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

Chemistry

Mathematics

1. If $$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are three vectors, $$|\overline{\mathrm{a}}|= 2. The centroid of tetrahedron with vertices at $$\mathrm{A}(-1,2,3), \mathrm{B}(3,-2,1), \mathrm{C}(2,1,3)$$ and $$\mathrm 3. Two adjacent sides of a parallelogram $$\mathrm{ABCD}$$ are given by $$\overline{A B}=2 \hat{i}+10 \hat{j}+11 \hat{k}$$ 4. The values of $$a$$ and $$b$$, so that the function $$f(x)=\left\{\begin{array}{l} x+a \sqrt{2} \sin x, 0 \leq x \leq \f 5. For a feasible region OCDBO given below, the maximum value of the objective function $$z=3 x+4 y$$ is 6. If $$\mathrm{g}(x)=1+\sqrt{x}$$ and $$\mathrm{f}(\mathrm{g}(x))=3+2 \sqrt{x}+x$$ then $$\mathrm{f}(\mathrm{f}(x))$$ is 7. The approximate value of $$\sin \left(60^{\circ} 0^{\prime} 10^{\prime \prime}\right)$$ is (given that $$\sqrt{3}=1.732, 8. The decay rate of radio active material at any time $$t$$ is proportional to its mass at that time. The mass is 27 grams 9. The derivative of $$\mathrm{f}(\tan x)$$ w.r.t. $$\mathrm{g}(\sec x)$$ at $$x=\frac{\pi}{4}$$ where $$\mathrm{f}^{\prime 10. The p.m.f of random variate $$\mathrm{X}$$ is $$P(X)= \begin{cases}\frac{2 x}{\mathrm{n}(\mathrm{n}+1)}, & x=1,2,3, \ldo 11. The angle between the tangents to the curves $$y=2 x^2$$ and $$x=2 y^2$$ at $$(1,1)$$ is 12. If the area of the triangle with vertices $$(1,2,0)$$, $$(1,0,2)$$ and $$(0, x, 1)$$ is $$\sqrt{6}$$ square units, then 13. An experiment succeeds twice as often as it fails. Then the probability, that in the next 6 trials there will be atleast 14. The co-ordinates of the points on the line $$2 x-y=5$$ which are the distance of 1 unit from the line $$3 x+4 y=5$$ are 15. If $$x=\operatorname{cosec}\left(\tan ^{-1}\left(\cos \left(\cot ^{-1}\left(\sec \left(\sin ^{-1} a\right)\right)\right) 16. Let $$\overline{\mathrm{A}}$$ be a vector parallel to line of intersection of planes $$P_1$$ and $$P_2$$ through origin. 17. $$\int \frac{\operatorname{cosec} x d x}{\cos ^2\left(1+\log \tan \frac{x}{2}\right)}=$$ 18. If the variance of the numbers $$-1,0,1, \mathrm{k}$$ is 5, where $$\mathrm{k} > 0$$, then $$\mathrm{k}$$ is equal to 19. The differential equation $$\cos (x+y) \mathrm{d} y=\mathrm{d} x$$ has the general solution given by 20. The area of the region bounded by the curves $$y=\mathrm{e}^x, y=\log x$$ and lines $$x=1, x=2$$ is 21. If $$x=-1$$ and $$x=2$$ are extreme points of $$\mathrm{f}(x)=\alpha \log x+\beta x^2+x, \alpha$$ and $$\beta$$ are cons 22. A plane is parallel to two lines whose direction ratios are $$1,0,-1$$ and $$-1,1,0$$ and it contains the point $$(1,1,1 23. The function $$\mathrm{f}(x)=\sin ^4 x+\cos ^4 x$$ is increasing in 24. If $$a > 0$$ and $$z=\frac{(1+i)^2}{a+i},(i=\sqrt{-1})$$ has magnitude $$\frac{2}{\sqrt{5}}$$, then $$\bar{z}$$ is equal 25. The integral $$\int \frac{\sin ^2 x \cos ^2 x}{\left(\sin ^5 x+\cos ^3 x \sin ^2 x+\sin ^3 x \cos ^2 x+\cos ^5 x\right)^ 26. The equation of the plane through $$(-1,1,2)$$ whose normal makes equal acute angles with co-ordinate axes is 27. If $$\mathrm{T}_{\mathrm{n}}$$ denotes the number of triangles which can be formed using the vertices of regular polygon 28. Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then the probability distributi 29. If $$\tan \theta=\frac{\sin \alpha-\cos \alpha}{\sin \alpha+\cos \alpha}, 0 \leq \alpha \leq \frac{\pi}{2}$$, then the v 30. The solution set of $$8 \cos ^2 \theta+14 \cos \theta+5=0$$, in the interval $$[0,2 \pi]$$, is 31. A ladder 5 meters long rests against a vertical wall. If its top slides downwards at the rate of $$10 \mathrm{~cm} / \ma 32. If $$\frac{\mathrm{d} y}{\mathrm{~d} x}=y+3$$ and $$y(0)=2$$, then $$y(\log 2)=$$ 33. $$\text { If } \log (x+y)=2 x y \text {, then } \frac{\mathrm{d} y}{\mathrm{~d} x} \text { at } x=0 \text { is }$$ 34. If general solution of $$\cos ^2 \theta-2 \sin \theta+\frac{1}{4}=0$$ is $$\theta=\frac{\mathrm{n} \pi}{\mathrm{A}}+(-1) 35. $$\overline{\mathrm{u}}, \overline{\mathrm{v}}, \overline{\mathrm{w}}$$ are three vectors such that $$|\overline{\mathrm 36. The distance of the point $$\mathrm{P}(-2,4,-5)$$ from the line $$\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}$$ is 37. $$\mathrm{A}$$ and $$\mathrm{B}$$ are independent events with $$\mathrm{P}(\mathrm{A})=\frac{1}{4}$$ and $$\mathrm{P}(\m 38. $$\int \frac{x^2+1}{x\left(x^2-1\right)} \mathrm{d} x=$$ 39. If the matrix $$\mathrm{A}=\left[\begin{array}{cc}1 & 2 \\ -5 & 1\end{array}\right]$$ and $$\mathrm{A}^{-1}=x \mathrm{~A 40. The inverse of the statement "If the surface area increase, then the pressure decreases.", is 41. In a triangle, the sum of lengths of two sides is $$x$$ and the product of the lengths of the same two sides is $$y$$. I 42. The contrapositive of "If $$x$$ and $$y$$ are integers such that $$x y$$ is odd, then both $$x$$ and $$y$$ are odd" is 43. $$y=(1+x)\left(1+x^2\right)\left(1+x^4\right) \ldots \ldots \ldots\left(1+x^{2 n}\right)$$, then the value of $$\frac{\m 44. $$\lim _\limits{x \rightarrow 0} \frac{\cos 7 x^{\circ}-\cos 2 x^{\circ}}{x^2}$$ is 45. $$\int_\limits0^4|2 x-5| d x=$$ 46. If $$\lambda$$ is the perpendicular distance of a point $$\mathrm{P}$$ on the circle $$x^2+y^2+2 x+2 y-3=0$$, from the l 47. If the line $$\frac{1-x}{3}=\frac{7 y-14}{2 p}=\frac{z-3}{2}$$ and $$\frac{7-7 x}{3 \mathrm{p}}=\frac{y-5}{1}=\frac{6-\m 48. The value of $$\sin \left(\cot ^{-1} x\right)$$ is 49. If $$\int \cos ^{\frac{3}{5}} x \cdot \sin ^3 x d x=\frac{-1}{m} \cos ^m x+\frac{1}{n} \cos ^n x+c$$, (where $$\mathrm{c 50. Let $$\mathrm{PQR}$$ be a right angled isosceles triangle, right angled at $$\mathrm{P}(2,1)$$. If the equation of the l

