List of top Mathematics Questions asked in VITEEE

The number of positive integral solutions of the equation \( x_1 + x_2 + x_3 + x_4 = 1050 \) is

The value of the integral \[ \int e^x \left( \frac{1 - x}{1 + x^2} \right)^2 dx \] is

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

The angle between the tangents at those points on the curve \( x = t^2 + 1 \) and \( y = t^2 - t - 6 \) where it meets the x-axis is

The area of the region bounded by the straight lines \( x = 0 \) and \( x = 2 \) and the curves \( y = 2x^2 \) and \( y = 2x - x^2 \) is equal to

The value of \( \int_{1}^{4} |x - 3| \, dx \) 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 \( \sin^{-1} x + \sin^{-1} y = \frac{\pi}{2} \), 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

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

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

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

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

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

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

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

A box contains $9$ tickets numbered $1$ to $9$ inclusive. If $3$ tickets are drawn from the box one at a time, the probability that they are alternatively either {odd, even, odd} or {even, odd, even} 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

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

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

The curve described parametrically by $x = t^2 + 2t - 1, y = 3t + 5$ represents