MHT CET 2023 12th May Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

Mathematics

1. The equation of the line, passing through $$(1,2,3)$$ and parallel to planes $$x-y+2 z=5$$ and $$3 x+y+z=6$$, is 2. $$\lim _\limits{x \rightarrow 0} \frac{x \cot 4 x}{\sin ^2 x \cdot \cot ^2(2 x)} \text { is equal to }$$ 3. $$\int \frac{1}{\cos ^3 x \sqrt{\sin 2 x}} d x=$$ 4. The shortest distance (in units) between the lines $$\frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2}$$ and $$\bar{r}=(2 \hat{i 5. The maximum value of $$z=7 x+8 y$$ subject to the constraints $$x+y \leq 20, y \geq 5, x \leq 10, x \geq 0, y \geq 0$$ i 6. The value of $$\int_\limits0^\pi\left|\sin x-\frac{2 x}{\pi}\right| \mathrm{d} x$$ is 7. If $$\mathrm{f}(x)=\sin ^{-1}\left(\frac{2 \log x}{1+(\log x)^2}\right)$$, then $$\mathrm{f}^{\prime}(\mathrm{e})$$ is 8. If the pair of lines given by $$(x \cos \alpha+y \sin \alpha)^2=\left(x^2+y^2\right) \sin ^2 \alpha$$ are perpendicular 9. The solution of $$\mathrm{e}^{y-x} \frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{y(\sin x+\cos x)}{(1+y \log y)}$$ is 10. For $$x>1$$, if $$(2 x)^{2 y}=4 \mathrm{e}^{2 x-2 y}$$, then $$\left(1+\log _e 2 x\right)^2 \frac{d y}{d x}$$ is equal t 11. A poster is to be printed on a rectangular sheet of paper of area $$18 \mathrm{~m}^2$$. The margins at the top and botto 12. The equation of the normal to the curve $$3 x^2-y^2=8$$, which is parallel to the line $$x+3 y=10$$, is 13. An irregular six faced die is thrown and the probability that, in 5 throws it will give 3 even numbers is twice the prob 14. If the curves $$y^2=6 x$$ and $$9 x^2+b y^2=16$$ intersect each other at right angle, then value of '$$b$$' is 15. The circles $$x^2+y^2+2 \mathrm{a} x+\mathrm{c}=0$$ and $$x^2+y^2+2 b y+c=0$$ touch each other externally, if 16. Given $$\mathrm{f}(x)=\left\{\begin{array}{cc}\frac{1-\cos 4 x}{x^2} & , \text { if } x0\end{array}\right.$$ If $$\mathr 17. $$A, B, C, D$$ are four points in a plane with position vectors $$\bar{a}, \bar{b}, \bar{c}, \bar{d}$$ respectively such 18. Two adjacent of sides parallelogram $$\mathrm{ABCD}$$ are given by $$\overline{\mathrm{AB}}=2 \hat{\mathrm{i}}+10 \hat{\ 19. The value of $$x$$, for which $$\sin \left(\cot ^{-1}(x)\right)=\cos \left(\tan ^{-1}(1+x)\right)$$, is 20. The unit vector which is orthogonal to the vector $$3 \hat{i}+2 \hat{j}+6 \hat{k}$$ and coplanar with the vectors $$2 \h 21. A ladder, 5 meters long, rests against a vertical wall. If its top slides downwards at the rate of $$10 \mathrm{~cm} / \ 22. If $$\vec{a}, \vec{b}, \vec{c}$$ are three non-zero vectors, no two of them are collinear, $$\vec{a}+2 \vec{b}$$ is coll 23. If $$|z-2+i| \leq 2$$, then the difference between the greatest and least value of $$|z|$$ is ________, $$(\mathrm{i}=\s 24. A box contains 100 tickets numbered 1 to 100 . A ticket is drawn at random from the box. Then the probability, that numb 25. If $$\int \frac{\sqrt{1-x^2}}{x^4} \mathrm{~d} x=\mathrm{A}(x)\left(\sqrt{1-x^2}\right)^{\mathrm{m}}+\mathrm{c}$$ for a 26. If $$\mathrm{k}_{\mathrm{i}}$$ are possible values of $$\mathrm{k}$$ for which lines $$\mathrm{k} x+2 y+2=0,2 x+\mathrm{ 27. A tank with a rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 4 meter 28. The length (in units) of the projection of the line segment, joining the points $$(5,-1,4)$$ and $$(4,-1,3)$$, on the pl 29. If the volume of tetrahedron, whose vertices are $$\mathrm{A}(1,2,3), \mathrm{B}(-3,-1,1), \mathrm{C}(2,1,3)$$ and $$D(- 30. Let Statement 1 : If a quadrilateral is a square, then all of its sides are equal. Statement 2: All the sides of a quadr 31. The number of words that can be formed by using the letters of the word CALCULATE such that each word starts and ends wi 32. The given following circuit is equivalent to 33. Water flows from the base of rectangular tank, of depth 16 meters. The rate of flow of the water is proportional to the 34. The area (in sq. units) of the smaller part of the circle $$x^2+y^2=\mathrm{a}^2$$ cut off by the line $$x=\frac{\mathrm 35. $$\cos ^2 48^{\circ}-\sin ^2 12^{\circ}=$$ _________, if $$\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}$$ 36. The discrete random variable $$\mathrm{X}$$ can take all possible integer values from 1 to $$\mathrm{k}$$, each with a p 37. If $$\tan y=\frac{x \sin \alpha}{1-x \cos \alpha}$$ and $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{\mathrm{m}}{x^2+2 \ma 38. The lengths of sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one 39. For 20 observations of variable $x$, if $$\sum\left(x_i-2\right)=20$$ and $$\sum\left(x_i-2\right)^2=100$$, then the sta 40. Equation of plane containing the line $$\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$$ and perpendicular to the plane containing 41. If $$(2+\sin x) \frac{\mathrm{d} y}{\mathrm{~d} x}+(y+1) \cos x=0$$ and $$y(0)=1$$, then $$y\left(\frac{\pi}{2}\right)$$ 42. If $$A=\left[\begin{array}{cc}2 a & -3 b \\ 3 & 2\end{array}\right]$$ and $$A \cdot \operatorname{adj} A=A A^T$$, then $ 43. $$\int\left(\frac{\tan \left(\frac{1}{x}\right)}{x}\right)^2 d x=$$ 44. $$\int \frac{1}{(x+2)(1+x)^2} d x$$ has the value 45. If two angles of $$\triangle \mathrm{ABC}$$ are $$\frac{\pi}{4}$$ and $$\frac{\pi}{3}$$, then the ratio of the smallest 46. In $$\triangle \mathrm{ABC}, \mathrm{m} \angle \mathrm{B}=\frac{\pi}{3}$$ and $$\mathrm{m} \angle \mathrm{C}=\frac{\pi}{ 47. If $$\tan ^{-1}\left(\frac{1-x}{1+x}\right)=\frac{1}{2} \tan ^{-1} x$$, then $$x$$ is 48. If then $$|\overrightarrow{\mathrm{u}} \times \overrightarrow{\mathrm{v}}| \text { is }$$ 49. Three fair coins with faces numbered 1 and 0 are tossed simultaneously. Then variance (X) of the probability distributio 50. If $$\mathrm{f}(x)=x^2+1$$ and $$\mathrm{g}(x)=\frac{1}{x}$$, then the value of $$\mathrm{f}(\mathrm{g}(\mathrm{g}(\math

