List of top Questions asked in BITSAT- 2024

A simple pendulum doing small oscillations at a place $ R $ height above the Earth's surface has a time period of $ T_1 = 4 \, {s} $. $ T_2 $ would be its time period if it is brought to a point which is at a height $ 2R $ from the Earth's surface. Choose the correct relation [$ R $ = radius of Earth]:

A conducting wire is stretched by applying a deforming force, so that its diameter decreases to 40% of the original value. The percentage change in its resistance will be:

If $ |z_1| = 2, |z_2| = 3, |z_3| = 4 $ and $ |2z_1 + 3z_2 + 4z_3| = 4 $, then the absolute value of $ 8z_2z_3 + 27z_1z_3 + 64z_1z_2 $ equals:

Inside a solenoid of radius $ 0.5 $ m, the magnetic field is changing at a rate of $ 50 \times 10^{-6} $ T/s. The acceleration of an electron placed at a distance of $ 0.3 $ m from the axis of the solenoid will be:

A long straight wire of radius $ a $ carries a steady current $ I $. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at $ a/2 $ and $ 2a $ from the axis of the wire is:

Evaluate the integral: \[ \int \frac{x^3 - 1}{x^3 + x} dx \]

In the given cycle ABCDA, the heat required for an ideal monoatomic gas will be:

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume immersed in water to that in kerosene oil is:

Two wires of the same material (Young’s modulus $ Y $) and same length $ L $ but radii $ R $ and $ 2R $ respectively, are joined end to end and a weight $ W $ is suspended from the combination. The elastic potential energy in the system is:

The final product in the following reaction Y is:

A photon of wavelength $ 3000 $ Å strikes a metal surface. The work function of the metal is $ 2.13 $ eV. What is the kinetic energy of the emitted photoelectron? ($ h = 6.626 \times 10^{-34} $ Js)

Number of subsets of set of letters of word 'MONOTONE' is:

The range of $8\sin(\theta) + 6\cos(\theta) + 2$ is:

Evaluate the integral: \[ \int \frac{x^2 (x \sec^2 x + \tan x)}{(x \tan x + 1)^2} dx \]

Evaluate the integral: \[ \int \sqrt{x + \sqrt{x^2 + 2}} \, dx. \]

The function \[ f(x) = \frac{\cos x}{\left\lfloor \frac{2x}{\pi} \right\rfloor + \frac{1}{2}}, \] where $ x $ is not an integral multiple of $ \pi $ and $ \lfloor \cdot \rfloor $ denotes the greatest integer function, is:

Consider the function $ f(x) = \frac{|x - 1|}{x^2} $. Then $ f(x) $ is:

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

The value of $ \int_0^\infty \frac{dx}{(x^2 + a^2)(x^2 + b^2)} $ is:

The distance from the origin to the image of $(1,1)$ with respect to the line $x + y + 5 = 0$ is:

The locus of the point of intersection of the lines $x = a(1 - t^2)/(1 + t^2)$ and $y = 2at/(1 + t^2)$ (t being a parameter) represents:

The locus of the mid-point of a chord of the circle $x^2 + y^2 = 4$ which subtends a right angle at the origin is:

In an examination, 62% of the candidates failed in English, 42% in Mathematics and 20% in both. The number of those who passed in both the subjects is:

If $ p $: 2 is an even number, $ q $: 2 is a prime number, and $ r $: $ 2 + 2 = 2^2 $, then the symbolic statement $ p \rightarrow (q \vee r) $ means:

The coefficient of the highest power of $x$ in the expansion of $(x + \sqrt{x^2 - 1})^8 + (x - \sqrt{x^2 - 1})^8$ is: