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

Let $$\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$$ be a function such that $$\mathrm{f}(x)=x^3+x^2 \mathrm{f}^{\prime}(1)+x \mathrm{f}^{\prime \prime}(2)+6, x \in \mathrm{R}$$, then $$\mathrm{f}(2)$$ is

$$-$$4

$$-$$2

MHT CET 2023 13th May Morning Shift

MCQ (Single Correct Answer)

-0

If $$A(1,4,2)$$ and $$C(5,-7,1)$$ are two vertices of triangle $$A B C$$ and $$G\left(\frac{4}{3}, 0, \frac{-2}{3}\right)$$ is centroid of the triangle $$A B C$$, then the mid point of side $$B C$$ is

$$\left(-2,-2, \frac{3}{2}\right)$$

$$\left(2,2, \frac{3}{2}\right)$$

$$\left(\frac{3}{2}, 2,-2\right)$$

$$\left(\frac{3}{2},-2,-2\right)$$

MHT CET 2023 13th May Morning Shift

MCQ (Single Correct Answer)

-0

The base of an equilateral triangle is represented by the equation $$2 x-y-1=0$$ and its vertex is $$(1,2)$$, then the length (in units) of the side of the triangle is

$$\sqrt{\frac{20}{3}}$$

$$\frac{2}{\sqrt{15}}$$

$$\sqrt{\frac{8}{15}}$$

$$\sqrt{\frac{15}{2}}$$

MHT CET 2023 13th May Morning Shift

MCQ (Single Correct Answer)

-0

Five persons $$\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$$ and $$\mathrm{E}$$ are seated in a circular arrangement. If each of them is given a cap of one of the three colours red, blue and green, then the number of ways of distributing the caps such that the persons seated in adjacent seats get different coloured caps, is

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