List of top Questions asked in MHT CET- 2024

Given, the function \( f(x) = \frac{a^x + a^{-x}}{2} \) (\( a > 2 \)), then \( f(x+y) + f(x-y) \) is equal to

If \( f(x) = |x| - |1| \), then points where \( f(x) \) is not differentiable, is/are:
The integral of \( \sec^{2/3}x \csc^{4/3}x \, dx \) from \( \pi/6 \) to \( \pi/3 \) is equal to:
The absolute maximum value of the function \( f(x) = 2x^3 - 3x^2 - 36x + 9 \) defined on \( [-3, 3] \) is
The equation of a circle with center \( (5, 4) \) and touching the \( Y \)-axis is:
Switching current of \( (p \land q) \lor (p \land (q \lor p \lor r)) \)?
The sides of a triangle are \(\sin\alpha\), \(\cos\alpha\), and \(\sqrt{1+\sin\alpha\cos\alpha}\) for some \(0 < \alpha < \frac{\pi}{2}\). Then, the greatest angle of the triangle is:

A student scores the following marks in five tests: 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is:

Let \( F(\alpha) = \begin{bmatrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{bmatrix} \), where \( \alpha \in \mathbb{R} \). Then \( [F(\alpha)]^{-1} \) is equal to:

\( \int_{\pi/11}^{9\pi/22} \frac{dx}{1 + \sqrt{\tan x}} \) is equal to:
If \( \mathbf{a} = \mathbf{i} + 2\mathbf{j} - 3\mathbf{k} \) and \( \mathbf{b} = 2\mathbf{i} - 3\mathbf{j} - 5\mathbf{k} \), then:
The distribution function \( F(X) \) of a discrete random variable \( X \) is given. Then \( P[X = 4] + P[X = 5] \):
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline F(X = x) & 0.2 & 0.37 & 0.48 & 0.62 & 0.85 & 1 \\ \hline \end{array} \]
Evaluate \( i^2 + i^3 + \dots + i^{4000} \):
Evaluate the following limit: \[ \lim_{\theta \to -\frac{\pi}{4}} \frac{\cos\theta + \sin\theta}{\theta + \frac{\pi}{4}}. \]
If \( f(x) \) is differentiable at \( x = 1 \) and \[ \lim_{h \to 0} \frac{1}{h} f(1 + h) = 5, \] then \( f'(1) \) is equal to:
The value of the integral \( \int_0^2 |2x - 3| \, dx \) is:
Let \( p: \) I am brave, \( q: \) I will climb the Mount Everest. The symbolic form of a statement, 'I am neither brave nor I will climb the Mount Everest' is:
If the curve \(y^2 = 6x\) and \(9x^2 + by^2 = 16\) intersect each other at right angles, then the value of \(b\) is:
The most reactive amine towards dilute hydrochloric acid is:
If \( n \) is the number density and \( d \) is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e., mean free path) is represented by:
In acidic medium, which of the following does not change its colour?
The pH of a saturated solution of \( \text{Ca(OH)}_2 \) is 9. The solubility product (\( K_{sp} \)) of \( \text{Ca(OH)}_2 \) is:

Which of the following diseases is a result of protein deficiency?

Which enzyme is responsible for cleaning neurotransmitters in the synaptic cleft?
Which hormone inhibits the growth of plants?