanced Problems in Mathematics · Mathematics · Quadratic Equation

(A) If a, b are the roots of equation x^2 + ax + b = 0 ( a, b ∈...

(A) If $a, b$ are the roots of equation $x^2 + ax + b = 0$ ( $a, b \in R$ ), then the number of ordered pairs $(a, b)$ is equal to	(P) $1$
(B) If $P = cosec\frac{\pi}{8} + cosec\frac{2\pi}{8} + cosec\frac{3\pi}{8} + cosec\frac{13\pi}{8} + cosec\frac{14\pi}{8} + cosec\frac{15\pi}{8}$ and $Q = 8\sin\frac{\pi}{18}\sin\frac{5\pi}{18}\sin\frac{7\pi}{18}$ , then $P + Q$ is equal to	(Q) $2$
(C) Let $a_1, a_2, a_3 ......$ be positive terms of a G.P. and $a_4, 1, 2, a_{10}$ are the consecutive terms of another G.P. If $\prod_{i=2}^{12} a_i = 4^n$ where $m$ and $n$ are coprime, then $(m + n)$ equals	(R) $3$
(D) For $x, y \in R$ , if $x^2 - 2xy + y^2 - 6y + 9 = 0$ , then the value of $5x - 4y$ is equal to	(S) $15$

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