List of practice Questions

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 $\cos(180? +A)+ \cos(180? - B) + \cos(180? - C) - \sin(90? - D) =$

If $ABCDEF$ is a regular hexagon, then $\overrightarrow{AD} + \overrightarrow{EB} + \overrightarrow{FC}$ is equal to

If air is blow n with a straw under of the pans of a physical balance present in equilibrium position, then that pan.

If $a^x = b^y = c^z$ and $a, b, c $ are in G.P. then $ x, y, z $ are in

If $A = \{ x : x^2 - 3x + 2 = 0 \}$ , and R is a universal relation on A, then R is

If $A = \{(x, y) : x^2 + y^2 = 25\}$ and $B = \{(x, y) : x^2 + 16y^2 = 144\}$ then $A \cap B$ contains

If a variable point P on an ellipse of eccentricity e is joined to the foci $S_1$ and $S_2$ then the incentre of the triangle $PS_1S_2$ lies on