List of practice Questions

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

If u represents object distance from pole of spherical mirror and $v$represents image distance from pole of mirror and f is the focal length of the mirror, then a straight line u = $v$ will,cut u versus $v$ graph at

If $u = \sin (m \cos^{-1} x), v = \cos (m \sin^{-1} x)$, then $\frac{du}{dv} = $

If two numbers $p$ and $q $ are chosen randomly from the set $\{1, 2, 3, 4\}$ with replacement, then the probability that $ p^2 \ge 4q$ is equal to

If two squares are chosen at random on a chess board, the probability that they have a side in common is

If $U= \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$, $A = \{2, 4, 7\}$, $B = \{3, 5, 7, 9, 11\}$ and $C = \{7, 8, 9, 10, 11\}$, compute $(A \cap U) \cap (B \cup C)$.

If two circular arcs of the same length subtend angles of $60^{\circ}$ and $80^{\circ}$ at their respective centres, then the ratio of their radii is

If two coins are tossed 5 times, the chance that there will be 5 heads and 5 tails is