JEE Main 2016 · 9 Apr · Shift 1 · Mathematics Q89

MathematicsSingle correct+4 / -1Question 89 of 90

If m and M are the minimum and the maximum values of $4+\dfrac12\sin^22x-2\cos^4x$ , $x\in\mathbb R$ , then M − m is equal to :

\dfrac{15}4

\dfrac94

\dfrac74

\dfrac14

Answer and worked solution

Official answer: B

With $c=\cos^2x$ the expression is $4+2c-4c^2$ on [0, 1]: maximum $\frac{17}4$ at $c=\frac14$ , minimum 2 at c = 1. So $M-m=\frac94$ .

JEE Main 2016 · 9 Apr · Shift 1, Mathematics question 89