List of top Mathematics Questions

A box contains 5 black and 4 white balls. A ball is drawn at random and its colour is noted. The ball is then put back in the box along with two additional balls of its opposite colour. If a ball is drawn again from the box, then the probability? that the ball drawn now is black, is :

Let the orthocenter an centroid of a triangle be $A(-3, 5)$ and $B(3, 3)$ respectively. If $C$ is the circumcentre of this triangle, then the radius of the circle having line segment $AC$ as diameter, is:

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 4x + 5 = 0$. then the quadratic equation whose roots are $\alpha^2 + \beta$ and $\alpha + \beta^2 $ is

If $\alpha, \beta, \gamma$ are any three angles, then $\cos \, \alpha + \cos \beta - \cos \, \gamma - \cos (\alpha + \beta + \gamma) =$

If $1 , \omega , \omega^2$ are the cube roots of unity, then $\frac{1}{1+2\omega} + \frac{1}{2+\omega } - \frac{1}{1+\omega } = $

In $\Delta ABC. a^3 . \cos (B - C) + b^3 . \cos(C - A) + c^3 . \cos (A - B) = $

If $z_{1} = 1 -2i ; z_{2} = 1 + i$ and $z_{3 } = 3 + 4i,$ then $ \left( \frac{1}{z_{1}} + \frac{3}{z_{2}}\right) \frac{z_{3}}{z_{2}} = $

The length of the transverse common tangent of the circles $x^2 + y^2 - 2x + 4y + 4 = 0$ and $x^2 + y^2 + 4x - 2y + 1 = 0 $ is

If $\frac{x^{4} + 24 x^{2} + 28}{\left(x^{2} + 1\right)^{3}} = \frac{A }{\left(x^{2} + 1\right)} + \frac{B}{\left(x^{2} + 1\right)^{2}} + \frac{C}{\left(x^{2} + 1\right)^{3}} $ then $A + C = $

If $\frac{x^{3}}{\left(2x-1\right)\left(x-1\right)^{2}} = A + \frac{B}{2x-1}+ \frac{C}{x-1}+ \frac{D}{\left(x-1\right)^{2}} $, then $2A - 3B + 4C + 5D = $

If the length of the latus rectum of an ellipse is $4$ units and the distance between a focus and its nearest vertex on the major axis is $\frac{3}{2}$ units, then its eccentricity is :

If the tangent at $(1, 7)$ to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x + 12y + c = 0$ then the value of c is:

\( f(x) = \left\{ \begin{array}{ll} \sin \frac{1}{x} , & \text{for} \, x \neq 0 \\ 0, & \text{for} \, x = 0 \end{array} \right. \) is:

The order and degree of the differential equation whose solution is \( y = cx + c^2 - 3c^3y^2 + 2 \), where \( c \) is a parameter, is:

The solution of \[ \frac{dv}{dt} + \frac{k}{m} v = -g \] is:

The mean and variance of a random variable \( X \) having binomial distribution are 4 and 2 respectively, then \( P(X = 1) \) is:

The value of \[ \int_{-1}^{1} (x - \lfloor x \rfloor) dx \quad (\text{where} \, \lfloor \cdot \rfloor \, \text{denotes the greatest integer function}) \] is:

The correct evaluation of \[ \int_0^{\frac{\pi}{2}} \sin^4 x \, dx \] is:

A unit vector perpendicular to the plane formed by the points \( (1, 0, 1) \), \( (0, 2, 2) \), and \( (3, 3, 0) \) is:

If \( \mathbf{a} = ( \hat{i} + \hat{j} + \hat{k} ) \), \( \mathbf{a} \times \mathbf{b} = \hat{i} - \hat{j} \), then \( \mathbf{b} \) is:

The two curves \( x^3 - 3x^2 + 2 = 0 \) and \( 3x y - y^3 - 2 = 0 \) intersect at an angle of:

The radius of the sphere \[ x^2 + y^2 + z^2 = 49, \quad 2x + 3y - z - 5\sqrt{14} = 0 \] is:

If at \( x = 1 \), the function \( x^4 - 62x^2 + ax + 9 \) attains its maximum value on the interval \( [0, 2] \), then the value of \( a \) is:

The value of \( \lambda \) does the line \( y = x + \lambda \) touches the ellipse \( 9x^2 + 16y^2 = 144 \) is: