List of top Mathematics Questions

$\int^{\frac{\pi}{2}}_0 \log(\tan\,x)dx=$
The value of $\int^2_{-2}(ax^3+bx +c)dx$ depends on the
If the coefficients of $x^5$ and $x^6$ in $\left(2+\frac{x}{3}\right)^{n}$ are equal, then $n$ is
Consider an experiment $E$ in which a box contains $10$ identical tickets numbered $1$ to $10$ and $2$ tickets are drawn at random from the box. What is the probability that both the tickets have even numbers on them?
The value of $\frac{\tan 330^{\circ} \sec 420^{\circ} \sin 300^{\circ}}{\tan 135^{\circ} \sin 210^{\circ} \sec 315^{\circ} } $ is equal to
Find the length of the diagonal of the parallelepiped formed by planes drawn through the points $ (2,3,5) $ and $ (5,9,7), $ parallel to the co-ordinate planes?
Let $n\ge2$ be an integer, $A=\begin{pmatrix}\cos\left(2\pi/ n\right)&\sin \left(2\pi / n\right)&0\\ -\sin\left(2\pi / n\right)&\cos\left(2\pi / n\right)&0\\ 0&0&1\end{pmatrix}$ and $?$ is the identity matrix of order $3$. Then
Suppose $M=\int\limits_{0}^{\pi / 2} \frac{\cos x}{x+2} d x$, $N=\int\limits_{0}^{\pi / 4} \frac{\sin x \cos x}{(x+1)^{2}} d x$ Then, the value of $(M-N)$ equals
Out of $7$ consonants and $4 $ vowels, the number of words (not necessarily meaningful) that can be made, each consisting of $3$ consonants and $2 $ vowels, is
The angle of intersection between the curves $y=\left[\left|\sin\,x\right|+\left|\cos\,x\right|\right]$ and $x^{2}+y^{2}=10, $ where $[x]$ denotes the greatest integer $= x,$ is
The minimum value of $2^{\sin\, x} + 2^{\cos\, x}$ is
The coefficient of $x^3$ in the infinite series expansion of $\frac{2}{\left(1-x\right)\left(2-x\right)},$ for $\left|x\right|< 1,$ is
Let \(R\) be the set of all real numbers and \(f : R \rightarrow R\) be given by \(f(x) = 3x^2 + 1\).Then the set \(f ^{-1}\left(\left[1, 6\right]\right)\) is
The equation of the common tangent with positive slope to the parabola $y^{2}=8\sqrt{3x}$ and the hyperbola $4x^2 - y^2 = 4$ is
The point on the parabola $y^2 = 64x$ which is nearest to the line $4x + 3y + 35 = 0$ has coordinates
The remainder obtained when \(1!+2!+3!+.....+11!\) is divided by 12 is
The area of the parallelogram whose adjacent sides are $\hat{i}+ \hat {k} $ and $2\hat {i}+\hat {j}+\hat {k}$ is
Area of the region bounded by two parabolas $y\, =\, x^2$ and $x \,= \, y^2 $ is
If $a, b$ and $c$ are in A.P., then the value of $\begin{vmatrix} {x+2}&{x+3} &{x+a}\\ {x+4}&{x+5}& {x+b} \\ {x+6}&{x+7} &{x+c}\\ \end{vmatrix}$ is
How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$, if each number starts with $67$ and no digit appears more than once ?
The order and degree of the differential equation $y=x\frac{dy}{dx}+\frac{2}{\frac{dy}{dx}}$ is
The value of $\sin (2\, \sin^{-1}\, 0.8)$ is equal to
The value of the integral $\int_\limits{-\pi/4}^{\pi/4} \log (\sec \theta-\tan \theta) d \theta$ is
A stone is dropped into a quiet lake and waves move in circles at the speed of $5\, cm/sec$. At that instant, when the radius of circular wave is $8 \,cm$, how fast is the enclosed area increasing ?
The standard deviation of $9, 16, 23, 30, 37, 44, 51$ is