List of practice Questions

If $\sin \, 4A - \cos \, 2A = \cos \, 4A- \sin \, 2A \left( 0 < A < \frac{\pi}{4} \right)$ then the value of tan 4A =

If $\sin 6\theta + \sin 4\theta + \sin 2\theta = 0$, then general value of $\theta$ is

If $\sin^{-1} x + \sin^{-1}y + \sin^{-1} z = \frac{3 \pi}{2} $ then the value of $x^{100} + y^{100} + z^{100} - \frac{ 3}{x^{101} + y^{101} + z^{101}} $ is

If $\sin^{-1}x +\sin^{-1}y+\sin^{-1}z=\pi $ , then $x^4+y^4+z^4+4x^2\,y^2\,z^2=K(x^2\,y^2+y^2\,z^2+z^2\,x^2)$ , where K =

If $\sin^2 \, \theta + 3 \, \cos \, \theta - 2 = 0$, then $\cos^3 \, \theta + \sec^3 \, \theta$ is equal to

$ If sin 4A - cos^2 A = cos 4A - sin 2A,\left(0< A

If $\sin^{-1} \alpha = \tan^{-1} \frac{3}{4}$, then $\alpha $ equals :

If $\sin^{-1}\left(\frac{5}{x}\right)+\sin^{-1}\frac{12}{x}=\frac{\pi}{2}$,then x =

If $\sin^{-1}x-\cos^{-1} x=\frac{\pi}{6}, $ then $x$ is

If $\sin^{-1}\left(\frac{x}{13}\right)+cosec^{-1}\left(\frac{13}{12}\right)=\frac{\pi}{2}$ , then the value of x is

If $\sec \, \alpha$ and $cosec \, \alpha$ are the roots of the equation $x^2 - px + q = 0, $ then

If $\sec \, \theta = x + \frac{1}{4x}, x \in R , x \neq 0$, then the value of $\sec \, \theta + \tan \, \theta $ is

If radius of earth shrinks by $1 %$ when mass remains same, the acceleration due to gravity on the surface of earth would

If S is the sum to infinity of a G.P. whose first term is a, then the sum of the first n terms is

If $S_m$ denotes the sum of first $m$ terms of a $G.P. $ of $n$ terms with common ratio $r$, then the sum of their products taken two by two is

If $PSQ$ is the focal chord of the parabola $y^2 = 8x$ such that $ SP = 6$ then the length $SQ $ is

If $R$ and $H$ represent horizontal range and maximum height of the projectile, then the angle of projection with the horizontal is

If R is the relation less than' from A={1, 2, 3, 4, 5} to B={1, 4}, the set of ordered pairs corresponding to R, then the inverse of R is

If pressure of $CO_2$ (real gas) in a container is given by $p = \frac{RT}{2V - b} - \frac{9}{4b^2},$ then mass of the gas in container ts

If p and q are true statement and r, s are false statements then the truth value of $\sim[(p \wedge \sim r) \vee (\sim q \vee s)]$ is

If p be the length of the perpendicular from the origin on the straight line x + 2by = 2p ,then what is the value of b?

if P =$\begin{bmatrix}i&0&-i\\ 0&-i&i\\ -i&i&0\end{bmatrix}$ and $Q=\begin{bmatrix}-i&i\\ 0&0\\ i&-i\end{bmatrix}$ then $PQ$ is equal to

If $P(A \cup B) = 0.8, P(A \cap B) = 0.3 $ then $P (\bar{A} ) + P(\bar{B})$ =

If one mole of a monatomic gas $(\gamma = 5/3)$ is mixed with one mole of a diatomic gas $(\gamma = 7/3)$, the value of g for the mixture is

If one person handshakes with the other only once and number of handshakes is $66$, then number of persons will be