The maximum value of 4 ^2 x + 3 ^2 x is - Vidyadip

Question

The maximum value of $4{\sin ^2}x + 3{\cos ^2}x$ is

✓

Answer

b
(b) $f\,(x) = 4{\sin ^2}x + 3{\cos ^2}x={\sin ^2}x + 3$ and $0 \le \,|\sin x|\, \le 1$

$\therefore $ Maximum value of ${\sin ^2}x + 3$ is $4.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $[t]$ denote the greatest integer $\leq t$. The number of points where the function

$f(x)=[x]\left|x^{2}-1\right|+\sin \left(\frac{\pi}{[x]+3}\right)-[x+1], x \in(-2,2)$

is not continuous is ..... .

The least positive value of $a$ for which the equation $2 \mathrm{x}^{2}+(\mathrm{a}-10) \mathrm{x}+\frac{33}{2}=2 \mathrm{a}$ has real roots is

If $\vec{a}$ and $\vec{b}$ are vectors such that $|\vec{a}+\vec{b}|=\sqrt{29}$ and $\vec{a} \times(2 \hat{i}+3 \hat{j}+4 \hat{k})=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \times \vec{b}$, then a possible value of $(\vec{a}+\vec{b}) \cdot(-7 \hat{i}+2 \hat{j}+3 \hat{k})$ is

If the variance of the terms in an increasing $A.P.$, $b _{1}, b _{2}, b _{3}, \ldots b _{11}$ is $90,$ then the common difference of this $A.P.$ is

If the sum of the first $20$ terms of the series

$\log _{\left(7^{\frac{1}{2}}\right)} x+\log _{\left(7^{\frac{1}{3}}\right)} x+\log _{\left(7^{\frac{1}{4}}\right)} x+\ldots$ is $460,$ then $x$ is equal to

If $\sum_{i=1}^{5}(x_i-10)=5$ and $\sum_{i=1}^{5}(x_i-10)^2=5$ then standard deviation of observations $2x_1 + 7, 2x_2 + 7, 2x_3 + 7, 2x_4 + 7$ and $2x_5 + 7$ is equal to-

The sum of all positive divisors of $ 960$ is

$\left| {\,\begin{array}{*{20}{c}}{{{\sin }^2}x}&{{{\cos }^2}x}&1\\{{{\cos }^2}x}&{{{\sin }^2}x}&1\\{ - 10}&{12}&2\end{array}\,} \right| = $

The least positive integer $n$ for which $\left( \frac{1 + i\sqrt 3 }{1 - i\sqrt 3 }\right)^n = 1,$ is?

Consider the function $f:(0, \infty) \rightarrow R$ defined by $f(x)=e^{-\left|\log _e x\right|}$. If $m$ and $n$ be respectively the number of points at which $f$ is not continuous and $f$ is not differentiable, then $\mathrm{m}+\mathrm{n}$ is