Download App

STD 12 - 5. continuity and differentiation — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 5. continuity and differentiation1 Mark
MCQ
Let $ y $ be an implicit function of  $x$ defined by ${x^{2x}} - 2{x^x}\cot y - 1 = 0$ .Then  $y'\left( 1 \right)$ equals
  • A
    $1$
  • B
    $log 2$
  • C
    $-log 2$
  • ✓
    $-1$
✓

Answer

Correct option: D.
$-1$
d
$x^{2 x}-2 x^{x} \text { cot } y-1=0$          ........$(i)$

at $x=1$ we have

$1-2 \cot y-1=0$

$\Rightarrow$ cot $y=0 \quad \therefore \quad y=\pi / 2$

Differentiating $(i)$ w.r.t. $x,$ we have

$2{x^{2x}}(1 + \ln x) - 2\left[ {{x^x}\left( { - \cos e{c^2}y} \right)\frac{{dy}}{{dx}}} \right.$

$\left. { + \cot y \cdot {x^x}(1 + \ln x)} \right] = 0$

At $P(1, \pi / 2)$ we have

$2(1+\ln 1)-2\left[1(-1)\left(\frac{d y}{d x}\right)_{P}+0\right]=0$

$\Rightarrow 2+2\left(\frac{d y}{d x}\right)_{P}=0 \quad \therefore\left(\frac{d y}{d x}\right)_{P}=-1$

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 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $\overrightarrow{ a }+\overrightarrow{ b }=\hat{ i }$ and $\overrightarrow{ a }=2 \hat{ i }-2 \hat{ j }+2 \hat{ k }$, then $|\overrightarrow{ b }|$ equals:
→
If $\int_0^\pi {x\,f({{\cos }^2}x + {{\tan }^4}x)\,dx} $ $ = k\int_0^{\pi /2} {f({{\cos }^2}x + {{\tan }^4}x)\,dx,} $ then the value of $k$ is
→
Let $X$ have a binomial distribution $B ( n , p )$ such that the sum and the product of the mean and variance of $X$ are $24$ and $128$ respectively. If $P ( X > n -3)=\frac{ k }{2^{ n }}$, then $k$ is equal to.
→
Choose the correct answer from the given four options.
The probability of guessing correctly at least 8 out of 10 answers on a true-false type examination is:
→
Let for a triangle $ABC$,

$\overline{A B}=-2 \hat{i}+\hat{j}+3 \hat{k}$

$\overline{C B}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}$

$\overline{C A}=4 \hat{i}+3 \hat{j}+\delta \hat{k}$

If $\delta > 0$ and the area of the triangle $ABC$ is $5 \sqrt{6}$, then $\overline{C B} \cdot \overline{C A}$ is equal to

→
The number of solutions of $y' = \frac{{y + 1}}{{x - 1}},\,y(1) = 2$ is
→
The value of $\left| {\,\begin{array}{*{20}{c}}{{5^2}}&{{5^3}}&{{5^4}}\\{{5^3}}&{{5^4}}&{{5^5}}\\{{5^4}}&{{5^5}}&{{5^7}}\end{array}\,} \right|$ is
→
Let $y = y _1( x )$ and $y = y _2( x )$ be the solution curves of the differential equation $\frac{d y}{d x}=y+7$ with initial conditions $y_1(0)=0, y_2(0)=1$ respectively. Then the curves $y=y_1(x)$ and $y=y_2(x)$ intersect at
→
$\left| {\,\begin{array}{*{20}{c}}1&1&1\\{\cos (nx)}&{\cos (n + 1)x}&{\cos (n + 2)x}\\{\sin (nx)}&{\sin (n + 1)x}&{\sin (n + 2)x}\end{array}\,} \right|$ is not depend
→
Choose the correct answer from the given four options.If $\text{A}=\frac{1}{\pi}\begin{bmatrix}\sin^{-1}(\text{x}\pi)&\tan^{-1}\Big(\frac{\text{x}}{\pi}\Big)\\\sin^{-1}\Big(\frac{\text{x}}{\pi}\Big)&\cot^{-1}(\pi\text{x})\end{bmatrix}$ and $\text{B}=\frac{1}{\pi}\begin{bmatrix}-\cos^{-1}(\text{x}\pi)&\tan^{-1}\Big(\frac{\text{x}}{\pi}\Big)\\\sin^{-1}\Big(\frac{\text{x}}{\pi}\Big)&\tan^{-1}(\pi\text{x})\end{bmatrix}$ then A - B is:
→