MHT CET 2025 21st April Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

Mathematics

1. Numbers are selected at random, one at a time from the two-digit numbers $00,01,02,-------, 99$ with replacement. An eve 2. A particular solution of $3 \mathrm{e}^x \tan y \mathrm{~d} x+\left(1-\mathrm{e}^x\right) \sec ^2 y \mathrm{~d} y=0$ wit 3. $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ are nonzero vectors such that $\overline{\mathrm{a 4. If $\sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{3}$ and $\cot ^{-1}\left(\frac{1}{x}\right)-\cot ^{-1}\left(\frac{1}{y}\right)= 5. The value of $\sin \left[\tan ^{-1}\left(\frac{1-x^2}{2 x}\right)+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right]$ is 6. The area of the region bounded by the curve $y=|x-2|$ between $x=1, x=3$ and X -axis is …… 7. $$ \int_{-1}^3\left(\tan ^{-1}\left(\frac{x}{x^2+1}\right)+\tan ^{-1}\left(\frac{x^2+1}{x}\right)\right) d x= $$ 8. Let A be a non-singular matrix of order n and $|A|=k$, then $(\operatorname{adj} A)^{-1}$ is 9. If $f(x)= \begin{cases}\frac{8^x-4^x-2^x+1^x}{x^2}, & \text { if } x>0 \\ \mathrm{e}^x \sin x+\mathrm{i} x+\lambda \log 10. If $\sqrt{\log _3 x^{16}}+9 \log _{27} \sqrt[3]{\frac{3}{x}}=5$, then $x=\ldots$. 11. The line passing through the point $(5,1, a)$ and $(3, \mathrm{~b}, 1)$ crosses the $y \mathrm{z}$-plane at $\left(0, \f 12. The direction ratios of the line of intersection of the planes $x-y+z-5=0$ and $x-3 y-6=0$, are 13. The distance between the line $\overline{\mathrm{r}}=3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}+\lambda(\hat 14. If $y=\sin ^2\left(\cot ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$ 15. $$ \int \frac{\sin x}{\sqrt{5 \sin ^2 x+6 \cos ^2 x}} d x $$ 16. If $\mathrm{f}(x)=\frac{\mathrm{k} \sin x+2 \cos x}{\sin x+\cos x}$ is strictly increasing for all real values of $x$, t 17. The locus of the points represented by $|z+3|-|z-3|=6$, where $z$ is a complex number, is …. 18. The locus of point of intersection of the tangents to the circle $x^2+y^2=16$, such that the angle between them is $60^{ 19. A random variable, $X$ has p.m.f. $\mathrm{P}(\mathrm{X}=x)=\frac{{ }^4 \mathrm{C}_x}{2^4}, x=0,1,2,3,4$ and $\mu$ and $ 20. $$ \text { The c.d.f. of a discrete random variable } \mathrm{X} \text { is } $$ $$ \begin{array}{|c|c|c|c|c|c|c|c|c|} \ 21. The distance between the lines represented by $16 x^2+9 y^2+48 x-24 x y-36 y+35=0$ is ......... units 22. The value of $\tan 20^{\circ} \tan 80^{\circ} \cot 50^{\circ}=$ 23. The equation of the curve passing through the origin and satisfying the equation $\left(1+x^2\right) \frac{\mathrm{d} y} 24. The value of $m \in \mathbb{R}$, when angle between the vectors $\overline{\mathrm{p}}=\mathrm{m} y \hat{\mathrm{i}}-6 \ 25. The volume of the tetrahedron whose coterminous edges are represented by $$ \bar{a}=-12 \hat{i}+p \hat{k}, \bar{b}=3 \ha 26. With usual notations, the perimeter of a triangle ABC is 6 times the arithmetic mean of sine of its angles. If $\mathrm{ 27. The angle between the lines whose direction cosines are $\frac{-\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}$ and $\fr 28. If $\sin \left(\frac{\pi}{4} \cot \theta\right)=\cos \left(\frac{\pi}{4} \tan \theta\right)$, then the general solution 29. The differential equation of all circles having their centres on the line $y=5$ and touching ( X -axis) is $\qquad$ 30. $$ \int_0^{\frac{\pi}{4}} \frac{\cos ^2 x \sin ^2 x}{\cos ^3 x+\sin ^3 x} d x= $$ 31. If $\{(\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\mathrm{p} \wedge \mathrm{r})\} \rightarrow \sim \mathrm{p} \vee \mathr 32. In a triangle ABC , with usual notations, $\tan \left(\frac{\mathrm{A}}{2}\right)=\frac{5}{6}, \tan \left(\frac{\mathrm{ 33. If ${ }^{n+4} C_{n+1}-{ }^{n+3} C_n=15(n+2)$, then $n=$ 34. The correct simplified circuit diagram for the logical statement $[\{\mathrm{q} \wedge(\sim \mathrm{q} \vee \mathrm{r})\ 35. $$ \mathop {\lim }\limits_{n \to \infty }\left[\frac{1}{1-n^4}+\frac{8}{1-n^4}+\ldots \ldots \ldots \ldots .+\frac{n^3}{ 36. If $f(\theta)=\cos \theta_1 \cdot \cos \theta_2 \cdot \cos \theta_3$ .............. $\cos \theta_n$, then $\tan \theta_1 37. The length of the altitude through the point $D$ of tetrahedron where the vertices of the tetrahedron are $A(2,3,1), B(4 38. The angle between the lines $\frac{x-1}{l}=\frac{y+1}{m}=\frac{z}{n}$ and $\frac{x+1}{\mathrm{~m}}=\frac{y-3}{\mathrm{n} 39. The distance of the point $\mathrm{P}(3,8,2)$ from the line $\frac{x-1}{2}=\frac{y-3}{4}=\frac{z-2}{3}$ measured paralle 40. The solution set for minimizing the function $\mathrm{z}=x+y$ with constraints $x+y \geqslant 2, x+2 y \leqslant 8, y \l 41. The abscissae of the points of the curve $y=x^3$ are in the interval $[-2,2]$, where the slope of the tangents can be ob 42. Let $x$ be the length of each of the equal sides of an isosceles triangle and $\theta$ be the angle between these sides. 43. $$ \int \cos \left(\frac{x}{16}\right) \cdot \cos \left(\frac{x}{8}\right) \cdot \cos \left(\frac{x}{4}\right) \cdot \si 44. $$ \int \frac{x^3}{(x+1)^2} d x= $$ 45. A wire of length 8 units is cut into two parts which are bent respectively in the form of a square and a circle. The lea 46. If $\mathrm{A}, \mathrm{B}, \mathrm{C}$ are mutually exclusive and exhaustive events of a sample space $S$ such that $P( 47. Angle between the parabola $y^2=4(x-1)$ and $x^2+4(y-3)=0$ at the common end of their latus rectum is 48. The points $(1,3)$ and $(5,1)$ are two opposite vertices of a rectangle. The other two vertices are lie on the line $y=2 49. If $y=\mathrm{a}^x \cdot \mathrm{~b}^{2 x-1}$, then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$ is equal to 50. In a culture bacteria count is $1,00,000$ initially. The number increases by $10 \%$ in first 2 hours. In how many hours

