List of practice Questions

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

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

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

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

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 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

If $x \frac{dy}{dx} =y \left(\log \,y - \log \,x\right)$ then the solution of the equation is

If $x, 2y, 3z$ are in $A.P$., where the distinct numbers $x, y, z$ are in $G.P$. then the common ratio of the $G.P$. is

If $x = 99^{50} + 100^{50}$ and $y = \left(101\right)^{50}$ then

If $x = a \cos \theta, y = b \sin \theta$, then $\frac{d^3 y}{dx^3}$ is equal to

If x + 1, 4x + 1, and 8x + 1 are in geometric progression, then what is the non-trivial value of x ?

If $x = 1 + a + a^2 + .................... $to infinity and $y = 1 + b + b^2 + ................... $to infinity, where a, b are proper fractions, then $1 + ab + a^2b^2 + .....$ to infinity is equal :

If $x^2 + 6x - 27 > 0$ and $x^2 - 3x - 4 < 0 $ then

If we add two vectors of equal magnitudes but in opposite directions, we get

If we plot volume of a certain mass of a gas against temperature at constant pressure, we get a straight line intersecting on the negative side at $ -273^{\circ}C$ which explains about absolute zero. This graph is known as

If work is done on a system, depends upon initial and final positions only it can be due to

If unit vectors $\hat{A}$ and $\hat{B}$ are inclined at an angle $\theta$, then $\left|\hat{A}-\hat{B}\right|$ is

If volume occupied by $CO_2$ molecules is negligible, then what will be the pressure $\left(\frac{p}{5.277}\right)$ exerted by one mole of $CO_{2}$ gas at $300\, K$? $\left(a = 3.592 atm L^{2} mol^{2}\right)$

If $ W_{1} $ be the work to be done to form a bubble of volume $ V $ from a given solution. The work required to be done to form a bubble of volume $ 2 V $ is