Physics

1. A uniform string is vibrating with a fundamental frequency '$$n$$'. If radius and length of string both are doubled keep 2. Let $$\gamma_1$$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of 3. A railway track is banked for a speed ',$$v$$' by elevating outer rail by a height '$$h$$' above the inner rail. The dis 4. In the given capacitive network the resultant capacitance between point $$\mathrm{A}$$ and $$\mathrm{B}$$ is 5. In Young's double slit experiment the intensities at two points, for the path difference $$\frac{\lambda}{4}$$ and $$\fr 6. A simple pendulum performs simple harmonic motion about $$\mathrm{x}=0$$ with an amplitude '$$\mathrm{a}$$' and time per 7. The molar specific heat of an ideal gas at constant pressure and constant volume is $$\mathrm{C}_{\mathrm{p}}$$ and $$\m 8. Resistance of a potentiometer wire is $$2 \Omega / \mathrm{m}$$. A cell of e.m.f. $$1.5 \mathrm{~V}$$ balances at $$300 9. $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ are three parallel conductors of equal lengths and carry currents I, I and 10. Two electric dipoles of moment $$\mathrm{P}$$ and $$27 \mathrm{P}$$ are placed on a line with their centres $$24 \mathrm 11. Converging or diverging ability of a lens or mirror is called 12. The following logic gate combination is equivalent to 13. Radiations of two photons having energies twice and five times the work function of metal are incident successively on m 14. Time period of simple pendulum on earth's surface is '$$\mathrm{T}$$'. Its time period becomes '$$\mathrm{xT}$$' when ta 15. Consider a soap film on a rectangular frame of wire of area $$3 \times 3 \mathrm{~cm}^2$$. If the area of the soap film 16. In Lyman series, series limit of wavelength is $$\lambda_1$$. The wavelength of first line of Lyman series is $$\lambda_ 17. The magnetic moment of a current (I) carrying circular coil of radius '$$r$$' and number of turns '$$n$$' depends on 18. A spherical drop of liquid splits into 1000 identical spherical drops. If '$$\mathrm{E}_1$$' is the surface energy of th 19. The displacement of two sinusoidal waves is given by the equation $$\begin{aligned} & \mathrm{y}_1=8 \sin (20 \mathrm{x} 20. $$I_1$$ is the moment of inertia of a circular disc about an axis passing through its centre and perpendicular to the pl 21. The equivalent capacity between terminal $$\mathrm{A}$$ and $$\mathrm{B}$$ is 22. Two similar coils each of radius $$\mathrm{R}$$ are lying concentrically with their planes at right angles to each other 23. The logic gate combination circuit shown in the figure performs the logic function of 24. Two sounding sources send waves at certain temperature in air of wavelength $$50 \mathrm{~cm}$$ and $$50.5 \mathrm{~cm}$ 25. In the given circuit, r.m.s. value of current through the resistor $$\mathrm{R}$$ is 26. A particle of mass '$$m$$' moving east ward with a speed '$$v$$' collides with another particle of same mass moving nort 27. The height at which the weight of the body becomes $$\left(\frac{1}{9}\right)^{\text {th }}$$ its weight on the surface 28. A single turn current loop in the shape of a right angle triangle with side $$5 \mathrm{~cm}, 12 \mathrm{~cm}, 13 \mathr 29. 41 tuning forks are arranged in increasing order of frequency such that each produces 5 beats/second with next tuning fo 30. In two separate setups for Biprism experiment using same wavelength, fringes of equal width are obtained. If ratio of sl 31. A composite slab consists of two materials having coefficient of thermal conductivity $$\mathrm{K}$$ and $$2 \mathrm{~K} 32. A black sphere has radius '$$R$$' whose rate of radiation is '$$E$$' at temperature '$$T$$'. If radius is made $$R / 3$$ 33. The potential on the plates of capacitor are $$+20 \mathrm{~V}$$ and $$-20 \mathrm{~V}$$. The charge on the plate is $$4 34. A thin uniform circular disc of mass '$$\mathrm{M}$$' and radius '$$R$$' is rotating with angular velocity '$$\omega$$', 35. A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If $$\frac{\mathrm{C}_{\mathrm{ 36. When light of wavelength $$\lambda$$ is incident on a photosensitive surface the stopping potential is '$$\mathrm{V}$$'. 37. One of the necessary condition for total internal reflection to take place is ( $$\mathrm{i}=$$ angle of incidence, $$\m 38. In the given circuit, if $$\frac{\mathrm{dI}}{\mathrm{dt}}=-1 \mathrm{~A} / \mathrm{s}$$ then the value of $$\left(V_A-V 39. An inductor of $$0.5 \mathrm{~mH}$$, a capacitor of $$20 ~\mu \mathrm{F}$$ and a resistance of $$20 \Omega$$ are connect 40. The wavelength of radiation emitted is '$$\lambda_0$$' when an electron jumps from the second excited state to the first 41. Two particles having mass '$$M$$' and '$$m$$' are moving in a circular path with radius '$$R$$' and '$$r$$' respectively 42. The excess pressure inside a first spherical drop of water is three times that of second spherical drop of water. Then t 43. When forward bias is applied to a p-n junction, then what happens to the potential barrier $$\left(V_B\right)$$ and the 44. Two inductors of $$60 \mathrm{~mH}$$ each are joined in parallel. The current passing through this combination is $$2.2 45. A beam of light is incident on a glass plate at an angle of $$60^{\circ}$$. The reflected ray is polarized. If angle of 46. Consider a light planet revolving around a massive star in a circular orbit of radius '$$r$$' with time period '$$T$$'. 47. A potentiometer wire has length of $$5 \mathrm{~m}$$ and resistance of $$16 \Omega$$. The driving cell has an e.m.f. of 48. Four massless springs whose force constants are $$2 \mathrm{~K}, 2 \mathrm{~K}, \mathrm{~K}$$ and $$2 \mathrm{~K}$$ resp 49. About black body radiation, which of the following is the wrong statement? 50. Two coils have a mutual inductance of $$0.004 \mathrm{~H}$$. The current changes in the first coil according to equation

