List of top Questions asked in BITSAT

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 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

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

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

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

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

Which of the following substances does not undergo hydrolysis in aqueous solution?

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

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

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

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 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

The combination of the gates shown in the following figure yields

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 equation of the normal to a parabola which is perpendicular to a given line. This involves:

The angle between two lines in 3D space can be found using:

In a Linear Programming Problem (LPP), the objective function Z is minimized subject to constraints. Where does the minimum value occur?

Find the term independent of \( x \) in the expansion of \( (1 + x)^{n} (1 + \frac{1}{x})^{n} \).

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

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

Let \( f : \mathbb{R} \to \mathbb{R} \) and \( g : \mathbb{R} \to \mathbb{R} \) such that \( g(x) \neq 0 \) for all \( x \in \mathbb{R} \), and \( f = f^{-1} \). Which of the following is correct?

A person travels from Hyderabad to Goa and returns, but does not use the same bus for both journeys. If there are 25 buses available for each direction, how many ways can the round trip be made?

If a fair coin is tossed 5 times, what is the probability of getting exactly 3 heads?

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