List of top Mathematics Questions

From the top of a lighthouse, the angles of depression of two stations on the oposite sides of it at a distance d apart are $\alpha$ and $\beta$. The height of the lighthouse is

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3 - 3x^2 + 3x + 7 = 0$, and w is cube root of unity, then the value of $\frac{\alpha-1}{\beta-1} + \frac{\beta-1}{\gamma-1} + \frac{\gamma-1}{\alpha-1}$ is equal to

The perimeter of the locus represented by arg $\left( \frac{z + i}{z-i}\right) = \frac{\pi}{4}$ is equal to

The number of solutions of the equation $\sin \, 2x + 2 \, \sin \, x - \cos \, x - 1 = 0$ in the range $0 \leq x \leq 2 \pi$ is

If $\cos^{-1} \frac{3}{5} + \cos^{-1} \frac{12}{13} = \cos^{-1} k$, then the value of $k$ is

If $\cos \, 3x \, \cos \, 2x \, \cos \, x = \frac{1}{4} $ and $0 < x < \frac{\pi}{4}$, then the value of $x$ is

If $(1 + \tan \, 1^{\circ})(1 + \tan \, 2^{\circ}) ...... (1 + \tan \, 45^{\circ}) = 2^n$, then n is

The interval in which the function $f\left(x\right) = \frac{4x^{2}+1}{x}$ is decreasing is :

If the parabola $y^2 = 4ax$ passes through the point $(1, -2)$, then the tangent at this point is

If two different numbers are taken from the set $\{0,1,2,3, \ldots \ldots, 10\}$then the probability that their sum as well as absolute difference are both multiple of $4$, is :

Let $z \in C$, the set of complex numbers. Then the equation, $2 | z + 3i| - | z - i| = 0 $ represents :

The normal to the curve $y(x-2)(x-3)=x+6$ at the point where the curve intersects the y-axis passes through the point :

The radical centre of the circles $x^{2}+y^{2}-4\,x-6 \,y+5=0$ $x^{2}+y^{2}-2\,x-4 \,y-1=0$ and $x^{2}+y^{2}-6 \,x-2 \,y=0=0$ lies on the line

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

Let $S$ and $S'$ be the foci of an ellipse and B be one end of its minor axis. If $SBS'$ is an isosceles right angled triangle then the eccentricity of the ellipse is

If $a$ is a unit vector, then $| a \times \hat{ i }|^{2}+| a \times \hat{ j }|^{2}+| a \times \hat{ k }|^{2}=$

If $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 ,$ then $\frac{d^2 y}{dx^2} = $

If $cosec\, \theta - \cot \theta = 2017$, then quadrant in which $\theta $ lies is

$A$ straight line makes an intercept on the $Y$-axis twice as long as that on $X$-axis and is at a unit distance from the origin. Then the line is represented by the equations

For the parabola $y^2 + 6\,y - 2x = - 5$ I. the vertex is $( - 2,-3)$ II. the directrix is $y + 3 = 0$ Which of the following is correct?

A bag contains $5$ red balls, $3$ black balls and $4$ white balls are drawn at random. The probability that they are not of same colour is

If $(27)^{999}$ is divided by $7$, then the remainder is :

The value of $(^{21}C_{1} - ^{10}C_{1}) + (^{21}C_{2} - ^{10}C_{2}) + (^{21}C_{3} - ^{10}C_{3}) +(^{21}C_{4} - ^{10}C_{4}) +....+(^{21}C_{10} - ^{10}C_{10})$ is :

The angle between a pair of tangents drawn from a point \( T \) to the curve \[ x^2 + y^2 + 4x - 6y - 9 = 3x + 1 \] is

If matrix \( A = \begin{pmatrix} 3 & 2 & 4 \\1 & 2 & -1 \end{pmatrix} \) and