List of practice Questions

If $\tan \, \theta + sec \, \theta = p$, then what is the value of $\sec \, \theta$ ?

If $tanA=\frac{1}{2}$, $tanB=\frac{1}{3}$, then $tan\left(2A+B\right)$ is equal to

If $\tan (\cot \, x) = \cot (\tan \, x)$, then $\sin \, 2x $ is equal to :

If $\tan^{-1}\frac{1-x}{1+x}=\frac{1}{2}\tan^{-1}x$, then the value of $x$ is

If $\tan^{-1} \left(2x\right) + \tan^{-1} \left(3x\right) = \frac{\pi}{4} $ then x is equal to :

If $t$ is the parameter for one end of a focal chord of the parabola $y^2 = 4ax$, then its length is

If $T_n$ denotes the $nth$ term of the series $2 + 3 + 6 + 11 + 18 + ...... ,$ then $T_{50}$ is equal to

If $sin\,x \frac{dy}{dx}+y\,cos\,x=x\,sinx$, then $\left(y-1\right)\,sin\,x=$

If $sinA=\frac{3}{5}$ and $A$ is in first quadrant, then the values of $sin2A$, $cos2A$ and $tan2A$ are

If spheres of radius $'r'$ are arranged in ccp fashion (ABCABC.....), the vertical distance between any two consecutive A layers is

If $\sin \alpha + \sin \beta = 0 = \cos \alpha + \cos \beta$, then $\cos 2\alpha + \cos 2\beta =$

If $\sin \, \theta = \frac{24}{25} $ and $0^{\circ} < \theta < 90^{\circ}$ then what is the value of $\sin \left( \frac{\theta}{2} \right)$ ?

If $\sin \, x + cosec \, x = 2$ then $\sin^n \, x + cosec^n \, x (n > 2)$ is equal to

If $\frac{sin\,A}{sin\,B}=m$ and $\frac{cos\,A}{cos\,B}=n$ then find the value of $tan \,B$; $n^2 < 1 < m^2$.

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