List of top Mathematics Questions

The integral
\(\frac{24}{\pi} \int_{0}^{\sqrt{2}} \frac{2 - x^2}{(2 + x^2) \sqrt{4 + x^4}} \, dx\)
is equal to _______.

In the given figure, the diameter of the circle is 3 cm. AB and MN are two diameters such that MN is perpendicular to AB. In addition, CG is perpendicular to AB such that \( AE : EB = 1 : 2 \), and DF is perpendicular to MN such that \( NL : LM = 1 : 2 \). The length of DH in cm is:
AB and MN are two diameters
The degree measure of \(\frac{\pi}{32}\) is equal to
Let the coefficients of the middle terms in the expansion of\(\begin{array}{l} \left(\dfrac{1}{\sqrt 6}+ \beta x\right)^4, \left(1 – 3\beta x\right)^2 \text{and}\left(1 – \dfrac{\beta}{2}x\right )^6, \beta > 0,\end{array}\)respectively form the first three terms of an A.P. If d is the common difference of this A.P., then \(\begin{array}{l} 50-\frac{2d}{\beta^2} \end{array}\)is equal to _______.
The differential equation of the family of circles passing through the points (0, 2) and (0, –2) is
The value of the integral \(∫^{ \frac{π}{2}}_{ \frac{-π}{2}} \frac{dx}{(1+e^x)(sin^6x+cos^6x)}\)  is equal to
The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is _________.
Let $PQRS$ be a quadrilateral in a plane, where $QR =1, \angle PQR =\angle QRS =70^{\circ}, \angle PQS =15^{\circ}$ and $\angle PRS =40^{\circ}$. If $\angle RPS =\theta^{\circ}, PQ =\alpha$ and $PS =\beta$, then the interval(s) that contain(s) the value of $4 \alpha \beta \sin \theta^{\circ}$ is/are
If a quadratic equation \(2x^2 + kx+3=0\) have two equal roots then \(k=\)
Let a, b be two non-zero real numbers. If p and r are the roots of the equation x2 – 8ax + 2a = 0 and q and s are the roots of the equation x2 + 12bx + 6b = 0, such that \(\frac{1}{p}\),\(\frac{1}{q}\),\(\frac{1}{r}\),\(\frac{1}{s}\) are in A.P., then a–1 – b–1 is equal to _________.
If \(\lim_{n\rightarrow \infty}\) \(\frac{(n+1)^{k-1}}{n^{k+1}}[(nk+1)+(nk+2)+....+(nk+n)]=33.\lim_{n\rightarrow \infty}\frac{1}{n^{k+1}}.[1^k+2^k+3^k+....+n^k]\)
then the integral value of k is equal to _______.
Let ⊙ be a binary operation on Q - {0} defined by a⊙b=\(\frac{a}{b}\). Then 1⊙(2⊙(3⊙4)) is equal to

Let P and Q be any points on the curves (x – 1)2 + (y + 1)2 = 1 and y = x2, respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interval

Let for some real numbers \(α\) and \(β\), \(a = α – iβ\). If the system of equations \(4ix + (1 + i) y = 0\) and \(8\bigg(cosx\frac{2π}{3}+i\;sin\frac{2π}{3}\bigg)x+\bar ay=0 \)has more than one solution, then \(\frac{α}{β}\) is equal to

The number of distinct real roots of the equation x5(x3 – x2 – x + 1) + x (3x3 – 4x2 – 2x + 4) – 1 = 0 is ______ .

A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If \(σ^2 \) is the variance of X, then 100 σ2 is equal to ____.

The number of solutions of |cos x| = sinx, such that –4π ≤ x ≤ 4π is :

Let the relation R is defined in N by \(a \mathbb{R} b\), if \(3a+2b = 27\) , then R is
The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is
Which of the following is not an irrational number?

If the sum of all the roots of the equation \(e^{2x} - 11e^x - 45e^{-x} + \frac{81}{2} = 0\)
 is logeP, then p is equal to _____.

Let \(S ={  (\begin{matrix}   -1 & 0 \\   a & b \end{matrix}), a,b, ∈(1,2,3,.....100)}\) and 
let \(T_n = {A ∈ S : A^{n(n + 1)} = I}. \)
Then the number of elements in \(\bigcap_{n=1}^{100}\) \(T_n \) is

Let A = {n∈N : H.C.F. (n, 45) = 1} and
Let B = {2k :k∈ {1, 2, …,100}}. Then the sum of all the elements of \(A∩B\) is ___________

The number of matrices
\(A=\begin{pmatrix}   a & b \\   c & d \\ \end{pmatrix}\), where a,b,c,d ∈−1,0,1,2,3,…..,10
such that A = A-1, is ______.

If the sum of solutions of the system of equations 2sin2θ – cos2θ = 0 and 2cos2θ + 3sinθ = 0 in the interval [0, 2π] is kπ, then k is equal to _______.