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

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

$3: 2$

$2: 3$

$3: 5$

$6: 7$