MHT CET 2023 12th May Morning Shift

MCQ (Single Correct Answer)

-0

The derivative of $$\mathrm{f}(\tan x)$$ w.r.t. $$\mathrm{g}(\sec x)$$ at $$x=\frac{\pi}{4}$$ where $$\mathrm{f}^{\prime}(1)=2$$ and $$\mathrm{g}^{\prime}(\sqrt{2})=4$$ is

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

$$\sqrt{2}$$

MHT CET 2023 12th May Morning Shift

MCQ (Single Correct Answer)

-0

The p.m.f of random variate $$\mathrm{X}$$ is $$P(X)= \begin{cases}\frac{2 x}{\mathrm{n}(\mathrm{n}+1)}, & x=1,2,3, \ldots \ldots, \mathrm{n} \\ 0, & \text { otherwise }\end{cases}$$

Then $$\mathrm{E}(\mathrm{X})=$$

$$\frac{\mathrm{n}+1}{3}$$

$$\frac{2 \mathrm{n}+1}{3}$$

$$\frac{\mathrm{n}+2}{3}$$

$$\frac{2 n-1}{3}$$

MHT CET 2023 12th May Morning Shift

MCQ (Single Correct Answer)

-0

The angle between the tangents to the curves $$y=2 x^2$$ and $$x=2 y^2$$ at $$(1,1)$$ is

$$\tan ^{-1}\left(\frac{15}{8}\right)$$

$$\tan ^{-1}\left(\frac{7}{8}\right)$$

$$\tan ^{-1}\left(\frac{3}{4}\right)$$

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