List of top Mathematics Questions asked in BITSAT

The equation of the curve passing through the point $\left(a, -\frac{1}{a}\right)$ and satisfying the differential equation $y-x \frac{dy}{dx}=a\left(y^{2}+\frac{dy}{dx}\right)$ is

Consider $\frac{x}{2}+\frac{y}{4} \ge1,$ and $\frac{x}{3}+\frac{y}{4} \le1, x, y \ge0.$ Then number of possible solutions are :

If $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$ are in A.P. where $a_{i}>0$ for all $i$, then $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\ldots .+$ $\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_{n}}}$ is?

With the usual notation $\displaystyle \int_1^2 ([x^2]-[x]^2)dx$ is equal to

What is the slope of the normal at the point (at, 2at) of the parabola y = 4ax ?

The coefficient of $x^2$ term in the binomial expansion of $\left(\frac{1}{3}x^{1/2}+x^{-1/4}\right)^{10}$ is :

For the following feasible region, the linear constraints are

The equation of the circle which passes through the point $(4, 5)$ and has its centre at $(2, 2)$ is

Let $y = e^{2x}$ . Then $\left(\frac{d^{2}y}{dx^{2}}\right) \left(\frac{d^{2}x}{dy^{2}}\right) $ is

In a binomial distribution, the mean is $4$ and variance is $3$. Then its mode is :

The probability of getting $10$ in a single throw of three fair dice is :

Let \(A, B, C\) be the angles of a plane triangle. If
\[ \tan \frac{A}{2} = \frac{1}{3} \quad \text{and} \quad \tan \frac{B}{2} = \frac{2}{3}, \]
then \(\tan \frac{C}{2}\) is equal to:

If the amplitude of \(z - 2 - 3i\) is \(\pi/4\), then the locus of \(z = x + i y\) is:

The coefficient of \(x^3\) in the expansion of
\[ \left(x - \frac{1}{x}\right)^7 \]
is:

If \(x > 0\), then
\[ 1 + \frac{\log x}{1!} + \frac{(\log x)^2}{2!} + \cdots = \]

The locus of the point of intersection of the lines
\[ x = \frac{1 - t^2}{1 + t^2}, \quad y = \frac{2 a t}{1 + t^2} \]
represents:

Eccentricity of ellipse
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \] if it passes through points \((9,5)\) and \((12,4)\) is:

The value of
\[ \lim_{n \to \infty} \frac{1 + 2 + 3 + \cdots + n}{n^2 + 100} \]
is equal to:

Evaluate
\[ \lim_{x \to 0} \sqrt{\frac{x - \sin x}{x + \sin^2 x}} \]

Number of solutions of the equation
\[ \tan^{-1}(1+x) + \tan^{-1}(1-x) = \frac{\pi}{2} \]
are:

If
\[ A = \frac{1}{3} \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix} \] is an orthogonal matrix, then:

The points represented by the complex numbers \[ 1 + i, \quad -2 + 3i, \quad \frac{5}{3} i \] on the Argand plane are:

If matrix
\[ A = \begin{bmatrix} 3 & -2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1 \end{bmatrix}, \quad \text{and} \quad A^{-1} = \frac{1}{k} \, \text{adj}(A), \]
then \(k\) is:

If \(x, y, z\) are complex numbers, and
\[ \Delta = \begin{vmatrix} 0 & -y & -z \\ \overline{y} & 0 & -x \\ \overline{z} & \overline{x} & 0 \end{vmatrix}, \]
then \(\Delta\) is: