List of top Mathematics Questions

Let $f(x) = \begin{cases} -2 \sin x, &x \leq - \pi /2 \\ a \sin x +b, & - \pi /2 < x < \pi /2 \\ \cos \, x , & x \geq \pi /2 \end{cases}$ then the? values of a and b so that $f(x)$ is continuous are
If the medians $AD$ and $BE$ of the triangle with vertices $A(0, b), B(0, 0), C(a, 0)$ are mutually perpendicular, then
If $A, B, C, D$ are four points and $\vec{AB} = \vec{DC}$ , then $\vec{AC} + \vec{BD} = $
$\frac{1+\tan ^{2} x}{1-\tan ^{2} x} d x$ is equal to
The ninth term of the expansion $\left(3x-\frac {1}{2x}\right)^8$ is
A vector perpendicular to the plane containing the points $A (1, -1, 2), B (2, 0, -1), C (0,2,1)$ is
The solution of $Tan^{-1}x+ 2cot^{-1}x=\frac {2\pi}{3}$ is
$Sin^2 \; 17.5^{\circ} + Sin^2 \; 72.5^{\circ}$ is equal to
The value of $\int \frac{x^2+1}{x^2-1}dx$ is
The value of $\int e^x(x^5+5x^4+1).dx $ is
If $x > 0$ and $\log_{3} x+\log_{3}\left(\sqrt{x}\right)+\log_{3}\left(\sqrt[4]{x}\right)+\log_{3}\sqrt[8]{x}+\log_{3}\left(\sqrt[16]{x}\right)+....=4,$ then x equals

The orthocentre of the triangle with vertices $O(0, 0), A(0,3/2)$ and $B(-5, 0)$ is

If $\frac {x^2}{36}-\frac{y^2} {k^2} = 1$ is a hyperbola, then which of the following statements can be true ?
If a and b are vectors such that $|a+b|=|a-b|$ then the angle between a and b is
The value of the integral $\int\limits_0^{\pi/2}$($Sin^{100} x-Cos^{100}x)dx$ is
If $3x + y + k = 0$ is a tangent to the circle $x^2+y^2=10$ the values of k are,
If $sin \, 3 \,\theta\, = \, Sin \, \theta$ , how many solutions exist such that $-2 \pi
Out of $15$ persons, $10$ can speak Hindi and $8$ can speak English. If two persons are chosen at random, then the probability that one person speaks Hindi only and the other speaks both Hindi and English is
If $A = \begin{bmatrix} {1}&{-2} &{2}\\ {0}&{2}& {-3} \\ {3}&{-2}&{4}\\ \end{bmatrix} $,then $A . adj(A)$ is equal to
If $\vec {a}= {2\hat{i}}+3\hat{j}-\hat k,\vec b = \hat i+2 \hat j-5 \hat k ,\vec{ c} =3 \hat i+ 5\hat j-\hat k,$ then a vector perpendicular to $\vec{a}$ and in the plane containing $\vec {b}$ and $\vec {c}$ is
OA and BO are two vectors of magnitudes 5 and 6 respectively. If $\angle B O A=60^{\circ}$, then $0 A \cdot O B$ is equal to
Which of the following statements is true?
$x^2 + y^2 -6x-6y + 4 = 0, x^2 + y^2 - 2x - 4y + 3 - 0 , x^2 + y^2 + 2k x + 2y +1 = 0$. If the Radical centre of the above three circles exists, then which of the following cannot be the value of $k$ ?
Let $\alpha$, $\beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha}{2},2\beta$ be the roots of the equation $x^2-qx+r=0.$ Then, the value of r is
$ lim_ { x \to \frac{\pi}{4}} \frac{ \int \limits_2^{sec^2 \, x} \, f \, (t) \, dt }{ x^2 - \frac{\pi^2}{ 16}} $ equals