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

Chemistry

Mathematics

1. If a random variable X follows the Binomial distribution $B(10, \quad p)$ such that $5 \mathrm{P}(\mathrm{X}=0)=\mathrm{ 2. A particular solution of $\frac{\mathrm{d} y}{\mathrm{~d} x}=(x+9 y)^2$, when $x=0, y=\frac{1}{27}$ is 3. $$ \mathop {\lim }\limits_{x \to \infty } \frac{\mathrm{e}^{x^4}-1}{\mathrm{e}^{x^4}+1}= $$ 4. The shortest distance between the lines $\bar{r}=(4 \hat{i}-\hat{j})+\lambda(\hat{i}+2 \hat{j}-3 \hat{k})$ and $\bar{r}= 5. If $\mathrm{f}(x)=\cos (\log x)$ then $\mathrm{f}\left(x^2\right) \cdot \mathrm{f}\left(y^2\right)-\frac{1}{2}\left[\mat 6. The general solution of $\frac{\mathrm{d} y}{\mathrm{~d} x}=2 x y \mathrm{e}^{x^2}$ is 7. Which of the following is not a homogeneous function? 8. The maximum value and minimum value of the volume of the parallelopiped having coterminous edges $\hat{\mathrm{i}}+x \ha 9. The following is the probability distribution of X $$ \begin{array}{|c|c|c|c|c|} \hline \mathrm{X} & 0 & 1 & 2 & 3 \\ \h 10. Let $\overline{\mathrm{a}}$ and $\overline{\mathrm{c}}$ be unit vectors at an angle $\frac{\pi}{3}$ with each other. If 11. A random variable X takes values $0,1,2,3$, ........ with probabilities. $\mathrm{P}(\mathrm{X}=x)=\mathrm{k}(x+1)\left( 12. The area inside the parabola $y^2=4 \mathrm{a} x$, between the lines $x=\mathrm{a}$ and $x=4 \mathrm{a}$ is equal to 13. $\int_2^4 \frac{\log x^2}{\log x^2+\log \left(36-12 x+x^2\right)} \mathrm{d} x$ is equal to 14. Let $\bar{a}, \bar{b}$, and $\bar{c}$ be unit vectors. Suppose that $\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}=\ 15. If $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$ are unit vectors such that $|\overline{\mathrm{a}}+\overline{\mat 16. The value of $\int_0^2\left[x^2\right] \mathrm{d} x$ is (where $[x]$ denotes the greatest integer function not greater t 17. If $\quad \int \frac{3 \sin x \cos x}{4 \sin x+7} \mathrm{~d} x=\mathrm{A} \sin x-\mathrm{Blog}(4 \sin x+7)+\mathrm{c}$ 18. Three vectors $\hat{\mathrm{i}}-\hat{\mathrm{k}}, \lambda \hat{\mathrm{i}}+\hat{\mathrm{j}}+(1-\lambda) \hat{\mathrm{k}} 19. $$ \int \frac{\mathrm{d} x}{x\left(x^2+1\right)}= $$ 20. The joint equation of the bisectors of the angles between the lines $x=5$ and $y=3$ is 21. If $\sin ^{-1} \frac{1}{3}+\sin ^{-1} \frac{3}{5}+\sin ^{-1} x=\frac{\pi}{2}$ then $x=$ 22. $\int \sqrt{x^2-6 x-16} \mathrm{~d} x$ equals 23. The value of $2 \tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{3}{8}$ is 24. With usual notation, in triangle ABC , $\mathrm{m} \angle \mathrm{A}=30^{\circ}$ then the value of $\left(1+\frac{\mathr 25. The greatest possible number of points of intersection of 8 distinct straight lines and 4 distinct circles is 26. In $\triangle A B C$, with usual notations, $a \cos B=b \cos A, a \cos C \neq c \cos A$ then $\mathrm{A}(\triangle \math 27. The radius of the base of a cone is increasing at the rate $3 \mathrm{~cm} /$ minute and the altitude is decreasing at t 28. In a triangle ABC , with usual notations if $\mathrm{a}=4, \mathrm{~b}=8, \angle \mathrm{C}=60^{\circ}$, then the value 29. The third element in the second row of adjoint of a matrix $A=\left[a_{i j}\right]_{3 \times 3}$ (where $a_{i j}=2 i+j$ 30. The function $x^5-5 x^4+5 x^3-10$ has a maximum, when $x$ is equal to 31. The function f defined by $\mathrm{f}(x)=(x+2) \mathrm{e}^{-x}$ is 32. If the function $\mathrm{f}(x)=x(x+3) \mathrm{e}^{-\frac{x}{2}}$ satisfies all the conditions of Rolle's theorem in $[-3 33. If $(\mathrm{a}+\mathrm{b} x) \mathrm{e}^{\frac{y}{x}}=x$, then $x^3 \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}$ is equal t 34. If $x=\log \mathrm{t}, \mathrm{t}>0$ and $y=\frac{1}{\mathrm{t}}$ then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}=$ 35. If $y=\frac{\mathrm{K}^{\cos ^{-1} x}}{1+\mathrm{K}^{\cos ^{-1} x}}$ and $\mathrm{t}=\mathrm{K}^{\cos ^{-1} x}$, then $\ 36. The complex numbers $\sin x+i \cos 2 x$ and $\cos x$ - $\mathrm{i} \sin 2 x,(\mathrm{i}=\sqrt{-1})$ are conjugate to eac 37. The probability that in a random arrangement of the letters of the word 'UNIVERSITY', the two 'I's do not come together 38. The logical statement $$ [\sim(\sim p \vee q) \vee(p \wedge r) \wedge(\sim q \wedge r)] $$ is equivalent to 39. The L.P.P. , minimize $z=30 x+20 y, x+y \leq 8$, $x+2 y \geq 4,6 x+4 y \geq 12, x \geqslant 0, y \geqslant 0$ has 40. If the distance of the point $\mathrm{P}(1,-2,1)$ from the plane $x+2 y-2 z=\alpha$, where $\alpha>0$ is 5 units, then t 41. The equation of the plane containing the line $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-4}{-2}$ and the point $(0,5,0)$ is 42. If the statement pattern $(p \wedge q) \rightarrow(r \vee \sim s)$ is false, then the truth values of $p, q, r$ and $s$ 43. If $f(x)= \begin{cases}\frac{8^x-4^x-2^x+1}{x^2}, & \text { if } x>0 \\ e^x \sin x+x+\lambda \log 4, & \text { if } x \l 44. The line of intersection of the planes $\bar{r} \cdot(3 \hat{i}-\hat{j}+\hat{k})=1 \quad$ and $\quad \bar{r} \cdot(\hat{ 45. The Y-intercept of the common tangent to the parabolas $y^2=32 x$ and $x^2=108 y$ is 46. If the line $2 x+y=\mathrm{k}$ passes though the point which divides the line segment joining the points $(1,1)$ and $(2 47. The minimum distance and maximum distance of the point $\mathrm{P}(2,-7)$ from the circle $x^2+y^2-14 x-10 y-151=0$ are 48. The lines $\overline{\mathrm{r}}=\overline{\mathrm{a}}+\lambda(\overline{\mathrm{b}} \times \overline{\mathrm{c}})$ and 49. $$ 3 \tan ^6 10^{\circ}-27 \tan ^4 10^{\circ}+33 \tan ^2 10^{\circ}= $$ 50. The assets of a person reduced in his business such that the rate of reduction is proportional to the square root of the

