List of top Questions asked in BITSAT

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:
If \[ y = \frac{x}{x+1} + \frac{x+1}{x}, \] then \[ \frac{d^2 y}{dx^2} \text{ at } x = 1 \text{ is equal to:} \]
Let \(y = e^{2x}\). Then \(\frac{d^2 y}{dx^2} \cdot \frac{d^2 x}{dy^2}\) is:
The value of the integral
\[ \int_a^b \frac{\sqrt{x} \, dx}{\sqrt{x} + \sqrt{a + b - x}} \]
is:
Evaluate
\[ \int e^{x^2} (2x + x^3) (3 + x^2)^2 \, dx \]
If
\[ \int_0^a f(2a - x) \, dx = m \quad \text{and} \quad \int_0^a f(x) \, dx = n, \]
then
\[ \int_0^{2a} f(x) \, dx \]
is equal to:
The integrating factor of the differential equation
\[ \sin x \frac{dy}{dx} + 2y \cos x = 1 \]
is:
The expression satisfying the differential equation \[ (x^2 - 1) \frac{dy}{dx} + 2xy = 1 \] is:
Let \(\mathbf{a} = \mathbf{i} - \mathbf{k}, \quad \mathbf{b} = x\mathbf{i} + \mathbf{j} + (1-x)\mathbf{k}, \quad \mathbf{c} = y\mathbf{i} + x\mathbf{j} + (1+x-y)\mathbf{k}\). Then \([\mathbf{a}, \mathbf{b}, \mathbf{c}]\) depends on:
The sum \[ 1 + \frac{1+a}{2!} + \frac{1+a+a^2}{3!} + \cdots \] is equal to:
The Boolean expression \(\sim(p \vee q) \vee (\sim p \wedge q)\) is equivalent to:

In the circuit shown, the symbols have their usual meanings. The cell has emf E. X is initially joined to Y for a long time. Then, X is joined to Z. The maximum charge on C at any later time will be: 

A point object O is placed in front of a glass rod having spherical end of radius of curvature 30cm. The refractive index of glass is μ = 1.5. The image would be formed at: