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

Chemistry

Mathematics

1. If a circle with centre at $(-1,1)$ touches the line $x+2 y+4=0$ then the co-ordinates of the point of contact are 2. A doctor assumes that patient has one of three diseases $\mathrm{d} 1, \mathrm{~d} 2$ or d 3 . Before any test he assume 3. A particle P starts from the point $\mathrm{Z}_0=1+2 \mathrm{i}$ where $\mathrm{i}=\sqrt{-1}$. It moves first horizontal 4. $$ \mathop {\lim }\limits_{x \to 0} \frac{63^x-9^x-7^x+1}{\sqrt{2}-\sqrt{1+\cos x}}=\ldots \ldots $$ 5. Consider the following three statements (A) If $3+2=7$ then $4+3=8$. (B) If $5+2=7$ then earth is flat. (C) If both (A) 6. If $\mathrm{A}=\left[\begin{array}{cc}5 \mathrm{a} & -\mathrm{b} \\ 3 & 2\end{array}\right]$ and A .adj $\mathrm{A}=\mat 7. The common principal solution of the equations $\sin \theta=-\frac{1}{2}$ and $\tan \theta=\frac{1}{\sqrt{3}}$ is 8. The slopes of the lines represented by $6 x^2+2 \mathrm{hxy}+y^2=0$ are in the ratio $2: 3$, then $\mathrm{h}=$ 9. If $\theta$ is an obtuse angle between vectors $\bar{a}$ and $\overline{\mathrm{b}}$ such that $|\overline{\mathrm{a}}|= 10. If the plane $\frac{x}{2}-\frac{y}{3}-\frac{\mathrm{z}}{5}=1$ cuts the co-ordinate axes in points $\mathrm{A}, \mathrm{B 11. The rate of increase of the population of a city is proportional to the population present at that instant. In the perio 12. The probability that a student is not a swimmer is $\frac{1}{5}$. The probability that out of 5 students selected at ran 13. A player tosses two coins. He wins ₹ 10 , if 2 heads appears, ₹ 5 , if one head appear and ₹ 2 if no head appears. Then 14. Consider the probability distribution $$ \begin{array}{|l|l|l|l|l|l|} \hline \mathrm{X}=x & 1 & 2 & 3 & 4 & 5 \\ \hline 15. The equation of the curve passing through origin and satisfying $\left(1+x^2\right) \frac{\mathrm{d} y}{\mathrm{~d} x}+2 16. If $y=\tan ^{-1}\left(\frac{12 x-64 x^3}{1-48 x^2}\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$ 17. The order of the differential equation whose general solution is given by $y=\left(\mathrm{C}_1+\mathrm{C}_2\right) \sin 18. In L.P.P., the maximum value of objective function $\mathrm{Z}=6 x+3 y$ subject to constraints $x+y \leq 5, x+2 y \geq 4 19. If the lines $x=a y-1=z-2$ and $x=3 y-2=\mathrm{bz}-2(\mathrm{ab} \neq 0)$ are coplanar, then 20. If $\left(\tan ^{-1} x\right)^2+\left(\cot ^{-1} x\right)^2=\frac{5 \pi^2}{8}$, then $x^2+1=$ 21. If $p \equiv$ The switch $S_1$ is closed, $q \equiv$ The switch $\mathrm{S}_2$ is closed, $\mathrm{r} \equiv$ switch $\m 22. Let $\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$ is differentiable function having $\mathrm{f}(3)=3, \mathrm{f}^{\pri 23. The area bounded by the curve $y=4 x-x^2$ and X - axis in square units, is $\qquad$ 24. The Cartesian equation of the plane $\overline{\mathrm{r}}=(2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}})+\lambda(\hat{\mathrm{ 