MHT CET 2025 25th April Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

Mathematics

1. If $\mathrm{f}(x)=\log \left(\frac{1+x}{1-x}\right)$ and $\mathrm{g}(x)=\frac{3 x+x^3}{1+3 x^2}$, then $(\mathrm{fog})(x 2. If $\sec x+\tan x=2,0 3. The eccentricity of the curve represented by $x=3(\cos t+\sin t), y=4(\cos t-\sin t)$ is 4. The rate at which the population of a city increases varies as the population. In a period of 20 years, the population i 5. If $\bar{a}=\hat{i}+\hat{j}+\hat{k}, \bar{b}=\hat{j}-\hat{k}$ then a vector $\bar{c}$ such that $\overline{\mathrm{a}} \ 6. The solution set of the constraints $|x-y| \leq 1, x, y \geq 0$ is 7. The lines $\frac{x-0}{1}=\frac{y-2}{2}=\frac{z+3}{\lambda}$ and $\frac{x-2}{2}=\frac{y-6}{3}=\frac{z-3}{\lambda}$ are co 8. $$ \int_1^3 \frac{\log x^2}{\log \left(16 x^2-8 x^3+x^4\right)} d x= $$ 9. If $\frac{x^2}{\mathrm{a}^2}+\frac{y^2}{\mathrm{~b}^2}=1$, then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$ is 10. If Rolle's theorem holds for the function $x^3+\mathrm{a} x^2+\mathrm{b} x, 1 \leq x \leq 2$ at the point $\frac{4}{3}$, 11. $$ \int \frac{1}{\mathrm{e}^x+1} \mathrm{~d} x= $$ 12. If $y=\tan ^{-1}\left(\frac{4 x}{1+5 x^2}\right)+\cot ^{-1}\left(\frac{3-2 x}{2+3 x}\right)$, then $\frac{\mathrm{d} y}{ 13. The differential equation $x \frac{\mathrm{~d} y}{\mathrm{~d} x}=2 y$ represents ________ 14. $\int \mathrm{e}^x\left(\frac{x+5}{(x+6)^2}\right) \mathrm{d} x$ is 15. The principal solution of of $(5+3 \sin \theta)(2 \cos \theta+1)=0$ are 16. Let X denote the number of hours you study on a Sunday. It is known that $$ \mathrm{P}(\mathrm{X}=x)=\left\{\begin{array 17. The principal value of $\cos ^{-1}\left[\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right 18. The length of the foot of the perpendicular from the point $\left(1, \frac{3}{2}, 2\right)$ to the plane $2 x-2 y+4 z+17 19. A tetrahedron has vertices $\mathrm{O}(0,0,0), \mathrm{A}(1,2,1)$, $B(2,1,3), C(-1,1,2)$. Then the angle between the fac 20. If $A=\left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right]_{3 \times 3}$, then $A^{-1}=$ 21. The area bounded by the parabolas $y=9 x^2, y=\frac{x^2}{16}$ and the line $y=1$ is 22. $\int \frac{\mathrm{d} x}{3 \cos 2 x+5}$ equals 23. The solution of the equation $x^2 y-x^3 \frac{\mathrm{~d} y}{\mathrm{~d} x}=y^4 \cos x$, where $y(0)=1$, is 24. If the statements $p, q$ and $r$ are true, false and true statements respectively, then the truth value of the statement 25. If the lines $\frac{1-x}{2}=\frac{7 y+4}{2 \lambda}=\frac{2 z-5}{2}$ and $\frac{7-7 x}{3 \lambda}=\frac{y-1}{7}=\frac{6- 26. The negation of the statement "The triangle is an equilateral or isosceles triangle and the