List of top Questions asked in BITSAT

Evaluate: \( \int e^{x} \sin x \cos x \, dx \)

In a Wheatstone Bridge, all four arms have equal resistance of 1 \(\Omega\) each. A battery is connected across the bridge, and a galvanometer is connected between the middle junctions. What is the current flowing through the galvanometer?

Evaluate: \( \cot^{-1}(2) - \cot^{-1}(8) - \cot^{-1}(18) - \dots \)

Let \( A = \begin{bmatrix} 1 & 0 & 0 0 & 1 & 0 3 & 2 & 1 \end{bmatrix} \). Find \( A^{100} \).

In a pulley system, two blocks are connected by a string over a frictionless pulley. If tensions \(T_1\) and \(T_2\) are given in two segments of the string, what is their relation?

The equation of a plane passing through three non-collinear points is determined using:

Statements:
• Some cashmere jackets are fashionable.
• Some cashmere jackets are not suede jackets.
• No suede jacket is fashionable.
Which of the following conclusions is correct?

Find the total mechanical energy of a satellite of mass \(m\) revolving in a circular orbit of radius \(a\) around the Earth (mass \(M\)).

For a reaction, the initial concentrations and corresponding rates are given. Which method is used to calculate the rate constant?

If \(\log_8 x = \frac{1}{3}\), find the value of \(x\).

A block is placed on a wedge with coefficient of friction \(\mu = 0.5\). The wedge is accelerated horizontally towards the block. What is the minimum acceleration required so that the block does not slide down the wedge?

If \( \vec{a} = 2\hat{i} + \hat{j} + 2\hat{k} \), then the value of \( |\hat{i} \times (\vec{a} \times \hat{i})|^2 + |\hat{j} \times (\vec{a} \times \hat{j})|^2 + |\hat{k} \times (\vec{a} \times \hat{k})|^2 \) is equal to

How many moles of oxygen are required to completely combust 1 mole of propane (C\(_3\)H\(_8\))?

Let the foot of perpendicular from a point \( P(1,2,-1) \) to the straight line \( L: \frac{x}{1} = \frac{y}{0} = \frac{z}{-1} \) be \( N \). Let a line be drawn from \( P \) parallel to the plane \( x + y + 2z = 0 \) which meets \( L \) at point \( Q \). If \( \alpha \) is the acute angle between the lines PN and PQ, then \( \cos \alpha \) is equal to

The value of \( \int e^{\tan \theta} (\sec \theta - \sin \theta) \, d\theta \) is

What is the IUPAC name of the compound: CH\(_3\) – CH\(_2\) – CH(CH\(_3\)) – CH\(_2\) – CH\(_3\)

The area of the region bounded by the curves \( x = y^2 - 2 \) and \( x = y \) is

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation \[ \frac{2}{1}\text{X} + \frac{2}{1}\text{X} = \frac{4}{2}\text{Y} \] The binding energies per nucleon of \( \frac{2}{1}\text{X} \) and \( \frac{4}{2}\text{Y} \) are 1.1 MeV and 7.6 MeV respectively. The energy released in this process is

The magnitude of projection of line joining (3, 4, 5) and (4, 6, 3) on the line joining (−1, 2, 4) and (1, 0, 5) is

A series LCR circuit consists of \( R = 80\,\Omega \), \( X_L = 100\,\Omega \), and \( X_C = 40\,\Omega \). The input voltage is \( 2500 \cos(100\pi t) \) V. The amplitude of current in the circuit is

Which of the following gases has the highest rate of diffusion?

The combination of the gates shown in the following figure yields

A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and of same material as that of P are now combined as shown in the figure. The ray will now suffer

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability \( \frac{4}{3} \) for this wavelength, will be:

A first-order reaction is 25% complete in 30 minutes. How much time will it take for the reaction to be 75% complete?