25. If the line $\frac{x-3}{2}=\frac{y+5}{-1}=\frac{z+2}{2}$ lies in the plane $\alpha x+3 y-z+\beta=0$, then values of $\al 26. $$ \int_{\log \frac{1}{2}}^{\log 2} \sin \left(\frac{\mathrm{e}^x-1}{\mathrm{e}^x+1}\right) \mathrm{d} x= $$ 27. If the vectors $\overline{\mathrm{a}}=\mathrm{c}\left(\log _7 x\right) \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathr 28. $$ \int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} \sin ^{-4} x d x= $$ 29. The altitude through vertex $A$ of $\triangle A B C$ with position vectors of points $A, B, C$ as $\bar{a}, \bar{b}, \ba 30. $$ \int \frac{\mathrm{d} x}{(x+\mathrm{a})^{\frac{9}{7}}(x-\mathrm{b})^{\frac{5}{7}}}= $$ 31. The lines $\bar{r}=(\hat{i}+\hat{j}-\hat{k})+\lambda(3 \hat{i}-\hat{j})$ and $\overline{\mathrm{r}}=(4 \hat{\mathrm{i}}- 32. If $\overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ are unit vectors and $|\overline{\mathrm{a}}|=7$, $\overline{\mat 33. With usual notations in $\triangle \mathrm{ABC}$, if $\angle \mathrm{B}=\frac{\pi}{2}$, and $\tan \frac{\mathrm{A}}{2}, 34. $\int \frac{\mathrm{d} x}{x\left(x^3+1\right)}=$ 35. If $\tan ^{-1}(x+1)+\tan ^{-1} x+\tan ^{-1}(x-1)=\tan ^{-1} 3$, then for $x 36. Let $\mathrm{f}: \mathbb{R}-\{2\} \rightarrow \mathbb{R}-\{1\}$ defined by $\mathrm{f}(x)=\frac{x-3}{x-2}$ and $\mathrm{ 37. There are 11 points in a plane of which 5 points are collinear. Then the total number of distinct quadrilaterals with ve 38. $\int \frac{x^4 \cos \left(\tan ^{-1} x^5\right)}{1+x^{10}} d x$ equals 39. The length of the perpendicular drawn from the origin on the normal to the curve $x^2+2 x y-3 y^2=0$ at the point $(2,2) 40. If $\mathrm{f}(x)=\log (1+x)-\frac{2 x}{2+x}$ then $\mathrm{f}(x)$ is increasing in 41. The angle $\theta$, at which the curves $y=3^x$ and $y=7^x$ intersect, is given by 42. The function $\mathrm{f}(x)=x^3-6 x^2+\mathrm{ax}+\mathrm{b}$ satisfies the conditions of Rolle's theorem in $[1,3]$. Th 43. If $$ \sqrt{y-\sqrt{y-\sqrt{y-\ldots \ldots \ldots \infty}}}=\sqrt{x+\sqrt{x+\sqrt{x+\ldots \ldots \ldots \infty}}} $$ t 44. If $x=\operatorname{sint}$ and $y=\sin p t$, then the value of $$ \left(1-x^2\right) \frac{\mathrm{d}^2 y}{\mathrm{~d} x 45. Let $\bar{a}=\hat{i}+\hat{j}-\hat{k}$ and $\bar{c}=5 \hat{i}-3 \hat{j}+2 \hat{k}$ and if $\overline{\mathrm{b}} \times \ 46. The circumradius of a triangle whose sides are 10 units, 8 units and 6 units is 47. The eccentricity of the hyperbola which passes through the points $(3,0)$ and $(3 \sqrt{2}, 2)$ is 48. $$ \cos ^4 \frac{\pi}{8}+\cos ^4 \frac{3 \pi}{8}+\cos ^4 \frac{5 \pi}{8}+\cos ^4 \frac{7 \pi}{8}= $$ 49. The straight line passing through $(-3,6)$ and midpoint of the line segment joining the points $(4,-5)$ and ( $-2,9$ ) h 50. The general solution of differential equation $\left(y^2-x^2\right) \mathrm{d} x=x y \mathrm{~d} y(x \neq 0)$ is

