List of top Questions asked in MHT CET- 2026

The statement \( \neg(p \leftrightarrow q) \) is logically equivalent to:
The lines \( \vec{r} \times \vec{a} = \vec{b} \times \vec{a} \) and \( \vec{r} \times \vec{b} = \vec{a} \times \vec{b} \) intersect at a point, where \( \vec{a} = \hat{i} + \hat{j} \) and \( \vec{b} = \hat{i} - \hat{k} \). Find the point of intersection.
For the parabola \( y^2 = 16x \), find the distance between the focus and the directrix.
The objective function is \( Z = 3x + 5y \). The difference between the maximum and minimum values of \( Z \) is \( 3a \), subject to constraints: \( x + y \ge 1 \), \( 5x + 10y \le 50 \), \( x, y \ge 0 \). Find the value of \( a \).
The surrounding temperature is \( 20^\circ\text{C} \). A body cools from \( 100^\circ\text{C} \) to \( 60^\circ\text{C} \) in 20 minutes. Find the time taken for the body to cool down to \( 30^\circ\text{C} \).
The area in sq. units bounded by the curve \( y = 2\sqrt{1 - x^2} \) and the x-axis is :
If \(A\) is a \(3\times3\) matrix satisfying \(2A=3A^2+kI\), and \(\det(A)=1\), then the value of \(k\) is:
Given \( f(x) = x - 1 \), \( h(1) = 4 \), and \( h'(1) = -2 \). If \( g(x) = (f[4(h(x)) + 3])^2 \), find the value of \( g'(1) \).
If \( \vec{a}=2\hat{i}-\hat{j}+3\hat{k} \) and \( \vec{b}=\hat{i}+2\hat{j}-\hat{k} \), then the vector perpendicular to both \( \vec a \) and \( \vec b \) is:
If slope of two lines represented by \( \dfrac{x^2}{a}+\dfrac{2xy}{h}+\dfrac{y^2}{b}=0 \) is twice the other, then \(ab:h^2=\ ?\)
If the area enclosed between the circle \(x^2+y^2=25\) and the parabola \(y^2=16x\) is \(A\), then \(A=\ ?\)
\( \displaystyle \lim_{x \to 2} \left( \frac{1}{x-2} - \frac{2}{x^3-3x^2+2x} \right) = \)
A wire 64 m long is bent into the shape of a rectangle. What should be its dimensions so that the enclosed area is maximum?
The area bounded by the X-axis and the curve \[ y=x(x-2)(x+1) \] is:
\[ \int \frac{1}{x^{1/2}+x^{1/3}}\,dx \] is equal to:
In a certain culture of bacteria, the rate of increase is proportional to the number of bacteria present at that instant. It is found that there are 10,000 bacteria at the end of 3 hours and 40,000 bacteria at the end of 5 hours, then the number of bacteria present in the beginning are:
The value of \[ \int \frac{x^2-1}{x^3\sqrt{2x^4-2x^2+1}}\,dx \] is:
Calculate the pH of \(0.01\ \text{M}\) strong dibasic acid.
Identify \(Base_2\) for the following equation according to Brønsted-Lowry theory:
\( HCl(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + Cl^-(aq) \)
What is the pH of \(2 \times 10^{-3}\ \text{M}\) solution of a monacidic weak base if it ionises to the extent of \(5\%\)?
Identify conjugate acid and conjugate base for \( HCO_3^- \) ion respectively:
A certain mass of a gas occupies a volume of \(2.5\ \text{dm}^3\) at NTP. Calculate the change in volume of gas at the same temperature if pressure of gas is changed to \(1.25\ \text{atm}\).
Find the number of atoms present in \(11.2\ \text{L}\) of nitrogen gas at STP.
The solubility product of \(PbCl_2\) at \(298\ \text{K}\) is \(3.2 \times 10^{-5}\). What is its solubility in \(\text{mol dm}^{-3}\)?
Calculate the solubility in \(\text{mol dm}^{-3}\) of sparingly soluble salt BaBr if its solubility product is \(4.9 \times 10^{-13}\) at the same temperature.