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

Chemistry

Mathematics

Physics

MHT CET 2024 9th May Evening Shift

MCQ (Single Correct Answer)

-0

The equations of two waves are given as

$$\begin{aligned} & y_1=a \sin \left(\omega t+\phi_1\right) \\ & y_2=a \sin \left(\omega t+\phi_2\right) \end{aligned}$$

If amplitude and time period of resultant wave is same as the individual waves, then $\left(\phi_1-\phi_2\right)$ is

$\cos ^{-1}\left(\frac{-1}{2}\right)$

$\cos ^{-1}\left(\frac{-1}{4}\right)$

$\cos ^{-1}\left(-\frac{1}{6}\right)$

$\cos ^{-1}\left(-\frac{1}{8}\right)$

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