List of top Questions asked in MHT CET

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 \[ (2\mathbf{a} - \mathbf{b}) \cdot \left[ (\mathbf{a} \times \mathbf{b}) \times (\mathbf{a} + 2\mathbf{b}) \right] \]
The integral $ \int e^x \left( \frac{x + 5}{(x + 6)^2} \right) dx $ is:
If \( z = 3 + 4i \), then the modulus of \( z \) is:
If ∫ (2x + 3)/((x - 1)(x^2 + 1)) dx = log_x {(x - 1)^(5/2)(x^2 + 1)^a} - (1/2) tan^(-1)x + C, then the value of a is:
Evaluate the definite integral: \( \int_{-2}^{2} |x^2 - x - 2| \, dx \)
Evaluate the determinant of the matrix: \[ \left| \begin{array}{cc} 1 & \tan x
-\tan x & 1 \end{array} \right| \]
A bag contains 5 red balls, 7 green balls, and 8 blue balls. One ball is drawn at random. What is the probability that the ball is either red or green?
If $ \tan \theta = \frac{3}{4} $, find the value of $ \sin \theta $.
Find the area of a triangle with base 12 cm and height 5 cm.
Given \( f'(1) = 3 \), \( f(1) = 1 \), and
\[ y = f\left(f(f(x))\right) + \left(f(x)\right)^2, \] then find \( \frac{dy}{dx} \) at \( x = 1 \).
If \( \tan \theta = 2 \), then the value of \( \sec^2 \theta \) is:
The value of the integral \( \int_0^1 x^2 \, dx \) is:
The general solution of the differential equation \( \frac{dy}{dx} = 3x^2 \) is:
If $ y = \frac{b}{a} $, then $ \frac{dy}{dx} $ is:
Find the roots of the quadratic equation $ x^2 - 5x + 6 = 0 $.
The sum of the ages of a father and his son is 60 years. The father is three times as old as the son. What is the son's age?
Solve for \( x \): \( \log_2 (x-1) = 3 \).
A simple pendulum of length 1 m is oscillating with a small amplitude. If the acceleration due to gravity is \( 9.8 \, \text{m/s}^2 \), what is the time period of the pendulum?
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.
Find the solution $ \frac{d^2y}{dm^2} - k^3 \frac{dy}{dm} = y \cos m, \quad y(0) = 1 $
The mass of an object is measured as \( (28 \pm 0.01) \) g and its volume as \( (5 \pm 0.1) \) cm\(^3\). What is the percentage error in density?
A particle is moving with a constant velocity of \( 5 \, \text{m/s} \) in a circular path of radius \( 2 \, \text{m} \). What is the centripetal acceleration of the particle?
A block of mass \( 5 \, \text{kg} \) is placed on a horizontal surface. The coefficient of friction between the block and the surface is \( 0.4 \). What is the force of friction acting on the block?
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?
Find the roots of the quadratic equation \( 2x^2 - 4x - 6 = 0 \).