List of top Questions asked in MHT CET- 2025

The integrating factor of \( y + \frac{d}{dx}(xy) = x(\sin x + \log x) \) is
Let \( \bar{a} = \hat{i} + \hat{j}, \bar{b} = 2\hat{i} - \hat{k}, \bar{c} = 3\hat{i} - \hat{j} + \hat{k} \), then vector \( \bar{p} \) satisfying \( \bar{p} \cdot \bar{a} = 0 \) and \( \bar{p} \times \bar{b} = \bar{c} \times \bar{b} \) is
Which from following statements is true regarding the cell emf at 298 K for \( \ominus Ni_{(s)} | Ni^{+2}(0.01M) || Ag^{+}(0.01M) | Ag_{(s)} \oplus \)?
Two stones of masses m and 3 m are whirled in horizontal circles, the heavier one in a radius $(\frac{r}{3})$ and lighter one in a radius r. The tangential speed of lighter stone is 'n' times the value of heavier stone. When the magnitude of centripetal force becomes equal the value of n is
An a.c. e.m.f. of peak value $230\text{ V}$ and frequency $50\text{ Hz}$ is connected to a circuit with $R = 11.5\Omega, L = 2.5\text{H}$ and a capacitor all in series. The value of capacitance is ' $C$ ' for the current in the circuit to be maximum. The value of ' $C$ ' and maximum current are respectively ($\pi^2 = 10$ )}
There are two identical small holes on the opposite side of a tank containing full of a liquid. The tank is open at the top. The difference in height between the two holes is ' $h$ '. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to
A solid sphere of mass ' $m$ ' and radius ' $R$ ' is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with angular speed twice that of sphere. The ratio of kinetic energy of sphere to kinetic energy of cylinder will be
The equation of the curve passing through $(2, \frac{9}{2})$ and having the slope $(1 - \frac{1}{x^2})$ at $(x, y)$ is
The value of the integral $\int_1^2 \frac{x \text{ d}x}{(x+2)(x+3)}$ is
Three urns respectively contain 2 white and 3 black, 3 white and 2 black and 1 white and 4 black balls. If one ball is drawn from each um, then the probability that the selection contains 1 black and 2 white balls is
If a random variable $X$ has p.d.f. $f(x) = \begin{cases} \frac{ax^2}{2} + bx & , \text{if } 1 \leq x \leq 3 \\ 0 & , \text{otherwise} \end{cases}$ and $f(2) = 2$, then the values of $a$ and $b$ are, respectively}
Considering only the principal values of the inverse trigonometric function, the value of $\tan \left( \cos^{-1} \frac{1}{5\sqrt{2}} - \sin^{-1} \frac{4}{\sqrt{17}} \right)$ is
Which from following solutions exhibits minimum boiling point elevation under identical conditions? (Assume complete dissociation)}
Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X is the random variable of getting queens, then the value of $2 E(X) + 3 E(X^2)$ for the number of queens is
Match the Column I with Column II.
Column (I)
(Parasite)		Column (II)
(Host)
i.Ticksa.Marine fish
ii.Copepodsb.Dog
iii.Cuscutac.Indian crow
iv.Asian Koeld.Hedge plants
Choose the correct option:

If \({ }^n \mathrm{C}_0+\frac{1}{2}{ }^n \mathrm{C}_1+\frac{1}{3}{ }^n \mathrm{C}_2+\ldots+\frac{1}{n}{ }^n \mathrm{C}_{n-1}+\frac{1}{n+1}{ }^n \mathrm{C}_n=\frac{1023}{10}\), then \(\mathrm{n}=\)

Which from following is a correct increasing order of basic strength of compounds?

Which of the following set of thermodynamic conditions is true for the reaction to be spontaneous at high temperature?

If \(3 \sin 2 \theta=2 \sin 3 \theta\) and \(0<\theta<\pi\), then the value of \(\sin \theta\) is equal to

Mucosa forms __________ in stomach and __________ in intestine respectively.
Match the parts of brain in Column I with their inclusions in Column II.
Column I: i. Telencephalon; ii. Rhinencephalon; iii. Mesencephalon; iv. Metencephalon
Column II: a. Olfactory lobes; b. Cerebellum and pons varolli; c. Crura cerebri and corpora quadrigemina; d. Cerebrum
Choose the correct option
Clones are produced by asexual reproduction and resulting individuals are identical __________.
Considering the concept of multiple alleles, one individual can have only __________ alleles for that character.
The volume of air that is present in the respiratory tract (from nose to the terminal bronchioles) but not involved in gaseous exchange is called __________
Select a correct pair of cells with identical set of chromosomes.