Physics

1. A glass prism deviates the red and violet rays through $$9^{\circ}$$ and $$11^{\circ}$$ respectively. A second prism of 2. Eight small drops of mercury each of radius '$$r$$', coalesce to form a large single drop. The ratio of total surface en 3. In the following digital logic circuit, the output Y will be '1' for inputs 4. Two different radioactive elements with half lives '$$\mathrm{T}_1$$' and '$$\mathrm{T}_2$$' have undecayed atoms '$$\ma 5. The equation of wave motion is $$Y=5 \sin (10 \pi t -0.02 \pi x+\pi / 3)$$ where $$x$$ is in metre and $$t$$ in second. 6. A potentiometer wire of length $$4 \mathrm{~m}$$ and resistance $$5 ~\Omega$$ is connected in series with a resistance o 7. Select the correct statement from the following. 8. End correction at open end for air column in a pipe of length '$$l$$' is '$$e$$'. For its second overtone of an open pip 9. In a stationary lift, time period of a simple pendulum is '$$\mathrm{T}$$'. The lift starts accelerating downwards with 10. A body is projected vertically upwards from earth's surface of radius '$$R$$' with velocity equal to $$\frac{1^{\text {r 11. Which one of the following statements is WRONG regarding LED? 12. A thin wire of length '$$L$$' and uniform linear mass density '$$m$$' is bent into a circular coil. The moment of inerti 13. A black body radiates maximum energy at wavelength '$$\lambda$$' and its emissive power is '$$E$$'. Now due to a change 14. If the charge on the capacitor is increased by 3 coulombs, the energy stored in it increases by $$44 \%$$. The original 15. In which figure, the junction diode is forward biased? 16. A particle starts from mean position and performs S.H.M. with period 4 second. At what time its kinetic energy is $$50 \ 17. For polyatomic gases, the ratio of molar specific heat at constant pressure to constant volume is ( $$\mathrm{f}=$$ degr 18. A particle is moving in a circle with uniform speed '$$v$$'. In moving from a point to another diametrically opposite po 19. Select the WRONG statement from the following. For an isothermal process 20. Two concentric circular coils of 10 turns each are situated in the same plane. Their radii are $$20 \mathrm{~cm}$$ and $ 21. Graph shows the variation of de-Broglie wavelength $$(\lambda)$$ versus $$\frac{1}{\sqrt{V}}$$ where '$$V$$' is the acce 22. SI units of self inductance is 23. When an inductor '$$L$$' and a resistor '$$R$$' in series are connected across a $$15 \mathrm{~V}, 50 \mathrm{~Hz}$$ a.c 24. When an electron is accelerated through a potential '$$V$$', the de-Broglie wavelength associated with it is '$$4 \lambd 25. Compare the rate of loss of heat from a metal sphere at $$627^{\circ} \mathrm{C}$$ with the rate of loss of heat from th 26. In Balmer series, wavelength of the $$2^{\text {nd }}$$ line is '$$\lambda_1$$' and for Paschen series, wavelength of th 27. A coil of '$$n$$' turns and radius '$$R$$' carries a current '$$I$$'. It is unwound and rewound again to make another co 28. An ink mark is made on a piece of paper on which a glass slab of thickness '$$t$$' is placed. The ink mark appears to be 29. A spherical metal ball of radius '$$r$$' falls through viscous liquid with velocity '$$\mathrm{V}$$'. Another metal ball 30. A body of mass '$$\mathrm{m}$$' attached at the end of a string is just completing the loop in a vertical circle. The ap 31. Select the WRONG statement from the following. In a streamline flow 32. Two point charges '$$q 1$$' and '$$q 2$$' are separated by a distance '$$d$$'. What is the increase in potential energy 33. The ratio of intensities of two points on a screen in Young's double slit experiment when waves from the two slits have 34. A simple pendulum is oscillating with frequency '$$F$$' on the surface of the earth. It is taken to a depth $$\frac{\mat 35. An a.c. source of $$15 \mathrm{~V}, 50 \mathrm{~Hz}$$ is connected across an inductor (L) and resistance (R) in series R 36. A ball is projected vertically upwards from ground. It reaches a height '$$h$$' in time $$t_1$$, continues its motion an 37. The volume of a metal block increases by $$0.225 \%$$ when its temperature is increased by $$30^{\circ} \mathrm{C}$$. He 38. A tuning fork gives 3 beats with $$50 \mathrm{~cm}$$ length of sonometer wire. If the length of the wire is shortened by 39. The depth at which acceleration due to gravity becomes $$\frac{\mathrm{g}}{2 \mathrm{n}}$$ is $$(\mathrm{R}=$$ radius of 40. Two resistance $$\mathrm{X}$$ and $$\mathrm{Y}$$ are connected in the two gaps of a meterbridge and the null points is o 41. Three point charges $$\mathrm{+Q,+2q}$$ and $$+\mathrm{q}$$ are placed at the vertices of a right angled isosceles trian 42. Resistor of $$2\Omega$$, inductor of $$100 \mu \mathrm{H}$$ and capacitor of $$400 \mathrm{pF}$$ are connected in series 43. An electron makes a full rotation in a circle of radius $$0.8 \mathrm{~m}$$ in one second. The magnetic field at the cen 44. In Young's double slit experiment when a glass plate of refractive index 1.44 is introduced in the path of one of the in 45. A monoatomic ideal gas initially at temperature '$$\mathrm{T}_1$$' is enclosed in a cylinder fitted with massless, frict 46. A tuning fork of frequency $$220 \mathrm{~Hz}$$ produces sound waves of wavelength $$1.5 \mathrm{~m}$$ in air at N.T.P. 47. An air craft of wing span $$40 \mathrm{~m}$$ files horizontally in earth's magnetic field $$5 \times 10^{-5} \mathrm{~T} 48. In $$\mathrm{P}^{\text {th }}$$ second, a particle describes angular displacement of '$$\beta$$' rad. If it starts from 49. Inductance per unit length near the middle of a long solenoid is $$\left(\mu_0=\right.$$ permeability of free space, $$\ 50. One of the slits in Young's double slit experiment is covered with a transparent sheet of thickness $$2.9 \times 10^{-3}

