List of practice Questions

If the parabola \(y^2=4ax\) passes through the point \((3,2)\), then the length of its latus rectum is:

The equation of a circle whose Centre is \((2,-1)\) and which passes through the point \((3,6)\) is

The equation of a circle whose Centre is \((-3,2)\) and area is \(176\) units is

The conjugate of \( (1+i)^3 \) is

If \( z_1=4i^{40}-5i^{35}+6i^{17}+2,\ z_2=-1+i \), then \( |z_1+z_2|= \)

\[ \tan^{-1}1+\tan^{-1}2+\tan^{-1}3= \]

\[ \cos 6^\circ \sin 24^\circ \cos 72^\circ= \]

If \( \cos\theta=\frac{1}{2}\left(a+\frac{1}{a}\right) \), then \(4\cos^3\theta-3\cos\theta=\)

\[ \tan 9^\circ-\tan 27^\circ-\tan 63^\circ+\tan 81^\circ= \]

\[ \frac{\tan x-1+\sec x}{\tan x-\sec x+1} = \]

If \( \tan\theta+\sec\theta=\sqrt{3} \), then the principal value of \( \theta \) in \( [0,2\pi] \) is

The number of solutions of the equation $\sin 2x - \cos 2x = 2 - \sin 2x$ lying in the interval $[0, \pi]$ is

If $\sin^{-1} \frac{5}{x} + \sin^{-1} \frac{12}{x} = \frac{\pi}{2}$ then $x =$

If $2 \sin^{-1} x = \sin^{-1} k$ then $k =$

If $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3}$, then $A+B =$

If $\frac{x}{(x-1)^{2}(x+2)}=\frac{A}{(x-1)^{2}}+\frac{B}{9(x-1)}+\frac{C}{(x+2)}$ then $A+B=$

If $\frac{x+4}{(x+2)^{2}(x+3)}=\frac{A}{(x+2)^{2}}+\frac{B}{(x+2)}+\frac{C}{(x+3)}$ then $A+B+C=$

Diffusion in Solids occurs mainly due to

A Covalent bond is formed due to

The eutectic point in the \(SiO_2-Na_2O\) phase diagram occurs at

Burger's vector is perpendicular to

A Cation vacancy and an anion vacancy in a crystal of the type \(AB\) is called

Which of the following is a non-oxide ceramic?

Advanced Ceramics are also known as

Bayer process is used to produce