List of top Questions asked in MHT CET- 2024

Let \(X\) be a random variable having binomial distribution \(B(7, p)\). If \(P(X = 3) = 5P(X = 4)\), then the sum of the mean and the variance of \(X\) is:
Which one of the carbanions is the least stable?
The negative of \( (p \land (\sim q)) \lor (\sim p) \) is equivalent to:
The Boolean expression \( (\sim(p \land q)) \lor q \) is equivalent to:
Two players A and B are alternately throwing a coin and a die together. A player who first throws a head and a 6 wins the game. If A starts the game, then the probability that B wins the game is:
The solution of the differential equation \( \sqrt{1 - y^2} \, dx + x \, dy - \sin^{-1} y \, dy = 0 \) is:
Which of the following represents the Gattermann-Koch reaction?
One of the principal solutions of \( \sqrt{3} \sec x = -2 \) is equal to:
Which of the following compounds is likely to be more soluble in water?
The value of \( \int \frac{x \sin^{-1} x}{\sqrt{1 - x^2}} dx \) is equal to:
A wire of length \( 1 \, \text{m} \) moving with velocity \( 8 \, \text{m/s} \) at right angles to a magnetic field of \( 2 \, \text{T} \). The magnitude of induced emf between the ends of the wire will be:
The solution of the differential equation \( y^2 dx + (x^2 - xy + y^2) dy = 0 \) is
If \( f(x) = 2x^3 - 15x^2 - 144x - 7 \), then \( f(x) \) is strictly decreasing in:

IUPAC name of the given ether is:

In a BCC (Body-Centered Cubic) structure, the radius of the atoms is:
A magnetic needle is kept in a non-uniform magnetic field. It experiences:
Which of the following correctly represents the AND logic gate?
Point charge of \( 10 \, \mu C \) is placed at the origin. At what location on the X-axis should a point charge of \( 40 \, \mu C \) be placed so that the net electric field is zero at \( x = 2 \, \text{cm} \) on the X-axis?
Tincture of iodine is the common name for:
What is the polymer of elastomer?
Identify the name reaction for Swarts reaction and Witting reaction.
Relative permittivity and permeability of a material are \( \varepsilon_r \) and \( \mu_r \), respectively. Which of the following values of these quantities are allowed for a diamagnetic material?
\( \sin^{-1}[\sin(-600^\circ)] + \cot^{-1}(-\sqrt{3}) = \)
A liquid is allowed to flow into a tube of truncated cone shape. Identify the correct statement:
If \( AX = B \), where \[ A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}, \quad B = \begin{bmatrix} 4 \\ 0 \\ 2 \end{bmatrix}, \] then \( 2x + y - z \) is: