MHT CET 2025 22nd April Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

Mathematics

1. If $y=y(x)$ and $\left(\frac{2+\sin x}{y+1}\right) \frac{\mathrm{d} y}{\mathrm{~d} x}=-\cos x, y(0)=1$, then $y\left(\fr 2. If $A=\left[\begin{array}{cc}1 & \cot \frac{\theta}{2} \\ -\cot \frac{\theta}{2} & 1\end{array}\right]$ then $A^{-1}=$ 3. If $\bar{a}, \bar{b}, \bar{c}$ are three unit vectors such that $|\overline{\mathrm{a}}+\overline{\mathrm{b}}|^2+|\overl 4. The probability that a certain kind of component will survive a given test is $\frac{2}{3}$. The probability that at mos 5. From the following options, the nearest line to the origin is …. 6. If the truth value of the statement pattern $[p \wedge \sim r] \rightarrow \sim r \wedge q$ is False, then which of the 7. $\bar{a}=\hat{i}-\hat{j}, \bar{b}=\hat{j}-\hat{k}, \bar{c}=\hat{k}-\hat{i}$ then a unit vector $\bar{d}$ such that $\ove 8. In $\triangle A B C$, with usual notations, if $\mathrm{a}^4+\mathrm{b}^4+\mathrm{c}^4-2 \mathrm{a}^2 \mathrm{c}^2-2 \m 9. If the planes $\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-\lambda \hat{\mathrm{j}}+\hat{\mathrm{k}})=3$ and $\overli 10. If $x$ is real, then the difference between the greatest and least values of $\frac{x^2-x+1}{x^2+x+1}$ is 11. The perimeter of a square whose two sides have equations $\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-3}{4}$ and $\frac{x}{2}=\f 12. In a triangle ABC with usual notations if, $\tan \left(\frac{\mathrm{B}-\mathrm{C}}{2}\right)=x \cot \frac{\mathrm{~A}}{ 13. A coin is tossed until one head appears or a tail appears 4 times in succession. The probability distribution of the num 14. The degree of the differential equation $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}+3\left(\frac{\mathrm{~d} y}{\mathrm{~d} 15. If the sum of the squares of the distances of a point $\mathrm{P}(x, y, z)$ from the three co-ordinate axes is 324 , the 16. For a real number $x,[x]$ denotes the greatest integer less than or equal to $x$. Then the value of $$ \begin{array}{r} 17. The angle between the lines $3 x=2 y=-\mathrm{z}$ and $-x=6 y=-4 z$ is 18. If $y+\frac{\mathrm{d}}{\mathrm{d} x}(x y)=x(\sin x+\log x)$ then 19. If the pair of straight lines $x y-x+y-1=0$ and the line $x+\mathrm{k} y-3=0$ are concurrent, then the value of $k$ is e 20. If the function $$ f(x)=\left\{\begin{array}{cc} x+a \sqrt{2} \sin x & \text { if } 0 \leq x \leq \frac{\pi}{4} \\ 2 x \ 21. Which of the following statements has the truth value T ? A: cube roots of unity are in Geometric progression and their 22. The p.d.f. of a continuous random variable X is $f(x)=\left\{\begin{array}{cl}\frac{x^2}{18} & , \text { if }-3 Then $\ 23. The population of a town increases at a rate proportional to the population at that time. If the population increases fr 24. If the vectors $m \hat{i}+m \hat{j}+n \hat{k}, \hat{i}+\hat{k}, n \hat{i}+n \hat{j}+p \hat{k}$ lie in a plane then… 25. The value of $$ \begin{aligned} \sin ^2 5^{\circ}+\sin ^2 10^{\circ} & +\sin ^2 15 +\ldots \ldots \ldots \ldots \ldots \ 26. The area bounded by the curve $x=2-y-y^2$ and the Y -axis is 27. If $y=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)+\sec ^{-1}\left(\frac{1+x^2}{1-x^2}\right)$ then the value of $\frac{d y} 28. $$ \int_{\frac{\pi}{3}}^{\frac{2 \pi}{3}} \frac{x}{1+\sin x} d x= $$ 29. $$ \int_0^2 \frac{3 x+1}{x^2+4} d x= $$ 30. $$ \int \frac{\sin 2 x \cos 2 x}{\sqrt{9-\cos ^4 2 x}} d x= $$ 31. $$ \int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x= $$ 32. 21 friends were invited for a party. Two round tables can accommodate 12 and 9 friends each, The number of ways of the s 33. The area of a parallelogram whose diagonals are the vectors $2 \bar{a}-\bar{b}$ and $4 \bar{a}-5 \bar{b}$, where $\bar{a 34. $$ \lim\limits_{x \rightarrow \infty}\left(\frac{x+8}{x+1}\right)^{x+5}=\ldots $$ 35. $$ \cot ^{-1}\left(2 \cos \left(2 \operatorname{cosec}^{-1}(\sqrt{2})\right)\right)=\ldots $$ 36. If $\mathrm{z}=x+\mathrm{i} y$ is a complex number, then the equation $\left|\frac{z+i}{z-i}\right|=\sqrt{3}$ represents 37. If $\int \frac{2 x^2+3}{\left(x^2-1\right)\left(x^2-4\right)} \mathrm{d} x=\log \left[\left(\frac{x-2}{x+2}\right)^{\mat 38. For $N \in \mathbb{N}, \frac{\mathrm{~d}^{\mathrm{n}}}{\mathrm{d} x^{\mathrm{n}}}(\log x)=$ 39. In a single toss of a fair die, the odds against the event that number 4 or 5 turns up is 40. If $\mathrm{f}(x)=x \cdot \mathrm{e}^{x(1-x)}$, then $\mathrm{f}(x)$ is 41. The approximate value of $\sqrt[3]{64 \cdot 04}$ is 42. The X and Y intercepts of the tangent to the hyperbola $\frac{x^2}{20}-\frac{y^2}{5}=1$ which is perpendicular to the li 43. If the lines $\frac{x-1}{2}=\frac{y+1}{\mathrm{k}}=\frac{\mathrm{z}}{2}$ and $\frac{x+1}{5}=\frac{y+1}{2}=\frac{\mathrm{ 44. The line $y=\mathrm{m} x+3$ is tangent to the parabola $y^2=4 x$, if the value of m is 45. If the tangent and the normal at the point $(\sqrt{3}, 1)$ to the circle $x^2+y^{2 }=4$, and the X -axis form a triangle 46. If $3 \sin ^{-1}\left(\frac{2 x}{1+x^2}\right)-4 \cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)+2 \tan ^{-1}\left(\frac{2 x} 47. If $x=\operatorname{acos}^3 \theta y=\operatorname{asin}^3 \theta$ Then $\sqrt{1+\left(\frac{\mathrm{d} y}{\mathrm{~d} x 48. If the difference between the maximum and minimum values of the objective function $\mathrm{z}=7 x-8 y$, subject to the 49. The number of solutions of $16^{\sin ^2 x}+16^{\cos ^2 x}=10$ in $0 \leqslant x \leqslant 2 \pi$ are 50. Let the line $\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$ lie in the plane $x+3 y-\alpha z+\beta=0$, then the value of $

