List of top Mathematics Questions

If \( \sin^{-1} x + \sin^{-1} y = \frac{\pi}{2} \), then \( \cos^{-1} x + \cos^{-1} y \) is equal to

If the normal to the curve \( y = f(x) \) at \( (3, 4) \) makes an angle \( \frac{3\pi}{4} \) with the positive x-axis, then \( f'(3) \) is equal to

The equation of a directrix of the ellipse \( \frac{x^2}{16} + \frac{y^2}{25} = 1 \) is

If the normal at \( (a^2, 2a^2) \) on the parabola \( y^2 = 4ax \), meets the parabola again at \( (a^2, 2a^2) \), then

The length of the straight line \( x - 3y = 1 \) intercepted by the hyperbola \( x^2 - 4y^2 = 1 \) is

The curve described parametrically by \[ x = t^2 + 2t - 1, \quad y = 3t + 5 \] represents

If \( \cos x + \cos 2x = 1 \), then the value of \( \sin^{12}x + 3\sin^{10}x + 3\sin^8x + \sin^6x - 1 \) is equal to

Let the pairs \( \mathbf{a}, \mathbf{b} \) and \( \mathbf{c}, \mathbf{d} \) each determine a plane. Then the planes are parallel if

The area of a parallelogram with \( 3\hat{i} + \hat{j} - 2\hat{k} \) and \( \hat{i} - 3\hat{j} + 4\hat{k} \) as diagonals is

A particular solution of $ \frac{dy}{dx} = (x+9y)^2$ when $ x = 0, y = \frac{1}{27}$ is

The imaginary part of $\frac{\left(1+i\right)^{2}}{i\left(2i-1\right)} $ is

The probability that the same number appear on throwing three dice simultaneously, is

The solution of the differential equation $\frac{d y}{d x}+\frac{2 y x}{1+x^{2}}=\frac{1}{1+x^{22}}$ is

If a=\(\log _{2} 3, b=\log _{2} 5, c=\log _{7} 2,\) then \(\log _{140} 63\) in terms of a, b, c is

If $(\cos \theta+i \sin \theta)(\cos 2 \theta+i \sin 2 \theta) \ldots . .(\cos n \theta+i \sin n \theta)=1$, then the value of $\theta$ is, $m \in N$

The length of the common chord of the ellipse $\frac{(x+1)^{2}}{9}+\frac{(y-2)^{2}}{4}=1$ and the circle $x-1^{2}+y-2^{2}=1$ is

If $\sin^{-1} \, x + \sin^{-1} \, y = \frac{\pi}{2},$ then $\frac{dy}{dx} $ is equal to

For the hyperbola $\frac{x^{2}}{\cos ^{2} \alpha}-\frac{y^{2}}{\sin ^{2} \alpha}=1$, which of the following remains constant when $\alpha$ varies

$(x -1) (x^2 - 5x + 7) < (x -,1),$ then $x$ belongs to

If $ P\left(A\right)=\frac{1}{12}, P\left(B\right)=\frac{5}{12},$ and $P\left(B|A\right) =\frac{1}{15}$ then $p\left(A\cup B\right)$ is equal to

The product of all values of $(\cos \alpha + i \sin \alpha)^{3/5}$ is equal to

If (x +y )sin u = $x^2y^2$, then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} = $

If the normal at $(ap^2, 2ap)$ on the parabola $y^2 = 4ax,$ meets the parabola again at $(aq^2, 2aq)$, then

The sum of the series $ \frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+... $ upto $ n $ term is

If the rank of the matrix $\begin{bmatrix}-1 &2&5\\ 2&-4&a-4\\ 1&-2&a+1\end{bmatrix}$ is 1, then the value of $a$ is