MHT CET 2023 13th May Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

Mathematics

1. If $$\mathrm{f}(x)=x^3+\mathrm{b} x^2+\mathrm{c} x+\mathrm{d}$$ and $$0 2. Differentiation of $$\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$$ w.r.t. $$\cos ^{-1}\left(\sqrt{\frac{1+\sqrt{1+x^ 3. The function $$\mathrm{f}(\mathrm{t})=\frac{1}{\mathrm{t}^2+\mathrm{t}-2}$$ where $$\mathrm{t}=\frac{1}{x-1}$$ is discon 4. A random variable $$X$$ has the following probability distribution .tg {border-collapse:collapse;border-spacing:0;} .t 5. If $$\mathrm{I}=\int \frac{2 x-7}{\sqrt{3 x-2}} \mathrm{~d} x$$, then $$\mathrm{I}$$ is given by 6. Let $$\mathrm{X}$$ be random variable having Binomial distribution $$B(7, p)$$. If $$P[X=3]=5 P[X=4]$$, then variance of 7. The scalar product of vectors $$\overline{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$$ and a unit 8. $$\int \frac{\log \left(x^2+a^2\right)}{x^2} d x=$$ 9. The parametric equations of the curve $$x^2+y^2+a x+b y=0$$ are 10. The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the 11. $$x, y, z$$ are in G.P. and $$\tan ^{-1} x, \tan ^{-1} y, \tan ^{-1} z$$ are in A.P., then 12. In $$\triangle A B C$$ with usual notation, $$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$$ and $$a=\frac{1}{\sqr 13. If $$\hat{\mathrm{a}}$$ and $$\hat{\mathrm{b}}$$ are unit vectors and $$\overline{\mathrm{c}}=\hat{\mathrm{b}}-(\hat{\ma 14. Angles of a triangle are in the ratio $$4: 1: 1$$. Then the ratio of its greatest side to its perimeter is 15. If a continuous random variable $$\mathrm{X}$$ has probability density function $$\mathrm{f}(x)$$ given by $$f(x)=\left\ 16. The value of $$\begin{aligned} \cos \left(18^{\circ}-\mathrm{A}\right) \cdot \cos ( & \left.18^{\circ}+\mathrm{A}\right) 17. If $$\int x^5 e^{-4 x^3} \mathrm{~d} x=\frac{1}{48} \mathrm{e}^{-4 x^3} \mathrm{f}(x)+\mathrm{c}$$, where $$\mathrm{c}$$ 18. The solution of the differential equation $$\mathrm{e}^{-x}(y+1) \mathrm{d} y+\left(\cos ^2 x-\sin 2 x\right) y \mathrm{ 19. If $$A=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$$ and $$A_{i j}$$ is a cofactor of 20. Rate of increase of bacteria in a culture is proportional to the number of bacteria present at that instant and it is fo 21. The slope of the normal to the curve $$x=\sqrt{t}$$ and $$y=t-\frac{1}{\sqrt{t}}$$ at $$t=4$$ is 22. If $$3 \mathrm{f}(x)-\mathrm{f}\left(\frac{1}{x}\right)=8 \log _2 x^3, x>0$$, then $$\mathrm{f}(2), \mathrm{f}(4)$$, $$f 23. If the angle between the lines given by $$x^2-3 x y+\lambda y^2+3 x-5 y+2=0 ; \lambda \geq 0$$ is $$\tan ^{-1}\left(\fra 24. A line drawn from the point $$\mathrm{A}(1,3,2)$$ parallel to the line $$\frac{x}{2}=\frac{y}{4}=\frac{z}{1}$$, intersec 25. The value of $$\frac{\mathrm{i}^{248}+\mathrm{i}^{246}+\mathrm{i}^{244}+\mathrm{i}^{242}+\mathrm{i}^{240}}{\mathrm{i}^{2 26. If $$\mathrm{f}(x)=\int \frac{x^2 \mathrm{~d} x}{\left(1+x^2\right)\left(1+\sqrt{1+x^2}\right)}$$ and $$\mathrm{f}(0)=0$ 27. A line $$\mathrm{L}_1$$ passes through the point, whose p. v. (position vector) $$3 \hat{i}$$, is parallel to the vector 28. If $$y=\tan ^{-1}\left(\frac{4 \sin 2 x}{\cos 2 x-6 \sin ^2 x}\right)$$, then $$\left(\frac{\mathrm{d} y}{\mathrm{~d} x} 29. The expression $$(p \wedge \sim q) \vee q \vee(\sim p \wedge q)$$ is equivalent to 30. The raw data $$x_1, x_2, \ldots \ldots, x_{\mathrm{n}}$$ is an A.P. with common difference $$\mathrm{d}$$ and first term 31. The particular solution of differential equation $$\mathrm{e}^{\frac{d y}{d x}}=(x+1), y(0)=3$$ is 32. A card is drawn at random from a well shuffled pack of 52 cards. The probability that it is black card or face card is 33. If $$\bar{a}=2 \hat{i}+3 \hat{j}-4 \hat{k}$$ and $$\bar{b}=\hat{i}-\hat{j}-\hat{k}$$, then the projection of $$\bar{b}$$ 34. If $$\mathrm{f}(x)=\left\{\begin{array}{ll}\mathrm{e}^{\cos x} \sin x & , \text { for }|x| \leq 2 \\ 2, & \text { otherw 35. The equation of the line passing through the point $$(-1,3,-2)$$ and perpendicular to each of the lines $$\frac{x}{1}=\f 36. Let $$\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$$ be a function such that $$\mathrm{f}(x)=x^3+x^2 \mathrm{f}^{\prime 37. If $$A(1,4,2)$$ and $$C(5,-7,1)$$ are two vertices of triangle $$A B C$$ and $$G\left(\frac{4}{3}, 0, \frac{-2}{3}\right 38. The base of an equilateral triangle is represented by the equation $$2 x-y-1=0$$ and its vertex is $$(1,2)$$, then the l 39. Five persons $$\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$$ and $$\mathrm{E}$$ are seated in a circular arrangement. 40. The distance of the point $$(-1,-5,-10)$$ from the point of intersection of the line $$\frac{x-2}{3}=\frac{y+1}{4}=\frac 41. Negation of inverse of the following statement pattern $$(p \wedge q) \rightarrow(p \vee \sim q)$$ is 42. If $$\mathrm{f}(x)=3 x^{10}-7 x^8+5 x^6-21 x^3+3 x^2-7$$, then $$\lim _\limits{\alpha \rightarrow 0} \frac{f(1-\alpha)-f 43. The area (in sq. units) of the region bounded by curves $$y=3 x+1, y=4 x+1$$ and $$x=3$$ is 44. Values of $$c$$ as per Rolle's theorem for $$f(x)=\sin x+\cos x+6$$ on $$[0,2 \pi]$$ are 45. A vector $$\bar{a}$$ has components 1 and $$2 p$$ with respect to a rectangular Cartesian system. This system is rotated 46. A line is drawn through the point $$(1,2)$$ to meet the co-ordinate axes at $$\mathrm{P}$$ and $$\mathrm{Q}$$ such that 47. If feasible region is as shown in the figure, then related inequalities are 48. The general solution of the equation $$3 \sec ^2 \theta=2 \operatorname{cosec} \theta$$ is 49. A right circular cone has height $$9 \mathrm{~cm}$$ and radius of base $$5 \mathrm{~cm}$$. It is inverted and water is p 50. If $$\theta$$ is angle between the vectors $$\bar{a}$$ and $$\bar{b}$$ where $$|\bar{a}|=4,|\bar{b}|=3$$ and $$\theta \i