Physics

1. A vehicle is moving with uniform speed along 3 different shaped roads as horizontal, concave and convex. The surface of 2. ${ }_{88} \mathrm{R}_{\mathrm{a}}^{226}$ is converted into ${ }_{82} \mathrm{P}_{\mathrm{b}}^{206}$ by emission of alpha 3. In a Young's double slit experiment wavelength of light used is $6000 \mathop {\rm{A}}\limits^{\rm{o}}$. The first order 4. In a pure silicon crystal electron-hole concentration is $10^{16}$ per $\mathrm{m}^3$ at 301 K . Now $10^{21}$ atoms of 5. A vehicle is moving with a constant speed of $10 \mathrm{~m} / \mathrm{s}$ in a circular horizontal track of radius 20 m 6. Assuming human pupil to have radius of 0.25 cm and comfortable viewing distance of 25 cm , the minimum separation betwee 7. Four charges $2 \mu \mathrm{C},-3 \mu \mathrm{C}, 4 \mu \mathrm{C},-4 \mu \mathrm{C}$ and $-1 \mu \mathrm{C}$ are enclos 8. A solid sphere of mass ' $m$ ' and radius ' $R$ ' is rotating about its diameter. A solid cylinder of the same mass and 9. A person standing between two parallel cliffs fires a gun and hears two echoes, first echo after 1 second and the second 10. A series combination of 10 capacitors, each of value ' $\mathrm{C}_1$ ' is charged by a source of potential difference ' 11. A solid sphere and thin walled hollow sphere have same mass and same material. Which of them have greater moment of iner 12. The total charge induced in a conducting loop when it is moved in a uniform magnetic field depends on 13. A rectangular film of liquid is expanded from $(5 \mathrm{~cm} \times 4 \mathrm{~cm})$ to $(7 \mathrm{~cm} \times 8 \mat 14. The temperature of a body on Kelvin scale is ' $x$ ' $K$. When it is measured by a Fahrenheit thermometer, it is found t 15. A capillary tube is taken from earth's surface to moon's surface. The rise of liquid column on the moon's surface is (ac 16. Two thin lenses having $\mathrm{R}_1, \mathrm{R}_2$ as the radii of curved surfaces are kept coaxially together. Their p 17. For a gas at a particular temperature on an average, the quantity which remains same for all molecules is 18. In a common emitter transistor amplifier, the output voltage and input voltage have a phase difference of 19. A body of mass 100 gram is tied to a spring of spring constant $8 \mathrm{~N} / \mathrm{m}$, while the other end of a sp 20. The voltmeter has range 10 V and its internal resistance is $50 \Omega$. To increase the range of voltmeter to 15 V , th 21. If 120 J of thermal energy is incident on area $3 \mathrm{~m}^2$, the amount of heat transmitted is 12 J , coefficient o 22. A circular coil of wire consisting of ' $n$ ' tums each of radius 8 cm carries a current of 0.4 A . The magnitude of the 23. There are two identical small holes on the opposite side of a tank containing full of a liquid. The tank is open at the 24. The graph shows the variation of voltage (v) across the plates of two parallel plate capacitos $A$ and $B$ versus increa 25. If force $\vec{F}=-3 \hat{i}+\hat{j}+5 \hat{k}$ acts along $\vec{r}=7 \hat{i}+3 \hat{j}+\hat{k}$ then the torque acting 26. Susceptibility of a paramagnetic substance is 27. When an ideal gas $\left(\gamma=\frac{5}{3}\right)$ is heated under constant pressure, then what percentage of given hea 28. In the given electrical network, the value of resistance ' $R$ ' when the current in the galvanometer will be zero, is 29. When a photosensitive metal surface is illuminated with radiation of wavelength ' $\lambda_1$ ', the stopping potential 30. The mean kinetic energy of the molecules of an ideal gas at $399^{\circ} \mathrm{C}$ is ' E '. The temperature at which 31. Three capacitors each of capacitance ' C ' and breakdown voltage ' $V$ ' are connected in series. The capacitance and br 32. When alternating current is passed through $\mathrm{L}-\mathrm{R}$ series circuit, the power factor is $\frac{\sqrt{3}}{ 33. Time period of a simple pendulum on earth's surface is ' T '. It time period becomes ' xT ' when taken to a height ' $2 34. The wire loop PQRSP formed by joining two semicircular wire of radii $R_1$ and $R_2$ carries a current $I$ as shown. The 35. A body of mass 1 kg begins to move under the action of a time dependent force $\overrightarrow{\mathrm{F}}=\left(\hat{\m 36. The period of oscillating simple pendulum is $\mathrm{T}=2 \pi \sqrt{\frac{l}{\mathrm{~g}}}$ where length ' $l$ ' is 100 37. If a centre tap transformer is used with two p-n junction diodes for full wave rectification then output voltage of rect 38. Out of the following transitions in hydrogen atom, identify the transition which emits photons of highest frequency. 39. An organ pipe has fundamental frequency 80 Hz . If its one end is closed, the frequencies produced will be (in Hz ) (Neg 40. An a.c. e.m.f. of peak value 230 V and frequency 50 Hz is connected to a circuit with $\mathrm{R}=11.5 \Omega, \mathrm{~ 41. A gas undergoes a change in which its pressure ' P ' and volume ' V ' are related as $\mathrm{PV}^{\mathrm{n}}=$ constan 42. From photoelectric effect experiment, select the correct statement. 43. The equation of wave is $y=60 \sin (1200 t-6 x)$, where ' $y$ ' is in micron, ' $t$ ' is in second and ' $x$ ' is in met 44. Two satellites P and Q go round a planet in circular orbits having radii ' $3 R$ ' and ' $R$ ' respectively. If the spee 45. For a particle performing S.H.M.; the total energy is ' $n$ ' times the kinetic energy, when the displacement of a parti 46. A copper ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ri 47. In a single slit diffraction pattern, identify the incorrect statement from the following. 48. If an alternating voltage is applied across a p-n junction diode in series with a load then 49. Two waves of same frequency ( n ) are approaching each other with same velocity $12 \mathrm{~m} / \mathrm{s}$ along the 50. A coil of resistance $400 \Omega$ is placed in ${ }^3$ magnetic field. If the magnetic flux ' $\phi$, ( Wb ) linked with

Chemistry

Mathematics

Physics

MHT CET 2025 22nd April Morning Shift

MCQ (Single Correct Answer)

-0

A coil of resistance $400 \Omega$ is placed in ${ }^3$ magnetic field. If the magnetic flux ' $\phi$, ( Wb ) linked with the coil varies with time ' $t$ ' ( $s$ ) ${ }^{\text {is }} \phi=50 \mathrm{t}^2+4$, the current in the coil at $\mathrm{t}=2 \mathrm{~s}$ will be

1 A

2 A

0.5 A

0.1 A

MHT CET Papers

2025