Physics

1. Error in the measurement of radius of the sphere is $2 \%$. The error in the calculated value of its volume is 2. In the circuit shown in the figure, $P \neq R$. The reading of the galvanometer remains the same with switch ' $S$ ' ope 3. A unit vector in the direction of resultant vector of $\vec{A}=-2 \hat{i}+3 \hat{j}+\hat{k}$ and $\vec{B}=\hat{i}+2 \hat 4. The moment of inertia of a ring about an axis passing through its centre and perpendicular to its plane is I. It is rota 5. The two coherent sources produce interference with intensity ratio ' $b$ '. In the interference pattern, the ratio $\fra 6. The radii of circular orbits of two satellites $A$ and $B$ of the earth are ' $4 R$ ' and ' $R$ ' respectively, where $R 7. The space within the current carrying toroid is filled with aluminium of susceptibility ' $\chi$ '. The percentage incre 8. Using Bohr's quantization condition, the rotational kinetic energy in the third orbit for a diatomic molecule is ( $h=$ 9. A body is rotating about its own axis. Its rotational kinetic energy is ' x ' and its angular momentum is ' $y$ '. Hence 10. A ray of light travelling through rarer medium is incident at a very small angle ' $i$ ' on a glass slab and after refra 11. A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered by the body in the $n^{ 12. A coil is wound on a core of rectangular crosssection. If all the linear dimensions of core are increased by a factor 3 13. In air, a charged soap bubble of radius R breaks into 64 small soap bubbles of equal radius $r$. The ratio of mechanical 14. When photons of energies twice and thrice the work function of a metal are incident on the metal surface one after other 15. According to Huygen's wave theory of light, which one of the following statements is not correct? 16. A conveyor belt is moving with constant velocity (V). Sand is being dropped on the belt at the rate of $\mathrm{M} \math 17. A coil having 9 turns carrying current produces magnetic field $B_1$ at the centre. Now that coil is rewounded into 3 tu 18. Two capillary tubes of same diameter are kept vertically in two liquids whose densities are in the ratio $4: 3$. If thei 19. An ideal inductor of $\left(\frac{1}{\pi}\right) \mathrm{H}$ is connected in series with a $300 \Omega$ resistor. If a $ 20. Hot water cools from $80^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ in 1 minutes. In cooling from $60^{\circ} \mathr 21. A Carnot engine has efficiency $\frac{1}{6}$. It becomes $\frac{1}{3}$, when the temperature of $\operatorname{sink}$ is 22. An alternating e.m.f. having voltage $\mathrm{V}=\mathrm{V}_0 \sin \omega t$ is applied to a series L-C-R circuit. Given 23. A simple pendulum oscillates with an angular amplitude $\theta$. If the maximum tension in the string is 4 times the min 24. An electron moves in Bohr orbit. The magnetic field at the centre is proportional to 25. The r.m.s. speed of gas molecules at 800 K will be 26. If the charge on the capacitor is increased by 3C, the energy stored in it increases by $21 \%$. The original charge on 27. A conducting ring of certain resistance is falling towards a current carrying straight long conductor. The ring and cond 28. In the following combination of logic gates, the output $Y$ can be written in the terms of inputs $A$ and B as 29. If a black body at 400 K surrounded by atmosphere at 300 K has rate of cooling ' $\mathrm{R}_0$ ', the same body at 900 30. The electric field intensity on the surface of a solid charged sphere of radius $\mathbf{r}$ and volume charge density $ 31. Two strings ' X ' and ' Y ' of a guitar produces a beat frequency of 6 Hz . When the tension of the string ' Y ' is incr 32. In common emitter mode of a transistor, the current gain is 8 . The input impedance is $25 \mathrm{k} \Omega$ and load r 33. A transverse displacement of vibrating string is $y=0.06 \sin \left(\frac{2 \pi}{3}\right) \times \cos (120 \pi t)$. If 34. The equation of a progressive wave is $\mathrm{Y}=3 \sin \left[\pi\left(\frac{\mathrm{t}}{3}-\frac{\mathrm{x}}{5}\right) 35. If the internal resistance of cell is negligible then current flowing through the circuit is 36. Water flows through a horizontal pipe of varying cross-section at the rate of $\pi \times 10^{-1} \mathrm{~m} / \mathrm{ 37. In an electrical circuit ' $R$ ', ' $L$ ', ' $C$ ' and an a.c. voltage source are all connected in series. When ' L ' is 38. A parallel plate capacitor having plate area ' $A$ ' and separation ' $d$ ' is charged to a potential difference ' $V$ ' 39. The length of the simple pendulum is made 3 times the original length. If ' T ' is its original time period, then the ne 40. A plano convex lens fits exactly in to a plano concave lens. Their plane surfaces are parallel to each other. Lenses are 41. Moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is ' $I$ '. If 42. If an ammeter is to be used in place of a galvanometer then we must connect 43. The temperature of an ideal gas is increased from 100 K to 400 K . If ' $x$ ' is the R.M.S. velocity of its molecules at 44. What is the phase difference between the flux linked with a coil rotating in a uniform magnetic field and the induced e. 45. A pendulum bob has a speed $4 \mathrm{~m} / \mathrm{s}$ at its lowest position. The pendulum is 1 m long. When the lengt 46. A vehicle starts from rest and accelerates along straight path at $2 \mathrm{~m} / \mathrm{s}^2$. At the starting point 47. When a light of wavelength $\lambda$ falls on the emitter of a photocell, maximum speed of emitted photoelectrons is V . 48. A parallel plate capacitor has plate area $50 \mathrm{~cm}^2$ and plate separation 3 mm . The space between the plates i 49. Heat is given to an ideal gas in an isothermal process. Then A. internal energy of the gas will decrease. B. internal en 50. Two long parallel wires carry currents $I_1$ and $\mathrm{I}_2\left(\mathrm{I}_1>\mathrm{I}_2\right)$. When currents are

Chemistry

Mathematics

Physics

MHT CET 2025 21st April Evening Shift

MCQ (Single Correct Answer)

-0

Heat is given to an ideal gas in an isothermal process. Then

A. internal energy of the gas will decrease.

B. internal energy of the gas will increase.

C. internal energy of the gas will not change.

D. the gas will do negative work.

MHT CET 2025 21st April Evening Shift

MCQ (Single Correct Answer)

-0

Two long parallel wires carry currents $I_1$ and $\mathrm{I}_2\left(\mathrm{I}_1>\mathrm{I}_2\right)$. When currents are flowing in the same direction, the magnetic field at a point midway between the wires is $6 \times 10^{-6} \mathrm{~T}$. If the direction of $\mathrm{I}_2$ is reversed the field at midpoint becomes $3 \times 10^{-5} \mathrm{~T}$. The ratio $\mathrm{I}_1: \mathrm{I}_2$ is

$3: 2$

$2: 3$

$3: 5$

$6: 7$