List of practice Questions

Evaluate:$\underset{x\to -2}{lim}\frac{x^5+2x^4+x^2+3x+2}{x^4+2x^3+3x^2-5x-22}$

If $\overrightarrow{a}=\hat{i}+2\hat{j}+3\hat{k}$ and $\overrightarrow{b}=\hat{i}\times (\overrightarrow{a}\times \hat{i})+\hat{j}\times (\overrightarrow{a}\times \hat{j})+\overrightarrow{k}\times (\overrightarrow{a}\times \hat{k})$ then length of $\overrightarrow{b}$ isequal to

The equation of the plane parallel to the planes x + 2y + 3z – 5 = 0 and x + 2y + 3z – 7 = 0 and equidistant from them is

The area (in sq. units) bounded by the parabola y = 2 – x² and the line x + y = 0 is

The solution of $\frac{dy}{dx}=\frac{x\log x^2+x}{\sin y+y\cos y}$

If two primary spermatocytes and two primary oocytes undergo meiosis simultaneously, what will be the ratio of spermatozoa and ova produced at the end of the gametogenesis?

If the wavelength of incident light changes from 400 nm to 300 nm, then the stopping potential of photoelectrons emitted from a surface becomes (approximately)

Which of the following statements is/are correct?

If fourth term of an A.P. is zero, then $\frac{t_{25}}{t_{11}}$ is, where $t_n$ denotes the $n^{\text{th }}$ term of AP.

$\sqrt{4},\sqrt[4]{4},\sqrt[8]{4},\sqrt[16]{4},\dots \dots \dots$up to ∞ are roots of the equation

$\int \frac{a^{x/2}}{\sqrt{a^{-x}-a^x}}\mathrm{dx}$ is equal to

The standard deviation of n observations $x_1,x_2,\dots x_n$ is 2 If $\sum _{i=1}^n{x}_i=20$ and $\sum _{i=1}^n{x}_i^2=100,$ then $n$ is equal to

The number of real solutions of the equation |x|² + 5|x| + 4 = 0 is

The coordinates of a moving point p are (2t² + 4, 4t + 6). Then  its locus will be a

The sum of n terms of two AP's are in the ratio of $(3n+8):(7n+15)$. Find the ratio of their ${12}^{\text{th }}$ terms.

If in a triangle ABC, sin A, sin B, sin C are in A.P., then 

The shortest distance from the point (1, 2, -1) to the surface of the sphere x² + y² + z² = 54 is

If a point P is equidistant from A(1, 3), B(-3, 5) and C(5, -1), then PA is equal to

If $\sin \theta =\frac{2t}{1+t^2}$ and $\theta$ lies in the second quadrant, then $\cos \theta$ is equal to

Evaluate the integral: ${\int }_1^2\log xdx$

A coin is biased so that the head is 3 times as likely to occur as tail.If the coin is tossed twice,find the probability distribution of number of tails.