MHT CET 2023 11th May Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

Mathematics

1. $$\int\limits_0^\pi \frac{d x}{4+3 \cos x}=$$ 2. If $$y=\log _{\sin x} \tan x$$, then $$\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{x=\frac{\pi}{4}}$$ has the value 3. $$\lim _\limits{x \rightarrow 2}\left[\frac{1}{x-2}-\frac{2}{x^3-3 x^2+2 x}\right]$$ is equal to 4. From a lot of 20 baskets, which includes 6 defective baskets, a sample of 2 baskets is drawn at random one by one withou 5. If the angle between the lines represented by the equation $$x^2+\lambda x y-y^2 \tan ^2 \theta=0$$ is $$2 \theta$$, the 6. Number of common tangents to the circles $$x^2+y^2-6 x-14 y+48=0$$ and $$x^2+y^2-6 x=0$$ are 7. The left-hand derivative of $$\mathrm{f}(x)=[x] \sin (\pi x)$$, at $$x=\mathrm{k}, \mathrm{k}$$ is an integer and [.] is 8. Let $$\mathrm{f}(x)=\int \frac{\sqrt{x}}{(1+x)^2} \mathrm{~d} x, x \geq 0$$, then $$\mathrm{f}(3)-\mathrm{f}(1)$$ is equ 9. Value of $$c$$ satisfying the conditions and conclusions of Rolle's theorem for the function $$\mathrm{f}(x)=x \sqrt{x+6 10. Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vert 11. If the direction cosines $$l, \mathrm{~m}, \mathrm{n}$$ of two lines are connected by relations $$l-5 \mathrm{~m}+3 \mat 12. Let $$\mathrm{f}(x)=\log (\sin x), 0 13. Five students are to be arranged on a platform such that the boy $$B_1$$ occupies the second position and such that the 14. If the volume of the parallelopiped is $$158 \mathrm{~cu}$$. units whose coterminus edges are given by the vectors $$\ba 15. Let $$\mathrm{f}(x)$$ be positive for all real $$x$$. If $$\mathrm{I}_1=\int_\limits{1-\mathrm{h}}^{\mathrm{h}} x \mathr 16. The mirror image of the point $$(1,2,3)$$ in a plane is $$\left(-\frac{7}{3},-\frac{4}{3},-\frac{1}{3}\right)$$. Thus, t 17. If $$\alpha=3 \sin ^{-1} \frac{6}{11}$$ and $$\beta=3 \cos ^{-1}\left(\frac{4}{9}\right)$$, where the inverse trigonomet 18. $$\text { The value of } \sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right) \text { is }$$ 19. The value of $$\tan \left(\frac{\pi}{8}\right)$$ is _________. 20. A plane is parallel to two lines, whose direction ratios are $$1,0,-1$$ and $$-1,1,0$$ and it contains the point $$(1,1, 21. The domain of the function given by $$2^x+2^y=2$$ is 22. If $$\mathrm{f}(x)=x \mathrm{e}^{x(1-x)}, x \in \mathrm{R}$$, then $$\mathrm{f}(x)$$ is 23. The solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{1+y^2}{1+x^2}$$ is 24. If $$\bar{a}, \bar{b}, \bar{c}$$ are three vectors such that $$\overline{\mathrm{a}} \cdot(\overline{\mathrm{b}}+\overli 25. Let $$\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}$$ and $$\bar{b}=\hat{i}+\hat{j}$$. If $$\bar{c}$$ is a vector such that $$\ove 26. $$\int_\limits{-1}^3\left(\cot ^{-1}\left(\frac{x}{x^2+1}\right)+\cot ^{-1}\left(\frac{x^2+1}{x}\right)\right) \mathrm{d 27. If $$P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$$ is the adjoint of a $$3 \tim 28. If $$\mathrm{f}(x)=\left\{\begin{array}{ll}\frac{\sqrt{1+\mathrm{m} x}-\sqrt{1-\mathrm{m} x}}{x}, & -1 \leq x 29. The area of the region bounded by the parabola $$y=x^2$$ and the curve $$y=|x|$$ is 30. Derivative of $$\tan ^{-1}\left(\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right)$$ w.r.t. $$\cos ^{-1} 31. A binomial random variable $$\mathrm{X}$$ satisfies $$9. p(X=4)=p(X=2)$$ when $$n=6$$. Then $$p$$ is equal to 32. If in $$\triangle \mathrm{ABC}$$, with usual notations, $$a \cdot \cos ^2 \frac{C}{2}+c \cos ^2 \frac{A}{2}=\frac{3 b}{2 33. The lines $$\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-1}{5} \quad$$ and $$\frac{x+2}{4}=\frac{y-1}{3}=\frac{z+1}{2}$$ 34. A curve passes through the point $$\left(1, \frac{\pi}{6}\right)$$. Let the slope of the curve at each point $$(x, y)$$ 35. For the following shaded area, the linear constraints except $$x,y \ge 0$$ are 36. Let $$\omega \neq 1$$ be a cube root of unity and $$S$$ be the set of all non-singular matrices of the form $$\left[\beg 37. The value of $$2 \tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{7}$$ 38. $$\int \frac{\mathrm{e}^x(1+x)}{\cos ^2\left(\mathrm{e}^x \cdot x\right)} \mathrm{d} x=$$ 39. In a triangle $$\mathrm{ABC}$$, with usual notations, if $$\mathrm{m} \angle \mathrm{A}=60^{\circ}, \mathrm{b}=8, \mathr 40. If variance of $$x_1, x_2 \ldots \ldots, x_n$$ is $$\sigma_x^2$$, then the variance of $$\lambda x_1, \lambda x_2, \ldot 41. If $$\quad \overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}, \quad \overline{\mathrm{b}}=2 \hat{\mathrm{j}}-\hat{ 42. If $$\mathrm{z}=x+\mathrm{i} y$$ and $$\mathrm{z}^{1 / 3}=\mathrm{p}+\mathrm{iq}$$, where $$x, y, \mathrm{p}, \mathrm{q} 43. If $$\int \frac{\mathrm{d} x}{x \sqrt{1-x^3}}=\mathrm{k} \log \left(\frac{\sqrt{1-x^3}-1}{\sqrt{1-x^3}+1}\right)+\mathrm 44. The statement pattern $$\mathrm{p} \rightarrow \sim(\mathrm{p} \wedge \sim \mathrm{q})$$ is equivalent to 45. $$\mathrm{a}$$ and $$\mathrm{b}$$ are the intercepts made by a line on the co-ordinate axes. If $$3 \mathrm{a}=\mathrm{b 46. Let $$\bar{a}, \bar{b}$$ and $$\bar{c}$$ be three unit vectors such that $$\bar{a} \times(\bar{b} \times \bar{c})=\frac{ 47. The vector equation of the line $$2 x+4=3 y+1=6 z-3$$ is 48. If $$\overline{\mathrm{a}}$$ and $$\overline{\mathrm{b}}$$ are two unit vectors such that $$\overline{\mathrm{a}}+2 \ove 49. $$\int \frac{\log (\cot x)}{\sin 2 x} d x=$$ 50. $$\text { If } y=\sqrt{\frac{1-\sin ^{-1}(x)}{1+\sin ^{-1}(x)}} \text {, then } \frac{\mathrm{d} y}{\mathrm{~d} x} \text

