MHT CET 2024 3rd May Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

Mathematics

1. The equation of the line passing through the point of intersection of the lines $3 x-y=5$ and $x+3 y=1$ and making equal 2. $$\int \frac{\operatorname{cosec} x d x}{\cos ^2\left(1+\log \tan \frac{x}{2}\right)}=$$ 3. The vectors $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$ are not perpendicular and $\overline{\mathrm{c}}$ and $\ 4. If the function $\mathrm{f}(x)=\left(\frac{5 x-8}{8-3 x}\right)^{\frac{3}{2 x-4}}$ if $x \neq 2$. $=\mathrm{k}$ if $x=2$ 5. The domain of definition of $\mathrm{f}(x)=\frac{\log _2(x+3)}{x^2+3 x+2}$ is 6. The equation of pair of lines $y=p x$ and $y=q x$ can be written as $(y-p x)(y-q x)=0$. Then the equation of the pair of 7. The equation $(\operatorname{cosp}-1) x^2+(\operatorname{cosp}) x+\sin p=0$ in the variable $x$, has real roots. Then p 8. If $\overline{\mathrm{a}}=\frac{1}{\sqrt{10}}(4 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+\hat{\mathrm{k}}), \overline{\mathrm 9. Let a random variable X have a Binomial distribution with mean 8 and variance 4 . If $\mathrm{P}(x \leqslant 2)=\frac{\m 10. If $\bar{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}, \bar{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k} \quad$ and $\bar{c}=c_1 \ha 11. The area of the region, bounded by the parabola $y=x^2+2$ and the lines $y=x, x=0$ and $x=3$, is 12. If $0 $$\sqrt{1+x^2}\left[\left\{x \cos \left(\cot ^{-1} x\right)+\sin \left(\cot ^{-1} x\right)\right\}^2-1\right]^{\fr 13. For the probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-sty 14. The number of all values of $\theta$ in the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ satisfying the equatio 15. Two cards are drawn successively with replacement from a well- shuffled pack of 52 cards. Let X denote the random variab 16. The curve $y=a x^3+b x^2+c x+5$ touches the $x$-axis at $(-2,0)$ and cuts the $y$-axis at a point Q where its gradient i 17. Let $\mathrm{L}_1$ $\frac{x+1}{3}=\frac{y+2}{2}=\frac{z+1}{1}$ and $\mathrm{L}_2: \frac{x-2}{2}=\frac{y+2}{1}=\frac{z-3} 18. If $y=a \log x+b x^2+x$ has its extreme value at $x=-1$ and $x=2$, then the value of $a+b$ is 19. The value of the integral $\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\left(x^2+\log \frac{\pi-x}{\pi+x}\right) \cos x d x$ is 20. For the system $x-y+z=4,2 x+y-3 z=0$, $x+y+z=2$, the values of $x, y, z$ respectively are given by 21. The value of $\int \sin \sqrt{x} \mathrm{dx}$ is equal to 22. If the vectors $\overline{A B}=3 \hat{i}+4 \hat{k}$ and $\overline{A C}=5 \hat{i}-2 \hat{j}+4 \hat{k}$ are the sides of 23. If $\mathrm{f}(x)=x^3+b x^2+c x+d$ and $0 24. If $\mathrm{f}\left(\frac{x-4}{x-2}\right)=2 x+1, x \in \mathbb{R}-\{1,-2\}$, then $\int \mathrm{f}(x) \mathrm{d} x$ is 25. If $\sin (\theta-\alpha), \sin \theta$ and $\sin (\theta+\alpha)$ are in H.P., then the value of $\cos ^2 \theta$ is 26. The equation of the plane passing through the point $(1,1,1)$ and perpendicular to the planes $2 x-y-2 z=5$ and $3 x-6 y 27. The tangent to the circle $x^2+y^2=5$ at $(1,-2)$ also touches the circle $x^2+y^2-8 x+6 y+20=0$ then the co-ordinates o 28. The general solution of the differential equation $x \cos y \mathrm{~d} y=\left(x \mathrm{e}^{\mathrm{x}} \log x+\mathrm 29. The equation $(\operatorname{cosp}-1) x^2+(\cos p) x+\operatorname{sinp}=0$ in the variable $x$, has real roots. Then p 30. A committee of 11 members is to be formed from 8 males and 5 females. If $m$ is the number of ways the committee is form 31. If $y=[(x+1)(2 x+1)(3 x+1) \ldots \ldots \ldots(n x+1)]^4$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=0$ is 32. Let $\alpha$ and $\beta$ be two real roots of the equation $(k+1) \tan ^2 x-\sqrt{2} \lambda \tan x=(1-k)$ where $k(\neq 33. Let $\overline{\mathrm{a}}=\hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\overline{\mathrm{c}}=\hat{\mathrm{i}}-\hat{\mathrm{j 34. The maximum value of $\mathrm{Z}=x+y$, subjected to $x+y \leq 10,5 x+3 y \geq 15, x \leq 6, x, y \geq 0$ 35. Equation of the plane containing the straight line $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and perpendicular to the plane 36. The new switching circuit for the following circuit by simplifying the given circuit is 37. The minimum value of the function $\mathrm{f}(x)=2 x^3-15 x^2+36 x-48$ on the set $\mathrm{A}=\left\{x \mid x^2+20 \leqs 38. For each $x \in \mathbb{R}$, Let $[x]$ represent greatest integer function, then $\lim _{x \rightarrow 0^{-}} \frac{x([x 39. If order and degree of the differential equation $\left(\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}\right)^5+4 \frac{\left(\f 40. A student scores the following marks in five tests : $54,45,41,43,57$. His score is not known for the sixth test. If the 41. If $y=\tan ^{-1}\left(\frac{3+2 x}{2-3 x}\right)+\tan ^{-1}\left(\frac{3 x}{1+4 x^2}\right)$, then $\frac{\mathrm{d} y}{ 42. The value of c for which Rolle's theorem for the function $\mathrm{f}(x)=x^3-3 x^2+2 x$ in the interval $[0,2]$ are 43. If $A(-4,5, P), B(3,1,4)$ and $C(-2,0, q)$ are the vertices of a triangle $A B C$ and $G(r, q, 1)$ is its centroid, then 44. The value of $\int \mathrm{e}^x\left(\frac{1-\sin x}{1-\cos x}\right) \mathrm{dx}$ is equal to 45. If a body cools from $80^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ in the room temperature of $30^{\circ} \mathrm{C 46. Derivative of $\sin ^2 x$ with respect to $e^{\cos x}$ 47. On which of the following lines lies the point of intersection of the line, $\frac{x-4}{2}=\frac{y-5}{2}=\frac{z-3}{1}$ 48. $$\sim[(\mathrm{p} \vee \sim \mathrm{q}) \rightarrow(\mathrm{p} \wedge \sim \mathrm{q})] \equiv$$ 49. If $z^2+z+1=0$ then $\left(z^3+\frac{1}{z^3}\right)^2+\left(z^4+\frac{1}{z^4}\right)^2=$ where $z=w=$ complex cube root 50. Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then mean of number of kings is

