List of top Mathematics Questions

In $n$ is an odd positive integer and $(1+x +x^2 +x^3)^n =\displaystyle\sum_{r=0}^{3n} a_rx^r$ then $a_0 -a_1+a_2-a_3 +\dots -a_{3n}$ is equal to

Angles of elevation of the top of a tower from three points (collinear) $A, B$ and $ C$ on a road leading to the foot of the tower are $30^\circ$, $45^\circ$ and $60^\circ$ respectively. The ratio of $AB$ to $BC$ is

The value of $\left| \frac{1+ i \sqrt{3}}{\left( 1 + \frac{1}{i+1}\right)^2} \right|$ is

The sum of the first n terms $ \frac {1^2}{1} +\frac {1^2+2^2}{1+2}+ \frac {1^2 +2^2+3^2}{1+2+3}+$ $\dots$ is

If $\alpha , \beta ,\gamma$ are the roots of $x^3-2x+1=0$, then the value of $(\sum \frac {1} {\alpha +\beta -\gamma}$) is

If the focii of $\frac {x^2}{16}+\frac{y^2}{4}=1 $ and $\frac {x^2}{a^2}-\frac{y^2}{3}=1 $ coincide, then value of $a$ is

Locus of a point which moves such that its distance from the $X-axis$ is twice its distance from the line $x - y = 0$ is

The sum of all the positive divisors less than $250$ of the number $484$ is

The area of the parallelogram with $\vec{a}$ and $\vec{b}$ as adjacent sides is $20\, s \,units$. Then the area of the parallelogram having $7\vec{a} + 5\vec{b}$ and $8\vec{a} + 11\vec{b}$ as adjacent sides is

The point of contact of the tangent $x + 2y + 2 = 0$ with the parabola $x^2 = 16y$ is

The equation of the line passing through $ (0,0) $ and intersection of $ 3x-4y=2 $ and $ x+2y=-4 $ is

If $A = \begin{bmatrix}3&x-1\\ 2x+3&x+2\end{bmatrix}$ is a symmetric matrix, then the value of $x$ is

The coordinates of a moving point $p$ are $(2t^2 + 4, 4t + 6)$. Then its locus will be a

The number of solutions of $2\,\sin x + \cos\, x = 3$ is

If $\sin\,\theta$ and $\cos \theta $ are the roots of the equation $ax^2 - bx + c = 0$, then $a, b$ and $c$ satisfy the relation

If the three points $A(1,6), B(3, -4)$ and $C(x, y)$ are collinear then the equation satisfying by $x$ and $y$ is

Let $\tan \,\alpha = \frac{a}{a+1}$ and $\tan \,\beta = \frac{1}{2a + 1}$ then $\alpha + \beta$ is

If $\log_{7} \,2 = ?$, then the value of $\log_{49}\, \left(28\right)$ is

If sin $\theta = \frac{2t}{1+t^{2}}$ and $?$ lies in the second quadrant, then $cos\,\theta$ is equal to

The solution of $\frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x}$ is

If $^nC_4,\, ^nC_5$ and $^nC_6$ are in $A.P.$, then $n$ is

Let $f(x) = \tan^{-1}x$. Then $f'(x) + f''(x)$ is = $0$, when $x$ is equal to