Physics

1. The fundamental frequencies of vibrations of air column in pipe open at both ends and in pipe closed at one end are ' $\ 2. A force F is applied on a square plate of side L . If the percentage error in determining F is $3 \%$ and that in L is $ 3. A bob of mass ' $m$ ' is tied by a massless string whose other end is wound on a flywheel (disc) of radius ' $R$ ' and m 4. A copper ring having a cut such as not to form a complete loop is held horizontally and a bar magnet is dropped through 5. In Young's double slit experiment, at two points $P$ and $Q$ on screen, waves from slits $S_1$ and $S_2$ have a path dif 6. One of the following values of inputs $\mathrm{A}, \mathrm{B}$ and C respectively gives output $(\mathrm{Y})$ of the fol 7. The initial average kinetic energy of the molecules was E , when a gas sample is at $27^{\circ} \mathrm{C}$. When the ga 8. A piece of semiconductor is connected in series in an electric circuit. On increasing the temperature, the current in th 9. Seven capacitors each of capacitance $2 \mu \mathrm{~F}$ are to be connected in a configuration to obtain an effective c 10. In an $L R$ circuit, the value of $L$ is $\left(\frac{0.3}{\pi}\right)$ henry and the value of R is $40 \Omega$, If in t 11. The depth at which the value of acceleration due to gravity becomes $\left(\frac{1}{n}\right)$ times the value at the su 12. A horizontal pipeline carries water in a streamline flow. At a point along the pipe, where the cross-sectional area is $ 13. Two simple pendulums have first (A) bob of mass ' $M_1$ ' and length ' $L_1$ ', second (B) of mass ' $\mathrm{M}_2$ ' an 14. If the frequency of incident light in a photoelectric experiment is doubled, then stopping potential will 15. A constant force $\vec{F}=3 \hat{i}-2 \hat{j}-\hat{k}$ newton has a displacement $\vec{r}=2 \hat{i}-3 \hat{j}-3 \hat{k}$ 16. In a common emitter amplifier configuration, the current gain is 62 . The collector resistance and input resistance are 17. A thin uniform rod of length ' $L$ ' and mass ' $M$ ' is swinging freely about a horizontal axis passing through its end 18. In a biprism experiment a steady interference pattern is observed on the screen using a light of wavelength $5000 \matho 19. Two girls are standing at the ends ' $A$ ' and ' $B$ ' of a ground where $\mathrm{AB}=\mathrm{b}$. The girl at ' B ' sta 20. A coil of wire of radius ' $r$ ' has 600 turns and a self-inductance of 108 mH . The self-inductance of a coil with same 21. A sample of an ideal gas $\left(\gamma=\frac{5}{3}\right)$ is heated at constant pressure. If 100 J of heat is supplied 22. Using Bohr's quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? ( $I=$ m 23. Assuming the drops to be spherical, 27 identical drops of mercury are charged simultaneously to the same potential of 20 24. An object of mass ' $m$ ' moving with velocity ' $u$ ' collides with another stationary object of mass ' $M$ ' and stops 25. In the following figure magnitude of the magnetic field at the point $p$ is 26. A balloon is filled at $27^{\circ} \mathrm{C}$ and 1 atmospheric pressure by volume $500 \mathrm{~m}^3$ helium gas. At $ 27. As shown in the figure, $S_1$ and $S_2$ are identical springs with spring constant K each. The oscillation frequency of 28. The volume of a metal sphere increases by $0.33 \%$ when its temperature is raised by $50^{\circ} \mathrm{C}$. The coeff 29. The amount of work done in blowing a soap bubble such that its diameter increases from 'd' to ' $D$ ' is ( $T=$ surface 30. In an a.c. circuit, a resistance ' $R$ ' is connected in series with an inductance ' $L$ '. If phase angle between volta 31. In an open end organ pipe of length ' $L$ ', if the velocity of sound is ' V ', then the fundamental frequency will be ( 32. Two batteries of e.m.f 4 V and 8 V with internal resistance $1 \Omega$ and $2 \Omega$ respectively are connected in a ci 33. At what speed should a source of sound move so that the observer finds the apparent frequency equal to half the original 34. A particle starts oscillating simple harmonically from its mean position with time period ' $T$ '. At time $\mathrm{t}=\ 35. A coil of ' $n$ ' turns and resistance $R \Omega$ is connected in series with a resistance $\frac{R}{2}$. The combinatio 36. An electron of mass ' $m$ ' and charge ' $e$ ' initially at rest gets accelerated by a constant electric field ' E '. Th 37. The moment of inertia of a solid sphere of mass ' $m$ ' and radius ' $R$ ' about its diametric axis is ' $I$ '. Its mome 38. A glass cube of length 21 cm has a small air bubble trapped inside. When viewed normally from the opposite face, its app 39. Two identical metal plates are given charges $q_1$ and $q_2\left(q_2 40. In hydrogen atom in its ground state, the first Bohr orbit has radius ' $\mathrm{r}_1$ '. When the atom is raised to one 41. Heat supplied $d Q=$ increased in internal energy dU is true for 42. With a resistance ' X ' connected in series with a galvanometer of resistance $100 \Omega$, it acts as a voltmeter of ra 43. When one end of a capillary tube is dipped in water, the height of water column is ' $h$ '. The upward force of 105 dyne 44. A tuning fork gives 5 beats per second with 40 cm length of sonometer wire. If the length of the wire is shortened by 1 45. A circular coil carrying current ' T ' has a radius ' $r$ ' and ' $n$ ' turns. The magnetic field along the axis of a co 46. Two equally charged small balls placed at a fixed distance experience a force ' $F$ '. A similar uncharged ball after to 47. An a.c. source of frequency ' f ' is connected to a circuit containing an inductance ' $L$ ' and resistance ' R ' in ser 48. A black body emits radiation of maximum intensity at wavelength ' $\lambda$ ' at temperature T K. Its corresponding wave 49. In a single slit diffraction experiment, slit of width ' $a$ ' is illuminated by light of wavelength ' $\lambda$ ' and t 50. To protect the instrument from magnetic field, it is completely surrounded by

Chemistry

Mathematics

Physics

MHT CET 2025 25th April Evening Shift

MCQ (Single Correct Answer)

-0

To protect the instrument from magnetic field, it is completely surrounded by

soft ferromagnetic substance.

diamagnetic substance only.

paramagnetic substance only.

both diamagnetic and paramagnetic substances.

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