List of top Questions asked in BITSAT- 2019

Universal set:
\[ U = \{ x \mid x^5 - 6x^4 + 11x^3 - 6x^2 = 0 \} \]

Subsets:
\[ A = \{ x \mid x^2 - 5x + 6 = 0 \}, \quad B = \{ x \mid x^2 - 3x + 2 = 0 \} \]

Find: \[ (A \cap B)' \]

If \[ \cos^{-1} x - \frac{\cos^{-1} y}{2} = \alpha, \] then \[ 4x^2 - 4xy \cos \alpha + y^2 \] is equal to:

Minimise \[ Z = \sum_{i=1}^{n} \sum_{j=1}^{m} c_{ij} x_{ij} \]

Subject to:
\[ \sum_{i=1}^{n} x_{ij} = b_j, \quad j = 1, 2, \dots, m \]
\[ \sum_{j=1}^{m} x_{ij} = b_i, \quad i = 1, 2, \dots, n \]

This is a linear programming problem (LPP) with number of constraints:

Two lines:
L₁: \(x = 5, \; \frac{y}{3 - \alpha} = \frac{z}{-2}\)

L₂: \(x = \alpha, \; \frac{y}{-1} = \frac{z}{2 - \alpha}\)

are coplanar. Then \(\alpha\) can take value(s):

The function \(f(x) = \frac{x}{2} + \frac{2}{x}\) has a local minimum at:

In the figure, two blocks are separated by a uniform strut attached to each block with frictionless pins. Block A weighs 400 N, block B weighs 300 N, and the strut AB weighs 200 N. If μ = 0.25 under block B, determine the minimum coefficient of friction under A to prevent motion.

A ray parallel to the principal axis is incident at 30° from normal on a concave mirror having a radius of curvature R. The point in principal axis where rays are focussed is Q such that PQ is

The masses of blocks A and B are m and M respectively. Between A and B, there is a constant frictional force F and B can slide on a smooth horizontal surface. A is set in motion with velocity v₀ while B is at rest. What is the distance moved by A relative to B before they move with the same velocity?

0.5 mole of an ideal gas at a constant temperature of 27°C is kept inside a cylinder of length L and cross-section area A, closed by a massless piston. The cylinder is attached to a conducting rod of length L, cross-section area A/19, and thermal conductivity k, whose other end is maintained at 0°C. The piston is moved such that the rate of heat flow through the rod is constant. The constant velocity of the piston when it is at height L/2 from the bottom is

A square gate of size 1m × 1m is hinged at its mid-point. A fluid of density ρ fills the space to the left of the gate. The force F required to hold the gate stationary is

A vessel of volume 20L contains a mixture of hydrogen and helium at temperature 27^∘C and pressure 2atm. The total mass of the mixture is 5g. Assuming ideal gases, the ratio of mass of hydrogen to that of helium is

In a YDSE, the light of wavelength λ = 5000AA is used, which emerges in phase from two slits at distance d = 3×10⁻7m apart. A transparent sheet of thickness t = 1.5×10⁻7m and refractive index μ = 1.17 is placed over one of the slits. What is the new angular position of the central maxima of the interference pattern from the centre of the screen? Find the value of y.

A load of mass m falls from a height h onto the scale pan hanging from a spring as shown in the figure. If the spring constant is k, mass of scale pan is zero, and the mass does not bounce relative to the pan, then the amplitude of vibration is

A thin rod of length 4l and mass M is bent at the points as shown in the figure. What is the moment of inertia of the rod about the axis passing through point O and perpendicular to the plane of paper?

A 2 m wide truck is moving with a uniform speed v₀ = 8m/s along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v so that he can cross the road safely is

In the circuit shown below, the AC source has voltage V = 20cos(ω t)V with ω = 2000rad/s. The amplitude of the current will be nearly

The carbylamine reaction is

Choose the correct answer figure which will make a complete square on joining with the problem figure.

In the following question, five figures are given. Out of them, find the three figures that can be joined to form a square.

Choose the answer figure which completes the problem figure matrix.

What is the opposite of 3, if four different positions of dice are shown below?