triangle is not isosceles an 27. $\mathrm{f}(x)=\frac{x}{2}+\frac{2}{x}, x \neq 0$ is strictly decreasing in 28. If $\mathrm{f}(x)=\frac{\sin \left(\pi \cos ^2 x\right)}{3 x^2}, x \neq 0$ is continuous at $x=0$ then $\mathrm{f}(0)=$ 29. Let $z$ be the complex number with $\operatorname{Im}(z)=10$ and satisfying $\frac{2 \mathrm{z}-\mathrm{n}}{2 \mathrm{z} 30. The rate of change of the volume of a sphere with respect to its surface area, when the radius is 5 m is 31. The maximum value of the function $a \sin x+b \cos x$ is 32. The number of values of $x$ in the interval $[0,3 \pi]$ satisfying the equation $2 \sin ^2 x+5 \sin x-3=0$ is 33. $$ \lim\limits_{x \rightarrow 5} \frac{\sqrt{2-2 \cos \left(x^2-12 x+35\right)}}{(x-5)}=\ldots \ldots $$ 34. If ${ }^n \mathrm{C}_0+\frac{1}{2}{ }^n \mathrm{C}_1+\frac{1}{3}{ }^n \mathrm{C}_2$$$+\ldots \frac{1}{n}^n C_{n-1}+\fra 35. A pair of fair dice is thrown 4 times. If getting the same number on both dice is considered as a success, then the prob 36. The position vectors of the points $A, B, C$ are $\hat{i}+2 \hat{j}-\hat{k}, \hat{i}+\hat{j}+\hat{k}, 2 \hat{i}+3 \hat{j 37. If the area of a parallelogram whose diagonals are represented by vectors $3 \hat{i}+\lambda \hat{j}+2 \hat{k}$ and $\ha 38. $y=\mathrm{e}^x(\mathrm{~A} \cos x+\mathrm{B} \sin x)$ is the solution of the differential equation 39. A family has 3 children. The probability that all the three children are girls, given that at least one of them is a gir 40. In a triangle ABC , with usual notations. $\frac{2 \cos \mathrm{~A}}{\mathrm{a}}+\frac{\cos \mathrm{B}}{\mathrm{b}}+\fra 41. A line passes through $\mathrm{P}(-4,1)$ and meets the co-ordinate axes at points A and B . If P divides the segment AB 42. In 3-dimensional space, the equation $x^2-8 x+12=0$ represents .... 43. A pair of tangents are drawn to the circle $x^2+y^2+6 x-4 y-12=0$ from a point $\mathrm{P}(-4,-5)$, then the area enclos 44. If $\bar{a}, \bar{b}, \bar{c}$ are non coplanar unit vectors such that $\overline{\mathrm{a}} \times(\overline{\mathrm{b 45. The joint equation of the bisector of the angle between the lines $2 x^2+11 x y+3 y^2=0$ is 46. If a random variable X has the following probability distribution of X $$ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \mat 47. $$ \int\limits_0^1 \frac{1}{2+\sqrt{x}} d x= $$ 48. Let M and N be foots of the perpendiculars drawn from the point $\mathrm{P}(\mathrm{a}, \mathrm{a}, \mathrm{a})$ on the 49. If $y=\log _3\left(\log _3 x\right)$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=3$ is $\ldots \ldots$ 50. If in triangle ABC , with usual notations $\sin \frac{\mathrm{A}}{2} \cdot \sin \frac{\mathrm{C}}{2}=\sin \frac{\mathrm{

