MHT CET 2024 9th May Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

Mathematics

1. The maximum value of $z=4 x+2 y$, subject to the constraints $3 x+4 y \geqslant 12, x+y \leqslant 5, x, y \geqslant 0$ i 2. The value of $\int \frac{x+1}{x\left(1+x \mathrm{e}^x\right)^2} \mathrm{dx}$ is equal to 3. If $\mathrm{p} \rightarrow(\sim \mathrm{p} \vee \sim \mathrm{q})$ is false, then the truth values of p and q are respect 4. Let $\alpha, \beta$ be the roots of the equation $x^2-\mathrm{p} x+\mathrm{r}=0$ and $\frac{\alpha}{2}, 2 \beta$ be the 5. Let $\quad \overline{\mathrm{a}}=\alpha \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}, \quad \overline{\mathrm{b} 6. The function $\mathrm{f}(x)=2 x^3-6 x+5$ is an increasing function, if 7. Let $2 \sin ^2 x+3 \sin x-2>0$ and $x^2-x-2 8. Let $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ be vectors of magnitude 2,3 and 4 respect 9. A square plate is contracting at the uniform rate $3 \mathrm{~cm}^2 / \mathrm{sec}$, then the rate at which the perimete 10. The area (in sq. units), in the first quadrant bounded by the curve $y=x^2+2$ and the lines $y=x+1, x=0$ and $x=2$, is 11. The vector $\bar{a}=\alpha \hat{i}+2 \hat{j}+\beta \hat{k}$ lies in the plane of the vectors $\overline{\mathrm{b}}=\hat 12. $2 \pi-\left(\sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{16}{65}\right)$ is equal to 13. For the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2\end{array}\right]$, the matrix of cofact 14. If $y=\sin ^{-1}\left(\frac{3 x}{2}-\frac{x^3}{2}\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to 15. A unit vector coplanar with $\hat{i}+\hat{j}+\hat{k}$ and $2 \hat{i}+\hat{j}+\hat{k}$ and perpendicular to $\hat{i}+\hat 16. Negation of the statement ' Horses have wings if and only if crows have tails. ' is 17. A plane which is perpendicular to two planes $2 x-2 y+z=0$ and $x-y+2 z=4$, passes through $(1,2,1)$. The distance of th 18. If $\log (x+y)=\sin (x+y)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is 19. $$\int \sqrt{\mathrm{e}^x-1} \mathrm{dx}=$$ 20. The variance of 20 observations is 5 . If each observation is multiplied by 3 and then 8 is added to each number, then v 21. The value of m such that $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z+m}{2}$ lies in the plane $2 x-4 y+z=7$ is 22. Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ res 23. A poster is to be printed on a rectangular sheet of paper of area $18 \mathrm{~m}^2$. The margins at the top and bottom 24. The approximate value of $(3.978)^{3 / 2}$ is 25. The number of integral values of $k$, for which the equation $7 \cos x+5 \sin x=2 \mathrm{k}+1$ has a solution, is 26. The domain of definition of the function $f(x)$ given by the equation $2^x+2^y=2$ is 27. Let $\bar{a}=3 \hat{i}-\alpha \hat{j}+\hat{k}$ and $\bar{b}=\hat{i}+\alpha \hat{j}+3 \hat{k}$. If the area of the parall 28. If $\mathrm{A}, \mathrm{B}, \mathrm{C}$ are the angles of a triangle with $\tan \frac{A}{2}=\frac{1}{3}, \tan \frac{B}{2 29. A line with positive direction cosines passes through the point $\mathrm{P}(2,1,2)$ and makes equal angles with the coor 30. The equation of the tangent to the curve $x=\operatorname{acos}^3 \theta, y=\operatorname{asin}^3 \theta$ at $\theta=\fr 31. $$\lim _\limits{x \rightarrow \frac{\pi}{2}} \frac{(1-\sin x)\left(8 x^3-\pi^3\right) \cos x}{(\pi-2 x)^4}$$ 32. The integral $\int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \frac{d x}{\sin 2 x\left(\tan ^5 x+\cot ^5 x\right)}$ is equal to 33. The equation of the circle, concentric with the circle $x^2+y^2-6 x-4 y-12=0$ and touching the $\mathrm{X}$-axis is 34. Let $\mathrm{f}(x)=\mathrm{e}^x, \mathrm{~g}(x)=\sin ^{-1} x$ and $\mathrm{h}(x)=\mathrm{f}(\mathrm{g}(x))$, then $\left 35. The joint equation of pair of lines through the origin and making an angle of $\frac{\pi}{6}$ with the line $3 x+y-6=0$ 36. A line $4 x+y=1$ passes through the point $\mathrm{A}(2,-7)$ meets the line BC whose equation is $3 x-4 y+1=0$ at the po 37. The value of $\int \frac{\mathrm{d} x}{(x+1)^{3 / 4}(x-2)^{5 / 4}}$ is equal to 38. The smallest positive value of $x$ in degrees satisfying the equation $\tan \left(x+100^{\circ}\right)=\tan \left(x+50^{ 39. If $\int \frac{\cos x-\sin x}{\sqrt{8-\sin 2 x}} d x=a \sin ^{-1}\left(\frac{\sin x+\cos x}{b}\right)+c$ Where c is a co 40. Let L be the line of intersection of the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$. If L makes an angle $\alpha$ with the p 41. Consider a group of 5 boys and 7 girls. The number of different teams, consisting of 2 boys and 3 girls that can be form 42. If the mean and the variance of a Binomial variate X are 2 and 1 respectively, then the probability that X takes a value 43. The general solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{y+\sqrt{x^2-y^2}}{x}$ is 44. A bag contains 4 red and 3 black balls. One ball is drawn and then replaced in the bag and the process is repeated. Let 45. In a certain culture of bacteria, the rate of increase is proportional to the number present. If there are $10^4$ at the 46. The number of solutions, of $2^{1+|\cos x|+|\cos x|^2+\ldots \ldots \cdots \cdots}=4$ in $(-\pi, \pi)$, is 47. Let $\mathrm{f}(x)=x\left[\frac{x}{2}\right]$, for $-10 48. Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\overline{\mathrm{c}}=\hat{\mathrm{a}}+2 \hat{\mathrm{~ 49. Integrating factor of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}+y=\frac{1+y}{x}$ is 50. A service station manager sells gas at an average of ₹ 100 per hour on a rainy day, ₹ 150 per hour on a dubious day, ₹ 2

Physics

1. A stationary wave is formed having 3 nodes along the length of the string 90 cm . The wavelength of the wave is 2. The spectral series observed for hydrogen atom found in visible region is 3. Three liquids of densities $\rho_1, \rho_2$ and $\rho_3$ (with $\rho_1>\rho_2>\rho_3$ ) having same value of surface ten 4. The following figures show the variation of displacement with time of a particular object. 5. A particle of mass ' m ' is rotating in a circular path of radius ' $r$ '. Its angular momentum is ' $L$ ' The centripet 6. Two identical galvanometers are converted into voltmeter and millivoltmeter. As compared to the series resistance of vol 7. The diagram shows the propagation of a progressive wave. A, B, C, D, E are five points on this wave Which of the follow 8. Using Einstein's photoelectric equation, the graph between kinetic energy of emitted photoelectrons and the frequency of 9. A string of mass 0.2 Kg is under a tension of 2.5 N . The length of the string is 2 m. A transverse wave starts from one 10. In the Young's double slit experiment, the intensity at a point on the screen, where the path difference is $\lambda(\la 11. The P-V diagrams for particular gas of different thermodynamic processes are given by 12. A musical instrument ' $P$ ' produces sound waves of frequency ' $n$ ' and amplitude ' $A$ '. Another musical instrument 13. Concave and convex lenses are placed touching each other. The ratio of magnitudes of their power is $2: 3$. The focal le 14. The figure shows the variation of photocurrent with anode potential for four different radiations. Let $f_a, f_b, f_c$ a 15. A disc at rest is subjected to a uniform angular acceleration about its axis. Let $\theta$ and $\theta_1$ be the angle m 16. Let ' $n$ ' is the number of liquid drops, each with surface energy ' $E$ '. These drops join to form single drop. In th 17. The van de Graaff Generator is not based on 18. Two coils of self-inductance 25 mH and 9 mH are placed close together such that the effective flux in one coil is comple 19. The electric flux over a sphere of radius ' $r$ ' is ' $\phi$ '. If the radius of the sphere is doubled without changing 20. Consider the following circuit. By keeping $\mathrm{S}_1$ closed, the capacitor is fully charged and then $S_1$ is opene 21. In the working of photodiode, the reverse current depends on 22. A satellite is revolving around a planet in a circular orbit close to its surface. Let ' $\rho$ ' be the mean density an 23. A current carrying circular loop of radius ' $R$ ' and current carrying long straight wire are placed in the same plane. 24. A square loop ABCD is moving with constant velocity ' $\vec{v}$ ' in a uniform magnetic field ' $\vec{B}$ ' which is per 25. The fringe width in an interference pattern is ' X '. The distance between the sixth dark fringe from one side of centra 26. A particle is executing a linear simple harmonic motion. Let ' $\mathrm{V}_1$ ' and ' $\mathrm{V}_2$ ' are its speed at 27. In hydrogen atom, if $\mathrm{V}_{\mathrm{n}}$ and $\mathrm{V}_{\mathrm{p}}$ are orbital velocities in $\mathrm{n}^{\tex 28. The work done in splitting a water drop of radius R into 64 droplets is ( $\mathrm{T}=$ Surface tension of water) 29. The potential difference that must be applied across the series and parallel combination of 4 identical capacitors is su 30. A metal rod of weight ' $W$ ' is supported by two parallel knife-edges A and B . The rod is in equilibrium in horizontal 31. Potential difference between the points A and B is nearly 32. An ideal gas $(\gamma=1.5)$ is expanded adiabatically. To reduce root mean square velocity of molecules two times, the g 33. An e.m.f. $E=E_0 \cos \omega t$ is applied to circuit containing L and R in series. If $\mathrm{X}_{\mathrm{L}}=2 \mathr 34. In the following circuit, the reading in the ammeter is 35. A black body radiates power ' P ' and maximum energy is radiated by it at a wavelength $\lambda_0$. The temperature of t 36. In Young's double slit experiment using monochromatic light of wavelength ' $\lambda$ ', the maximum intensity of light 37. When a capacitor is connected in series LR circuit, the alternating current flowing in the circuit 38. The correct relation between total magnetic field $(B)$, magnetic intensity $(\mathrm{H})$, permeability of free space 39. The resultant gate and its Boolean expression in the given circuit is 40. The temperature of a liquid falls from 365 K to 359 K in 3 minutes. The time during which temperature of this liquid fal 41. Air capacitor has capacitance of $1 \mu \mathrm{~F}$. Now the space between two plates of capacitor is filled with two d 42. In an isobaric process of an ideal gas, the ratio of work done by the system (W) during the expansion and the heat excha 43. A long solenoid carrying a current produces magnetic field B along its axis. If the number of turns per cm are tripled a 44. An astronomical telescope has a large aperture to 45. A sonometer wire is in unison with a tuning fork of frequency ' $n$ ' when it is stretched by a weight of specific gravi 46. The radius of the planet is double that of the earth, but their average densities are same. $\mathrm{V}_{\mathrm{p}}$ an 47. Three thin rods, each mass ' 2 M ' and length ' L ' are placed along $\mathrm{x}, \mathrm{y}$ and z axis which are mutua 48. The magnetic potential energy stored in certain inductor is $64 \times 10^{-3} \mathrm{~J}$, when the current in the ind 49. Two identical drops of water are falling through air with steady velocity ' V '. If the two drops come together to form 50. The equations of two waves are given as $$\begin{aligned} & y_1=a \sin \left(\omega t+\phi_1\right) \\ & y_2=a \sin \lef

MHT CET 2024 9th May Evening Shift

MCQ (Single Correct Answer)

-0

A poster is to be printed on a rectangular sheet of paper of area $18 \mathrm{~m}^2$. The margins at the top and bottom of 75 cm each and at the sides 50 cm each are to be left. Then the dimensions i.e. height and breadth of the sheet so that the space available for printing is maximum, are _______ respectively.

$2 \sqrt{3} \mathrm{~m}, 3 \sqrt{3} \mathrm{~m}$

$3 \sqrt{3} \mathrm{~m}, 2 \sqrt{3} \mathrm{~m}$

$3 \mathrm{~m}, 6 \mathrm{~m}$

$6 \mathrm{~m}, 3 \mathrm{~m}$

MHT CET 2024 9th May Evening Shift

MCQ (Single Correct Answer)

-0

The approximate value of $(3.978)^{3 / 2}$ is

7.096

8.096

7.934

8.934