List of top Questions asked in Maharashtra Health Sciences and Technical CET- 2025

If \( \mathbf{a} = \frac{1}{\sqrt{10}} (4\hat{i} - 3\hat{j} + \hat{k}) \) and \( \mathbf{b} = \frac{1}{5} (\hat{i} + 2\hat{j} + 2\hat{k}) \), then the value of \[ (2\mathbf{a} - \mathbf{b}) \cdot \left[ (\mathbf{a} \times \mathbf{b}) \times (\mathbf{a} + 2\mathbf{b}) \right] \]
In a dihybrid cross between two heterozygous pea plants (RrYy × RrYy), what is the phenotypic ratio of the offspring for seed shape and seed color? (R = round, r = wrinkled; Y = yellow, y = green)
Population of Town A and B was 20,000 in 1985. In 1989, the population of Town A was 25,000, and Town B had 28,000. What will be the difference in population between the two towns in 1993?
A car of mass 800 kg is moving in a circular path with a radius of 50 m at a speed of 20 m/s. Calculate the centripetal force acting on the car.
A die was thrown \( n \) times until the lowest number on the die appeared. If the mean is \( \frac{n}{g} \), then what is the value of \( n \)?
Evaluate the integral: \[ \int \frac{\sqrt{\tan x}}{\sin x \cos x} \, dx \]
Let \( \mathbf{a} \), \( \mathbf{b} \), and \( \mathbf{c} \) be vectors of magnitude 2, 3, and 4 respectively. If: - \( \mathbf{a} \) is perpendicular to \( (\mathbf{b} + \mathbf{c}) \), - \( \mathbf{b} \) is perpendicular to \( (\mathbf{c} + \mathbf{a}) \), - \( \mathbf{c} \) is perpendicular to \( (\mathbf{a} + \mathbf{b}) \), then the magnitude of \( \mathbf{a} + \mathbf{b} + \mathbf{c} \) is equal to:
The angle between the lines whose direction cosines satisfy the equations: \[ l + m + n = 0 \quad \text{and} \quad m^2 + n^2 - l^2 = 0 \] Find the angle between the two lines.
Which part of the human brain is responsible for regulating the body's balance and coordination?
In the word "UNIVERSITY", find the probability that the two "I"s do not come together.
A car accelerates uniformly from rest to a velocity of \( 25 \, \text{m/s} \) in \( 10 \, \text{seconds} \). What is the acceleration of the car?
Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of \( x \).
The value of the definite integral \( \int_0^{\pi} \sin^2 x \, dx \) is:
Evaluate the integral: \[ \int \frac{1}{\sin^2 2x \cdot \cos^2 2x} \, dx \]
Evaluate the integral: ∫ log((2 + x)2 + x) dx
The magnetic moment of \( \text{Mn}^{3+} \) is:
For a first-order reaction, the slope of the graph between \(\log[A]\) vs time is equal to:
What is the correct order of thermal stability of the following carbonates?
BaCO\(_3\), MgCO\(_3\), SrCO\(_3\), CaCO\(_3\)
A charge of 2 $\mu C$ is placed in an electric field of intensity \( 4 \times 10^3 \, \text{N/C} \). What is the force experienced by the charge?
If the volume of the tetrahedron, whose vertices are \( A(1, 2, 3), B(-3, -1, 1), C(2, 1, 3) \) and \( D(-1, 2, x) \), is \( \frac{11}{6} \) cubic units, then the value of \( x \) is:
The distance between the points \( A(3, 4) \) and \( B(-1, -2) \) is:
There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.
The equation for the RMS velocity is given as \[ v_{\text{rms}} = \sqrt{\frac{3RT}{M_0}} \] where \( R \) is the gas constant, \( T \) is the temperature, and \( M_0 \) is the molecular mass. If the temperature is increased, find the new RMS velocity \( v_{\text{rms}} \) when the temperature is doubled.}
If \( \tan^{-1} (\sqrt{\cos \alpha}) - \cot^{-1 (\cos \alpha) = x \), then what is \( \sin \alpha \)?}
A body of mass 0.2 kg is attached to a light string of length 1 m and revolved in a vertical circle. What is the minimum speed at the lowest point so that the body can complete the circular motion? (Take \( g = 10 \, \text{m/s}^2 \))