Physics

1. Two planets A and B have densities ' $\rho_1$ ', ' $\rho_2$ ' and have radii ' $r_1$ ', ' $r_2$ ', respectively. The rat 2. A rectangular black body of temperature $127^{\circ} \mathrm{C}$ has surface area $4 \mathrm{~cm} \times 2 \mathrm{~cm}$ 3. If the two sources of light emit waves of different amplitudes and interfere then 4. The reactance of a capacitor is $\mathrm{X}_{\mathrm{C}}$. If the frequency and the capacitance are doubled, then the ne 5. Two discs of moment of inertia ' $\mathrm{I}_1$ ' and ' $\mathrm{I}_2$ ' and angular speeds ' $\omega_1$ ' and ' $\omega 6. A wire has a mass $0.3 \pm 0.003$ gram, radius $0.5 \pm 0.005 \mathrm{~mm}$ and length $6 \pm 0.06 \mathrm{~cm}$. The ma 7. Two particles ' $A$ ' and ' $B$ ' execute SHMs of periods ' $T$ ' and $\frac{3 T}{2}$. If they start from the mean posit 8. The current (I) drawn from the battery in the given circuit is 9. If the electron in hydrogen atom jumps from third Bohr orbit to ground state directly and the difference between energie 10. Vector $\vec{A}$ of magnitude $5 \sqrt{3}$ units, another vector $\vec{B}$ of magnitude of 10 units are inclined to each 11. The magnetic field intensity H at the centre of a long solenoid having $n$ turns per unit length and carrying a current 12. Four particles each of mass M are placed at the corners of a square of side L . The radius of gyration of the system abo 13. In Fraunhofer diffraction pattern, slit width is 0.3 mm and screen is at 1.5 m away from the lens. If wavelength of ligh 14. Two boys are standing at points A and B on ground, where distance $\mathrm{AB}=\mathrm{x}$. The boy at B stars running p 15. The temperature of an ideal gas is increased from 100 K to 400 K . If ' $x$ ' is the root mean square velocity of its mo 16. Current $I$ is carried in a wire of length ' $L$ '. If wire is bent into a circular coil of single turn, the maximum tor 17. The equivalent inductance between A and B is equal to 18. Five capacitors, each of capacity ' $C$ ' are connected as shown in the figure. The resultant capacity between A and B i 19. A machine gun fires a bullet of mass 35 gram with a speed of $600 \mathrm{~m} / \mathrm{s}$. The person holding the gun 20. According to the kinetic theory of gases, when two molecules of a gas collide with each other then 21. An a. c. voltage is applied to pure inductor. The current in the inductor 22. During the isothermal expansion, a confined ideal gas does $(-150) \mathrm{J}$ of work against its surroundings. This me 23. A single slit diffraction pattern is formed with light of wavelength $6384 \mathop {\rm{A}}\limits^{\rm{o}}$. The second 24. When a metal surface is illuminated by light of wavelength $\lambda_1$ and $\lambda_2$, the maximum velocities of photoe 25. A point mass ' $m$ ' attached at one end of a massless, inextensible string of length ' $l$ ' performs a vertical circul 26. A body cools from $80^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ in 5 min . In the next time of ' t ' in, the body c 27. A square of side ' $L$ ' metre lies in $x-y$ plane in a region where the magnetic field is $\overline{\mathrm{B}}$ and $ 28. Three charges $Q(-2 q)$ and $(-2 q)$ are placed at the vertices of an isosceles right angled triangle as shown in figure 29. In a capillary tube of area of cross-section 'a' water rises to height ' $h$ '. To what height will water rise in a capi 30. A small sphere oscillates simple harmonically in a watch glass whose radius of curvature is 1.6 m . The period of oscill 31. The logic gate for which the output goes 'HIGH' or ' 1 ' only when an odd number of 'HIGH' or ' 1 ' are at its input, is 32. A long straight wire of radius ' $r$ ' carries a steady current ' $I$ '. The current is uniformly distributed over its c 33. A sound source is moving towards a stationary observer with $\left(\frac{1}{10}\right)^{\text {th }}$ the speed of sound 34. The velocity of small spherical ball of mass ' $m$ ' and density ' $\mathrm{d}_1$ ', when dropped in a container filled 35. The fundamental frequency of a closed pipe is 400 Hz . If $\left(\frac{1}{3}\right)^{\text {rd }}$ length of the pipe is 36. To get output of the following logic circuit as ' 0 ' (zero), the inputs $A, B, C$ should NOT be, respectively, 37. The displacement of particle in S.H.M. is $\mathrm{x}=\mathrm{A} \cos (\omega \mathrm{t}+\pi / 6)$. Its speed will be ma 38. The power factor of a CR circuit is $\frac{1}{\sqrt{2}}$, If the frequency of a.c. signal is halved, then the power fact 39. The image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to mov 40. The volume of given mass of a gas is increased by $7 \%$ at constant temperature. The pressure should be increased by 41. At poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting, to 42. A radioactive element has rate of disintegration 9000 disintegration per minute at a particular instant. After two minut 43. Two point charges $\mathrm{q}_1$ and $\mathrm{q}_2$ are ' $l$ ' distance apart. If one of the charges is doubled and dis 44. A monoatomic ideal gas is compressed adiabatically to $\left(\frac{1}{27}\right)$ of its initial volume. If initial temp 45. In LCR series circuit, when ' $L$ ' is removed from the circuit, the phase difference between voltage and current in the 46. The value of the shunt resistance that allows $10 \%$ of the main current through the galvanometer of $99 \Omega$ is 47. In which of the following figures, the p.n. junction diode is reverse biased? 48. Two tuning forks of frequencies 256 Hz and 258 Hz are sounded together. The time interval between two consecutive maxima 49. ' $n$ ' identical small spherical drops of water, each of radius ' $r$ ' and charged to the same potential ' v ' are com 50. Sodium and copper have work functions 2.3 eV and 4.5 eV respectively. The ratio of threshold wavelength of sodium to tha

Chemistry

Mathematics

Physics

MHT CET 2025 25th April Morning Shift

MCQ (Single Correct Answer)

-0

Sodium and copper have work functions 2.3 eV and 4.5 eV respectively. The ratio of threshold wavelength of sodium to that of copper is nearest to

$1: 4$

$4: 1$

$1: 2$

$2: 1$

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