Physics

1. A gas expands in such a way that its pressure and volume satisfy the condition $\mathrm{PV}^2=$ constant. Then the tempe 2. A thin ring of radius ' $R$ ' carries a uniformly distributed charge. The ring rotates at constant speed ' $N$ ' r.p.s. 3. The r.m.s. velocity of gas molecules kept at temperature $27^{\circ} \mathrm{C}$ in a vessel is $61 \mathrm{~m} / \mathr 4. A regular hexagon of side 10 cm has a charge $1 \mu \mathrm{C}$ at each of its vertices. The potential at the centre of 5. A wheel of radius 1 m rolls through $180^{\circ}$ over a plane surface. The magnitude of the displacement of the point o 6. The end correction of resonance tube is 1 cm. If the shortest length resonating with a tuning fork is 15 cm , the next r 7. When 80 volt d.c. is applied across a solenoid, a current of 0.8 A flows in it. When 80 volt a.c. is applied across the 8. The earth is assumed to be a sphere of radius ' $R$ ' and mass ' $M$ ' having period of rotation ' $T$ '. The angular mo 9. When a galvanometer is shunted by a resistance ' $S$ ', its current capacity increases ' $n$ ' times. If the same galvan 10. In projectile motion two particles of masses $\mathrm{m}_1$ and $m_2$ have velocities $\vec{V}_1$, and $\vec{V}_2$ respe 11. The magnetic susceptibility of the material of a rod is 599. The absolute permeability of the material of the rod will b 12. If ' $l$ ' is the length of pipe, ' $r$ ' is the internal radius of the pipe and ' $v$ ' is the velocity of sound in air 13. A charged particle is moving along a magnetic field line. What is the magnetic force acting on the particle? $\left(\sin 14. A diatomic gas undergoes adiabatic change. Its pressure P and temperature T are related as $\mathrm{P} \propto \mathrm{T 15. The height at which the weight of the body becomes $\frac{1^{\text {th }}}{16}$ of its weight on the surface of the eart 16. A transformer is used to set up an alternating e.m.f. of 220 V to 4.4 kV to transmit 6.6 kW of power. The primary coil h 17. A monoatomic gas is heated at constant pressure. The percentage of total heat used for doing external work is 18. A parallel plate capacitor is charged and then isolated. If the separation between the plates is increased, which one of 19. The ratio of the radius of the first Bohr orbit to that of the second Bohr orbit of the orbital electron is 20. White light is incident on the interface of glass and air as shown in figure. If green light is just totally internally 21. Two loops ' $A$ ' and ' $B$ ' of radii ' $R_1$ ' and ' $R_2$ ' are made from uniform wire. If moment of inertia of ' A ' 22. A series LCR circuit containing a resistance ' R ' has angular frequency ' $\omega$ '. At resonance the voltage across r 23. The period of a simple pendulum gets doubled when 24. The Boolean expression for ' $x-O R$ ' gate $C=(A \oplus B)$ is equal to 25. Two identical metal spheres are kept in contact with each other, each having radius ' $R$ ' cm and ' $\rho$ ' is the den 26. A violin emits sound waves of frequency ' $n_1$ ' under tension T. When tension is increased by $44 \%$, keeping the len 27. The graph of stopping potential ' $\mathrm{V}_{\mathrm{s}}$ ' against frequency ' $v$ ' of incident radiation is plotted 28. A steel ball of radius 6 mm has a terminal speed of $12 \mathrm{cms}^{-1}$ in a viscous liquid. What will be the termina 29. Two coils are kept near each other. When no current passess through first coil and current in the $2^{\text {nd }}$ coil 30. Two rods, one of copper ( Cu$)$ and the other of iron ( Fe ) having initial lengths $\mathrm{L}_1$ and $\mathrm{L}_2$ re 31. Frequency of a particle performing S.H.M. is 10 Hz . The particle is suspended from a vertical spring. At the highest po 32. Two charged particles each having charge ' $q$ ' and mass ' $m$ ' are held at rest