List of practice Questions

If $y =\log_{\sin x } \left(\tan x\right),$ then $\left(dy/dx\right)\pi/{4} = $

If $y = e^{(1 + \log_e \, x)}$, then $\frac{dy}{dx}$ is equal to :

If $y=e^{3x+7}$, then the value of $\frac{dy}{dx} \bigg|_{x=0}$ is

If $y =\log_{e}x \left(x-2\right)^{2}$ for $ x \ne0 , 2 $ then $y' \left(3\right) = $

If $ y = \log \{ \log ( \log \:x)^2 \} $ then $\frac{dy}{dx}$ is equal to :

If $y=e^{\frac{1}{2}log\left(1+tan^{2}\,x\right)}$, then $\frac{dy}{dx}$ is equal to

If $y=2^{x}\cdot3^{2x-1}$, then $\frac{dy}{dx}$ is equal to

If $y = 3x^2 + 2$ and if x changes from 10 to 10.1, then the approximate change in y will be?

If $y = ax^2 + b$, then $\frac{dy}{dx}$ at $x = 2$ is equal to

If $y = \frac{ax - b}{\left(x-1\right)\left(x-4\right)}$ has a turning point $P(2, -1)$, then find the value of $a$ and $b$ respectively.

If $\begin{bmatrix}x+y+z\\ x+y\\ y+z\end{bmatrix} = \begin{bmatrix}9\\ 5\\ 7\end{bmatrix} $ then the value of (x, y, z) is:

If $x, y, z$ are positive integers, then value of expression $(x + y)(y + z)(z + x)$ is

If xy + yz + zx = 1, then :

If $y = \sqrt{\left(\frac{1+\cos 2\theta}{1 -\cos 2\theta}\right)} $ , then $\frac{dy}{d\theta} $ at $\theta =\frac{3\pi}{4}$ is:

If $y^2 = p(x),$ a polynomial of degree 3, then $2 \frac{d}{dx} \left(y^{3} \frac{d^{2}y}{dx^{2}}\right) $ is equal to

if $\begin{bmatrix}x\\ y\\ z\end{bmatrix} = \frac{1}{40} \begin{bmatrix}5&10&-5\\ -5&-2&13\\ 10&-4&6\end{bmatrix}\begin{bmatrix}5\\ 0\\ 5\end{bmatrix}$, then the value of $x + y + z$ is

If $x = \sin\: t \: \cos \: 2t$ and $y = \cos\: t\: \sin\: 2t$, then at $ t = \frac{\pi}{4}$, the value of $ \frac{dy}{dx} $ is equal to :

If $X = {x_1, x_2, x_3}$ and $Y = {x_1, x_2, x_3, x_4, x_5}$ then find which is a reflexive relation of the following ?

If $x=\sin(2\,\tan^{-1}2)$ and $y=\sin\left(\frac{1}{2}\tan^{-1}\frac{4}{3}\right)$ ,than

If $(x+iy) (2-3i)=4+i$, then values of $x$, $y$ are

If $x \in \left(-\frac{\pi}{2}, \frac{\pi }{2}\right)$, then the value of $tan^{-1}\left(\frac{tan\,x}{4}\right)+tan^{-1}\left(\frac{3\,sin\,2x}{5 + 3\,cos\,2x}\right)$ is

If x g of a metal forms y g of metal chloride, equivalent weight of metal is

If X is a member of chalcogen family, the chemicalhighest stability of $X^{2-}$ is exhibited by

If $\overrightarrow{x}\times\overrightarrow{b} \,=\,\overrightarrow{c}\times\overrightarrow{b} $ and $ \overrightarrow{x}\,\bot\, \overrightarrow{a},$ then $\overrightarrow{x}$ is equal to

If {x} denotes the fractional part of x, then $\lim_{x \to\left[a\right]} \frac{e^{\left\{x\right\}} - \left\{x\right\}-1}{\left\{x\right\}^{2}} $, where [a] denotes the integral part of a, is equal to