MHT CET 2023 12th May Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{1}{(x+2)(1+x)^2} d x$$ has the value

$$2 \log \left(\frac{x+2}{x^2+1}\right)+4 \tan ^{-1} x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$\log \frac{x+2}{x^2+1}-4 \tan ^{-1} x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$\log \frac{(x+2)^2}{\left(x^2+1\right)}+4 \tan ^{-1} x+c$$, where c is a constant of integration.

None

MHT CET 2023 12th May Evening Shift

MCQ (Single Correct Answer)

-0

If two angles of $$\triangle \mathrm{ABC}$$ are $$\frac{\pi}{4}$$ and $$\frac{\pi}{3}$$, then the ratio of the smallest and greatest sides are

$$(\sqrt{3}-1): 1$$

$$\sqrt{3}: \sqrt{5}$$

$$\sqrt{2}: \sqrt{3}$$

$$(\sqrt{3}-1): 4$$

MHT CET 2023 12th May Evening Shift

MCQ (Single Correct Answer)

-0

In $$\triangle \mathrm{ABC}, \mathrm{m} \angle \mathrm{B}=\frac{\pi}{3}$$ and $$\mathrm{m} \angle \mathrm{C}=\frac{\pi}{4}$$. Let point $$\mathrm{D}$$ divide $$\mathrm{BC}$$ internally in the ratio $$1: 3$$, then $$\frac{\sin (\angle B A D)}{\sin (\angle C A D)}$$ has the value

$$\frac{1}{3}$$

$$\frac{1}{\sqrt{3}}$$

$$\frac{1}{\sqrt{6}}$$

$$\sqrt{\frac{2}{3}}$$

MHT CET 2023 12th May Evening Shift

MCQ (Single Correct Answer)

-0

If $$\tan ^{-1}\left(\frac{1-x}{1+x}\right)=\frac{1}{2} \tan ^{-1} x$$, then $$x$$ is

$$\sqrt{3}$$

$$\frac{1}{\sqrt{3}}$$

$$\frac{1}{2 \sqrt{3}}$$

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