Physics

1. Select the 'WRONG' statement out of the following. 2. Two cells $$E_1$$ and $$E_2$$ having equal EMF '$$E$$' and internal resistances $$r_1$$ and $$r_2\left(r_1>r_2\right)$$ 3. Which one of the following represents correctly the variation of volume (V) of an ideal gas with temperature $$(\mathrm{ 4. Using variation of force and time given below, final velocity of a particle of mass $$2 \mathrm{~kg}$$ moving with initi 5. $$\mathrm{dQ}$$ is the heat energy supplied to an ideal gas under isochoric conditions. If $$\mathrm{dU}$$ and $$\mathrm 6. A black body at temperature $$127^{\circ} \mathrm{C}$$ radiates heat at the rate of $$5 \mathrm{~cal} / \mathrm{cm}^2 \m 7. The following graph represents 8. A rigid body rotates with an angular momentum L. If its rotational kinetic energy is made four times, its angular moment 9. A radioactive sample has half-life of 5 years. The percentage of fraction decayed in 10 years will be 10. Three coils of inductance $$\mathrm{L}_1=2 \mathrm{H}, \mathrm{L}_2=3 \mathrm{H}$$ and $$\mathrm{L}_3=6 \mathrm{H}$$ are 11. A Carnot engine has the same efficiency between (i) $$100 \mathrm{~K}$$ and $$600 \mathrm{~K}$$ and (ii) $$\mathrm{T} \m 12. For which of the following substances, the magnetic susceptibility is independent of temperature? 13. When a light of wavelength $$300 \mathrm{~nm}$$ fall on a photoelectric emitter, photo electrons are emitted. For anothe 14. In a given meter bridge, the current flowing through $$40 \Omega$$ resistor is 15. A body of mass $$0.04 \mathrm{~kg}$$ executes simple harmonic motion (SHM) about $$\mathrm{x}=0$$ under the influence of 16. A large number of water droplets each of radius '$$t$$' combine to form a large drop of Radius '$$R$$'. If the surface t 17. In resonance tube, first and second resonance are obtained at depths $$22.7 \mathrm{~cm}$$ and $$70.2 \mathrm{~cm}$$ res 18. Twenty seven droplets of water each of radius $$0.1 \mathrm{~mm}$$ merge to form a single drop then the energy released 19. If two inputs of a NAND gate are shorted, the resulting gate is 20. Venturimeter is used to 21. Which of the following statements is 'WRONG' for the conductors? 22. A circular coil of radius '$$r$$' and number of turns ' $n$ ' carries a current '$$I$$'. The magnetic fields at a small 23. A spherical surface of radius of curvature '$$R$$' separates air from glass of refractive index 1.5. The centre of curva 24. The rotational kinetic energy and translational kinetic energy of a rolling body are same, the body is 25. Two concentric circular coils A and B have radii $$20 \mathrm{~cm}$$ and $$10 \mathrm{~cm}$$ respectively lie in the sam 26. A charged spherical conductor of radius '$$R$$' is connected momentarily to another uncharged spherical conductor of rad 27. The magnet is moved towards the coil with speed '$$\mathrm{V}$$'. The induced e.m.f. in the coil is '$$\mathrm{e}$$'. Th 28. A uniform wire $$20 \mathrm{~m}$$ long and weighing $$50 \mathrm{~N}$$ hangs vertically. The speed of the wave at mid po 29. A large number of bullets are fired in all directions with same speed '$$U$$'. The maximum area on the ground on which t 30. A transformer has 20 turns in the primary and 100 turns in the secondary coil. An ac voltage of $$\mathrm{V}_{\text {in 31. On increasing the reverse bias to a large value in a P-N junction diode, current 32. For an ideal gas the density of the gas is $$\rho_0$$ when temperature and pressure of the gas are $$T_0$$ and $$P_0$$ r 33. The temperature gradient in a rod of length $$75 \mathrm{~cm}$$ is $$40^{\circ} \mathrm{C} / \mathrm{m}$$. If the temper 34. In an oscillating LC circuit, the maximum charge on the capacitor is '$$Q$$'. When the energy is stored equally between 35. A body of mass '$$\mathrm{m}$$' is raised through a height above the earth's surface so that the increase in potential e 36. With increase in frequency of a.c. supply, the impedance of an L-C-R series circuit 37. A passenger is sitting in a train which is moving fast. The engine of the train blows a whistle of frequency '$$n$$'. If 38. If the magnitude of intensity of electric field at a distance '$$r_1$$' on an axial line and at a distance '$$r_2$$' on 39. In an a.c. circuit the instantaneous current and emf are represented as $$\mathrm{I}=\mathrm{I}_0, \sin [\omega \mathrm{ 40. In a biprism experiment, monochromatic light of wavelength '$$\lambda$$' is used. The distance between two coherent sour 41. Three charges each of value $$+q$$ are placed at the corners of an isosceles triangle $$\mathrm{ABC}$$ of sides $$\mathr 42. Light of frequency 1.5 times the threshold frequency is incident on photosensitive material. If the frequency is halved 43. A solid cylinder of mass $$3 \mathrm{~kg}$$ is rolling on a horizontal surface with velocity $$4 \mathrm{~m} / \mathrm{s 44. Which one of the following statements is Wrong? 45. The fundamental frequency of a sonometer wir carrying a block of mass '$$M$$' and density '$$\rho$$' is '$$n$$' Hz. When 46. A simple pendulum has a time period '$$T$$' in air. Its time period when it is completely immersed in a liquid of densit 47. Array of light is incident at an angle of incidence '$$i$$' on one surface of a prism of small angle $$\mathrm{A}$$ and 48. An isotope of the original nucleus can be formed in a radioactive decay, with the emission of following particles. 49. If two identical spherical bodies of same material and dimensions are kept in contact, the gravitational force between t 50. $$\mathrm{A}$$ and $$\mathrm{B}$$ are two interfering sources where $$\mathrm{A}$$ is ahead in phase by $$54^{\circ}$$ r

MHT CET 2023 13th May Morning Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{\log \left(x^2+a^2\right)}{x^2} d x=$$

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

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

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

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

MHT CET 2023 13th May Morning Shift

MCQ (Single Correct Answer)

-0

The parametric equations of the curve $$x^2+y^2+a x+b y=0$$ are

$$x=\frac{\mathrm{a}}{2}+\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \cos \theta, y=\frac{\mathrm{b}}{2}+\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \sin \theta$$

$$x=\frac{\mathrm{a}}{2}-\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \cos \theta, y=\frac{\mathrm{b}}{2}-\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \sin \theta$$

$$x=-\frac{\mathrm{a}}{2}+\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \cos \theta, y=-\frac{\mathrm{b}}{2}+\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \sin \theta$$

$$x=-\frac{\mathrm{a}}{2}-\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \cos \theta, y=-\frac{\mathrm{b}}{2}-\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{4}} \sin \theta$$

MHT CET 2023 13th May Morning Shift

MCQ (Single Correct Answer)

-0

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the sides of the triangle (in units) are

3, 4, 5

4, 5, 6

5, 6, 7

2, 3, 4

MHT CET 2023 13th May Morning Shift

MCQ (Single Correct Answer)

-0

$$x, y, z$$ are in G.P. and $$\tan ^{-1} x, \tan ^{-1} y, \tan ^{-1} z$$ are in A.P., then

$$6 x=4 y=3 z$$

$$2 x=3 y=6 z$$

$$6 x=3 y=2 z$$

$$x=y=\mathrm{z}$$