List of top Mathematics Questions

$Sin^2 \; 17.5^{\circ} + Sin^2 \; 72.5^{\circ}$ 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

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

Which is true ?

Let $A=\begin{vmatrix} 5& 5\alpha & \alpha \\[0.3em] 0 &\alpha &5\alpha \\[0.3em] 0 &0& 5 \end{vmatrix}$ , If $\left|\,A^2\,\right|=25$,then $\left|\,\alpha\,\right|$ equals

The equation of a tangent to the parabola $y^2 = 8x$ is $y = x + 2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

A tower stands at the centre of a circular park. $A$ and $B$ are two points on the boundary of the park such that $AB (= a)$ subtends an angle of $60^\circ$ at the foot of the tower, and the angle of elevation of the top of the tower from $A$ or $B$ is $30^??. The height of the tower is

Consider a family of circles which are passing through the point (-1, 1) and are tangent to xaxis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval

The largest interval lying in $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ for which the function $f \left(x\right)=4^{-x^2}+cos^{-1}\left(\frac{x}{2}-1\right)+log\left(cos\,x\right)$ is defined, is

The set $S=\left\{1, 2, 3, \dots, 12\right\}$ is to be partitioned into three sets $A, B, C$ of equal size. Thus, $A\cup B\cup C=S, A\cap B = B\cap C = A \cap C=\phi.$ The number of ways to partition $S$ is