Download App

STD 12 - 6. Application of derivatives — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 6. Application of derivatives1 Mark
MCQ
The range of $a \in R$ for which the function $ f(x)=(4 a-3)\left(x+\log _{e} 5\right)+2(a-7) \cot \left(\frac{x}{2}\right) \sin ^{2}\left(\frac{x}{2}\right)$ $x \neq 2 n \pi, n \in N ,$ has critical points, is
  • A
    $(-3,1)$
  • ✓
    $\left[-\frac{4}{3}, 2\right]$
  • C
    $[1, \infty)$
  • D
    $(-\infty,-1]$
✓

Answer

Correct option: B.
$\left[-\frac{4}{3}, 2\right]$
b
$f(x)=(4 a-3)\left(x+\log _{e} 5\right)+(a-7) \sin x$

$f'(x)=(4 a-3)(1)+(a-7) \cos x=0$

$\Rightarrow \quad \cos x=\frac{3-4 a}{a-7}$

$-1 \leq \frac{3-4 a}{a-7}<1$

$\frac{3-4 a}{a-7}+1 \geq 0$

$\frac{3-4 a+a-7}{a-7} \geq 0$

$\frac{-3 a-4}{a-7} \geq 0$

$\frac{3 a+4}{a-7} \leq 0$

$\frac{3-4 a}{a-7}<1$

$\frac{3-4 a}{a-7}-1<0$

$\frac{3-4 a-a+7}{a-7}<0$

$\frac{-5 a+10}{a-7}<0$

$\frac{5 a-10}{a-7}>0$

$\frac{5(a-2)}{a-7}>0$

$\alpha \in\left[-\frac{4}{3}, 2\right)$

Check end point $\left[-\frac{4}{3}, 2\right)$

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

More "M.C.Q (1 Marks)" from STD 12 - 6. Application of derivatives→STD 12 - 6. Application of derivatives — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The slope of the tangent to the curve $x = t^2+ 3t - 8, y = 2t^2- 2t - 5$ at the point $(2, -1)$ is:
→
Let $\text{y}=\sqrt{\sin\text{x}+\text{y}},$ then $\frac{\text{dy}}{\text{dx}}=$
→
If the projections of the line segment AB on the coordinate axes are 2, 3, 6, then the square of the sine of the angle made by AB with x = 0, is:
→
Let $a, b$ and $c$ be vectors with magnitudes $3, 4$ and $5$ respectively and $a + b + c = 0,$ then the values of $a.b + b.c + c.a$ is:
→
Solution of differential equation $\frac{{dy}}{{dx}} = \frac{{y - x}}{{y + x}}$ is
→
The function $f(x)=x^2 e^{-x}$ is monotonic increasing when :
→
The integral $\int_{0}^{1} \frac{1}{{ }_{7}^{\left[\frac{1}{x}\right]}} d x=$ where [.] denotes the greatest integer function is equal to
→
$\int\limits^\infty_0\frac{1}{1+\text{e}^\text{x}}\text{dx}$ equals :
→
The point of discontinuity of the function $f ( x )=\left\{\begin{array}{ll}2 x+3, & \text { if } x \leq 2 \\ 2 x-3, & \text { if } x>2\end{array}\right.is$
→
The motion of stone thrown up vertically is given by $s = 13.8t - 4.9{t^2}$, where $s$ is in metre and  $t $ is in seconds. Then its velocity at $t = 1$ second is ........ $m/s$
→