List of top Mathematics Questions

The value of $k$ which makes $f(x)=\{\begin{array}{l}\sin x,x\ne 0\\ k,x=0\end{array}$ continuous at $x=0$, is:

The equation xy = 0 in three-dimensional space represents

The value of C in (0, 2) satisfying the mean value theorem for the function \(f(x)=x(x-1)^2, x∈[0,2]\) is equal to

If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7, then the number of relations from A to B is

In the following trigonometry expression, find the value of (MN).$\frac{(1+\cos x)}{(1-\sin x)}(\sin x+\cos x-1{)}^2=M{\sin }^{N}x$

What is the number of different messages that can be represented by three a’s and two b’s?

The solution of differential equation $dy=(4+y^2)dx$ is:

Let $\overrightarrow{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k},\overrightarrow{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k}$ be three non-zero vectors such that $\overrightarrow{c}$ is a vector perpendicular to both $\overrightarrow{a}$ and $\overrightarrow{b}$. If the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\pi }{6}$ then $\left|\begin{array}{lll}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|=?$

In a binomial distribution, the mean is $\frac{2}{3}$ and variance is $\frac{5}{9}$. What is the probability that random variable $D=2?$

What is ${\int }_0^a\frac{f(a-x)}{f(x)+f(a-x)}dx$ equal to?

If $(1 + x + x^2)^{48} = a_0 + a_1x + a_2x^2+ ..... + a_{96}x^{96},$ then value of $a_0-a_2 +a_4 -a_6..... + a_{96} $ is

Directions: The following question has four choices, out of which one or more are correct. Assume that the nuclear binding energy per nucleon $\left(\frac{B}{A}\right)$ versus mass number (A) is as shown in the figure. Use this plot to choose the correct answer(s) from the choices given below.

If the coordinates of one end of a diameter of the circle  x²+y²+4x–8y+5=0, is (2,1), the coordinates of the other end is 

A plane x + 2y + 2z – 15 = 0 cuts a sphere x² + y² + z² – 2y – 4z – 11 = 0 in a circular section. What is the radius of the cut section?

Directions: The following question has four choices, out of which one or more are correct. The potential energy function of a particle moving in one dimension is $U=k[x-\frac{x^3}{3a^2}],$ where $a$ and $k$ areconstants. Then,

Directions: The following question has four choices, out of which one or more are correct.In a triangle $\mathrm{\Delta }PQR,\cos (P-R)\cos (Q)+\cos (2Q)=0$Which of the following options is/are correct?

The cubic equation whose roots are the AM, GM and HM of the roots of x² - 2px + q² = 0 is

The number of solutions of the equation tan x + sec x = 2 cos x and cos x ≠ lying in the interval (0, 2π) is

$\int e^{x\log a}\cdot e^{x}dx$ is equal to

The radius of a cylinder is increasing at the rate of 3 m/s and its altitude is decreasing at the rate of 4 m/s. The rate of change of volume, when radius is 4 m and altitude is 6 m, is

 If ⁿC4, ⁿC5 and ⁿC6 are in A.P., then n is 

If the coefficients of 5th, 6th and 7th terms in the expansion of (1+x)n are in A.P. then n =

The radius of a circle is increasing at the rate of 0.1 cm/s. When the radius of the circle is 5 cm, the rate of change of its area is

In a triangle ABC, tan C < 0. Then