Physics

1. Two simple harmonic motions of angular frequency $300 \mathrm{rad} / \mathrm{s}$ and $3000 \mathrm{rad} / \mathrm{s}$ ha 2. Two very long straight conductors (wires) are set parallel to each other. Each carries a current ' I ' in the same direc 3. A rectangular block of surface area A emits energy E per second at $27^{\circ} \mathrm{C}$. If length and breadth is red 4. A pipe open at both ends of length 1.5 m is dipped in water at one end such that $2^{\text {nd }}$ overtone of vibrating 5. A physical quantity A can be determined by measuring parameters $\mathrm{B}, \mathrm{C}, \mathrm{D}$ and E using the rel 6. In series LCR resonant circuit, R $=800 \Omega$, $\mathrm{C}=2 \mu \mathrm{~F}$ and voltage across resistance is 200 V . 7. When a diatomic gas (rigid) undergoes adiabatic change, its pressure $(\mathrm{P})$ and temperature $(\mathrm{T})$ are r 8. Two coils $P$ and $Q$ are kept near each other. When no current flows through coil $P$ and current increases in coil Q a 9. A mass $m$ is suspended from a spring of negligible mass. The spring is pulled a little and then released, so that mass 10. The three vector $\vec{A}=3 \hat{i}-2 \hat{j}+\hat{k}, \vec{B}=\hat{i}-3 \hat{j}+5 k$ and $\vec{C}=2 \hat{i}-\hat{j}+4 \ 11. Two identical long parallel wires carry currents ' $\mathrm{I}_1$ ' and ' $\mathrm{I}_2$ ' such that $\mathrm{I}_1>\math 12. A disc of mass 25 kg and radius 0.2 m is rotating at 240 r.p.m. A retarding torque brings it to rest in 20 second. If th 13. Interference fringes are produced on the screen by using two light sources of intensities I and 9I. The phase difference 14. Which of the following logic gates is called as Universal gate? 15. For an ideal gas, the density of the gas is $\rho_0$ when temperature and pressure of the gas are $\mathrm{T}_0$ and $P_ 16. Which graph shows correctly the temperature (T). dependence of resistivity $(\rho)$ of a semiconductor? 17. Two uniform wires of same material are vibrating under the same tension. If the $1^{\text {st }}$ overtone of $1^{\text 18. The variation of magnetic susceptibility $(\chi)$ with temperature for a diamagnetic substance is shown correctly by gra 19. A liquid drop of volume V is placed on the surface of glass plate. Then another glass plate is placed on it such that li 20. If maximum energy is stored in a capacitor at $\mathrm{t}=0$ then the time after which, current in the circuit will be m 21. The velocity time graph of a body moving in a straight line is shown in figure. The ratio of displacement to distance tr 22. The length of a potentiometer wire is ' $L$ ' . A cell of e.m.f. $E$ is balanced at a length $\frac{L}{5}$ from the posi 23. In LCR series circuit, R = 18 $\Omega$ and impedance $33 \Omega$. An r.m.s. voltage of 220 V is applied across the circu 24. A child stands on a weighing machine inside a lift. When the lift is going down with acceleration $\mathrm{g} / 3$, the 25. The equivalent capacitance between plates ' A ' and ' B ' ( A -area of each plate, d-separation between plates) ( $\vare 26. Which of the following transitions in hydrogen atom emit photons of highest frequency? ( $\mathrm{n}=$ principle quantum 27. Water rises up to height ' $x$ ' in a capillary tube immersed vertically in water. When the whole arrangement is taken t 28. In Young's double slit experiment, in an interference pattern, a minimum is observed exactly in front of one slit. The d 29. The total energy of a circularly orbiting satellite is 30. The de-Broglie wavelength $(\lambda)$ of a particle 31. An incompressible fluid flows steadily through a cylindrical pipe having radius R at point A and $\left(\frac{\mathrm{R} 32. Two radioactive materials $A$ and $B$ having decay constant ' $7 \lambda$ ' and ' $\lambda$ ' respectively, initially ha 33. A centigrade and Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenhe 34. Photoelectric emission is observed from a metallic surface for frequencies $v_1$ and $v_2$ of the incident light rays $\ 35. The electric charges ' $+2 q$ ', ' $+2 q$ ', ' $-2 q$ ' and ' $-2 q$ ' are placed at the corners of square of side ' 2 L 36. Two circular loops P and Q of radii ' r ' and ' nr ' are made respectively from a uniform wire. Moment of inertia of loo 37. An observer on sea-coast counts 45 waves in one minute. If the wavelength of the waves is 7 m , then the velocity of the 38. A simple pendulum has time period ' $\mathrm{T}_1$ '. The point of suspension is now moved upward according to equation 39. To manufacture a solenoid of length ' $l$ ' and inductance ' $L$ ', the length of the thin wire required is (Diameter of 40. An engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac{1}{5}$. When $T_2$ is lowered by 45 K , i 41. In an n-p-n transistor amplifier, the collector current is 8 mA . If $80 \%$ of the electrons from the emitter reach the 42. An electric dipole having each charge of magnitude $2 \mu \mathrm{C}$ is placed in an electric field of intensity $8 \ti 43. Two sources of sound are emitting progressive waves $\mathrm{y}_1=4 \sin 710 \pi \mathrm{t}$ and $\mathrm{y}_2=3 \sin 70 44. Three spheres, each of mass ' $m$ ' and radius ' $r$ ' are placed as shown in figure. Consider an axis $\mathrm{YY}^{\pr 45. $$ \text { The value of current I in the given circuit is } $$ 46. Three polarised sheets are co-axially placed. Pass axis of polaroids 2 and 3 make $30^{\circ}$ and $90^{\circ}$ with pas 47. Two cylinders A and B fitted with pistons contain equal amount of an ideal rigid diatomic gas at 303 K . The piston of c 48. The phenomenon, which is not due to total internal reflection is 49. Initially a rectangular coil with length vertical is moving out with constant velocity ' $v$ ' in a constant magnetic fi 50. The voltage between the plates of a parallel plate capacitor of capacity $1 \mu \mathrm{~F}$ is changing at the rate of

Chemistry

Mathematics

Physics

MHT CET 2025 21st April Morning Shift

MCQ (Single Correct Answer)

-0

The voltage between the plates of a parallel plate capacitor of capacity $1 \mu \mathrm{~F}$ is changing at the rate of $4 \mathrm{~V} / \mathrm{s}$. the displacement current in the capacitor is

$4 \mu \mathrm{~A}$

$3 \mu \mathrm{~A}$

$1 \mu \mathrm{~A}$

$6 \mu \mathrm{~A}$

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