List of practice Questions

If $E$ is the energy of $n^{th}$ orbit of hydrogen atom the energy of $n^{th}$ orbit of $He$ atom will be

If $cot \left(cos^{-1}\, x\right) = sec \left(tan^{-1} \frac{a}{\sqrt{b^{2} - a^{2}}}\right)$, then $x$ is equal to

If displacement of a particle is zero, distance covered by it

If $\displaystyle\lim_{x \to 5} \frac{x^k - 5^k}{x - 5} = 500$ then k is equal to :

If cos $\alpha$, cos $\beta$, cos $\gamma$, are direction cosine of a line then value of $\sin^2 \, \alpha + \sin^2 \, \beta + \sin^2 \gamma$ is:

If $cosec \theta - \cot \, \theta = q$, then the value of $\cot \, \theta$ is:

If $\cos \, T = \frac{3}{5}$ and if $\sin \, R = \frac{8}{17}$, where T is in the fourth quadrant and R is in the second quadrant, then cos (T - R) is equal to:

If $(\cos^{-1}x)^2-(\sin^{-1}x)^2>0$, then

If C denotes the velocity of light, velocity of cathode rays is

If $Cl_2$ gas is passed into aqueous solution of KI containing some $CCl_4$ and the mixture is shaken :

If B is an invertible matrix and A is a matrix, then

If both the length and radius of the wire are doubled, how does the modulus of elasticity change ?

If $\bar{x}$ is the mean of $x_1, x_2, ........, x_n$ then for $a \neq 0$, the mean of $ax_1,ax_2 , .....,ax_n , \frac{x_1}{a} , \frac{x_2}{a} , ...... , \frac{x_n}{a}$is

If $?

If an event has more than one sample point, then it is called a/an______.

If $b^2 - 4ac = 0$, $a > 0$, then the domain of the function $y = log(ax^3 + (a + b)x^2 + (b + c)x + c)$ is

If Amp $( \frac {z-1} {z+1})= \frac {\pi} {3}$, then $z$ represents a point on

If an angle $\theta$ is divided into 2 parts A and B such that $A - B = k$ and $A + B = \theta$ and tan $A : tan \,B = k :\, 1$, then the value of sin k is :

If $aN = {ax : x \in N}$ and $bN \cap cN = dN$, where $b,\, c \in N$ are relatively prime, then

If all permutations of the letters of the word are arranged in the order as in a dictionary, what is the $49^{th}$ word?

If $\alpha$ and $\beta$ are the roots of the equation $x^{2} + 2x + 4 = 0$, then $\frac{1}{\alpha^{3}}+\frac{1}{\beta^{3}}$ is equal to

If $\alpha , \beta $ are complementary angles, then $\cos^2 \, \alpha +\cos^2 \,\beta $ is equal to

If $\alpha \,,\beta,\,\gamma\,$ are the angles which a half ray makes with the positive directions of the axes, then $\sin^2\alpha \,,\sin^2\beta,\,\sin^2\gamma\,$ is equal to

If $AB = A$ and $BA = B$, then $B^2$ is equal to

If $ABCD$ is a cyclic quadrilateral then $\cos(180? +A)+ \cos(180? - B) + \cos(180? - C) - \sin(90? - D) =$