while their separation is ' $r$ '. Th 33. The pressure inside a soap bubble $A$ is 1.01 atmosphere and that in a soap bubble B is 1.02 atmosphere. The ratio of vo 34. In Young's double slit experiment, in an interference pattern, second minimum is observed exactly in front of one slit. 35. An observer moves towards a stationary source of sound with a velocity of one-fifth of the velocity of sound. The percen 36. A diatomic molecule has moment of inertia ' I ', By applying Bohr's quantization condition, its rotational energy in the 37. The frequency of incident light falling on a photosensitive material is doubled, the K.E. of the emitted photoelectrons 38. A screen is placed at 50 cm from a single slit, which is illuminated with light of wavelength 600 nm . If separation bet 39. A rod of length ' $l$ ' is rotated with angular velocity ' $\omega$ ' about its one end, perpendicular to a magnetic fie 40. A convex lens of focal length ' $f$ ' produces a real image whose size is ' $n$ ' times the size of an object. The dista 41. A liquid drop of density ' $\rho$ ' is floating half immersed in a liquid of density ' $d$ '. If ' $T$ ' is the surface 42. When the electron orbiting in hydrogen atom in its ground state moves to the third excited state, the de-Broglie wavelen 43. When a particle in linear S.H.M. completes two oscillations, its phase increases by 44. Resistances in the left gap and right gap of a meter bridge are $10 \Omega$ and $30 \Omega$ respectively. If the resista 45. A charge $+Q$ is placed at each of the diagonally opposite corners of a square. A charge -q is placed at each of the oth 46. A 42 mH inductor is connected to $200 \mathrm{~V}, 50 \mathrm{~Hz}$ a.c. supply. The r.m.s. value of current in the circ 47. In Young's double slit experiment using monochromatic light of wavelength ' $\lambda$ ', the intensity of light at a poi 48. Which one of the following statements is true? A p-type semiconductor is doped with 49. The specific heat of argon at constant pressure and constant volume are $C_p$ and $C_v$ respectively. It's density ' $\r 50. The combination of NAND gates is shown in figure (I) and (II). For the given inputs, the outputs in both the combination

MHT CET 2024 3rd May Evening Shift

MCQ (Single Correct Answer)

-0

Let $\alpha$ and $\beta$ be two real roots of the equation $(k+1) \tan ^2 x-\sqrt{2} \lambda \tan x=(1-k)$ where $k(\neq-1)$ and $\lambda$ are real numbers. If $\tan ^2(\alpha+\beta)=50$, then a value of $\lambda$ is

$5 \sqrt{2}$

$10 \sqrt{2}$

MHT CET 2024 3rd May Evening Shift

MCQ (Single Correct Answer)

-0

Let $\overline{\mathrm{a}}=\hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\overline{\mathrm{c}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}$. Then the vector $\overline{\mathrm{b}}$ satisfying $\overline{\mathrm{a}} \times \overline{\mathrm{b}}+\overline{\mathrm{c}}=\overline{0}$ and $\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}=3$, is

$-\hat{i}+\hat{j}-2 \hat{k}$

$2 \hat{i}-\hat{j}+2 \hat{k}$

$\hat{i}-\hat{j}-2 \hat{k}$

$\hat{i}+\hat{j}-2 \hat{k}$

MHT CET 2024 3rd May Evening Shift

MCQ (Single Correct Answer)

-0

The maximum value of $\mathrm{Z}=x+y$, subjected to $x+y \leq 10,5 x+3 y \geq 15, x \leq 6, x, y \geq 0$

occurs only at unique point

occurs only at two distinct points

occurs at infinitely many points

does not exist

MHT CET 2024 3rd May Evening Shift

MCQ (Single Correct Answer)

-0

Equation of the plane containing the straight line $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and perpendicular to the plane containing the straight lines $\frac{x}{3}=\frac{y}{4}=\frac{z}{2}$ and $\frac{x}{4}=\frac{y}{2}=\frac{z}{3}$ is

$x+2 y-2 z=0$

$3 x+2 y-2 z=0$

$x-2 y+z=0$

$5 x+2 y-4 z=0$

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2024