Physics

1. A coil of radius '$$r$$' is placed on another coil (whose radius is $$\mathrm{R}$$ and current flowing through it is cha 2. Two capillary tubes of the same diameter are kept vertically in two different liquids whose densities are in the ratio $ 3. Two spherical black bodies of radii '$$r_1$$' and '$$r_2$$' at temperature '$$\mathrm{T}_1$$' and '$$\mathrm{T}_2$$' res 4. For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at certain displacement '$$x$$' from 5. The maximum kinetic energies of photoelectrons emitted are $$\mathrm{K}_1$$ and $$\mathrm{K}_2$$ when lights of waveleng 6. A particle moves along a circular path with decreasing speed. Hence 7. Identify the correct circuit diagrams for the normal operation from the following. 8. With the gradual increase in frequency of an a. c. source, the impedance of an LCR series circuit 9. In energy band diagram of insulators, a band gap and the conduction band is respectively 10. Two positively charged identical spheres separated by a distance 'd' exert some force (F) on each other when they are ke 11. A string fixed at both the ends forms standing wave with node separation of $$5 \mathrm{~cm}$$. If the velocity of the w 12. A ball of mass '$$\mathrm{m}$$' is attached to the free end of a string of length '$$l$$'. The ball is moving in horizon 13. Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its pl 14. When a current of $$1 \mathrm{~A}$$ is passed through a coil of 100 turns, the flux associated with it is $$2.5 \times 1 15. A spherical liquid drop of radius $$\mathrm{R}$$ is divided into 8 equal droplets. If surface tension is $$\mathrm{S}$$, 16. The rate of flow of heat through a metal rod with temperature difference $$40^{\circ} \mathrm{C}$$ is $$1600 \mathrm{~ca 17. Two charges of equal magnitude '$$q$$' are placed in air at a distance '$$2 r$$' apart and third charge '$$-2 \mathrm{q} 18. The size of the real image produced by a convex lens of focal length $$F$$ is '$$m$$' times the size of the object. The 19. A double slit experiment is immersed in water of refractive index 1.33. The slit separation is $$1 \mathrm{~mm}$$, dista 20. Potential difference between the points P and Q is nearly 21. An electron in the hydrogen atom jumps from the first excited state to the ground state. What will be the percentage cha 22. In series LCR circuit, the voltage across the inductance and the capacitance are not 23. If the temperature of a hot body is increased by $$50 \%$$, then the increase in the quantity of emitted heat radiation 24. The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe of length '$$L$$'. The 25. The radius of earth is $$6400 \mathrm{~km}$$ and acceleration due to gravity $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$. For th 26. A car sounding a horn of frequency $$1000 \mathrm{~Hz}$$ passes a stationary observer. The ratio of frequencies of the h 27. The time period of a simple pendulum inside a stationary lift is '$$T$$'. When the lift starts accelerating upwards with 28. The mutual inductance of a pair of coils, each of '$$N$$' turns, is '$$M$$' henry. If a current of '$$I$$' ampere in one 29. To manufacture a solenoid of length $$1 \mathrm{~m}$$ and inductance $$1 \mathrm{~mH}$$, the length of thin wire require 30. In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at time $$t=\frac{1 31. A bullet is fired on a target with velocity '$$\mathrm{V}$$'. Its velocity decreases from '$$\mathrm{V}$$' to '$$\mathrm 32. In the experiment of diffraction due to a single slit, if the slit width is decreased, the width of the central maximum 33. A cylindrical magnetic rod has length $$5 \mathrm{~cm}$$ and diameter $$1 \mathrm{~cm}$$. It has uniform magnetization $ 34. In biprism experiment, if $$5^{\text {th }}$$ bright band with wavelength $$\lambda_1^{\prime}$$ coincides with $$6^{\te 35. A body of mass '$$\mathrm{m}$$' kg starts falling from a distance 3R above earth's surface. When it reaches a distance ' 36. In the case of NAND gate, if A and B are the inputs and $$\mathrm{Y}$$ is the output then 37. A monoatomic gas at pressure '$$\mathrm{P}$$', having volume '$$\mathrm{V}$$' expands isothermally to a volume '$$2 \mat 38. In potentiometer experiments, two cells of e. m. f. '$$E_1$$' and '$$E_2$$' are connected in series $$\left(E_1>E_2\righ 39. A diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ is compressed adiabatically to volume $$\frac{V_i}{32}$$ where $$V_i$ 40. A disc has mass $$M$$ and radius $$R$$. How much tangential force should be applied to the rim of the disc, so as to rot 41. An electron moving with velocity $$1.6 \times 10^7 \mathrm{~m} / \mathrm{s}$$ has wavelength of $$0.4 \mathop A\limits^o 42. The prism has refracting angle '$$\mathrm{A}$$'. The second refracting surface of the prism is silvered. Light ray falli 43. Two parallel wires of equal lengths are separated by a distance of $$3 \mathrm{~m}$$ from each other. The currents flowi 44. Three point charges $$+\mathrm{q},+2 \mathrm{q}$$ and $$+\mathrm{Q}$$ are placed at the three vertices of an equilateral 45. If a gas is compressed isothermally then the r.m.s. velocity of the molecules 46. The bob of a simple pendulum of length '$$L$$' has a mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$'. The pendulum is 47. An electron is projected along the axis of circular conductor carrying current I. Electron will experience 48. Two identical capacitors have the same capacitance '$$C$$'. One of them is charged to a potential $$V_1$$ and the other 49. A transverse wave $$\mathrm{Y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})$$ moves on a stretched string from one end to anot 50. A body of density '$$\rho$$' is dropped from rest at a height '$$h$$' into a lake of density '$$\sigma' (\sigma>\rho)$$.

MHT CET 2023 11th May Morning Shift

MCQ (Single Correct Answer)

-0

If $$\bar{a}, \bar{b}, \bar{c}$$ are three vectors such that $$\overline{\mathrm{a}} \cdot(\overline{\mathrm{b}}+\overline{\mathrm{c}})+\overline{\mathrm{b}} \cdot(\overline{\mathrm{c}}+\overline{\mathrm{a}})+\overline{\mathrm{c}} \cdot(\overline{\mathrm{a}}+\overline{\mathrm{b}})=0 \quad$$ and $$\quad|\overline{\mathrm{a}}|=1$$, $$|\bar{b}|=8$$ and $$|\bar{c}|=4$$, then $$|\bar{a}+\bar{b}+\bar{c}|$$ has the value _________.

MHT CET 2023 11th May Morning Shift

MCQ (Single Correct Answer)

-0

Let $$\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}$$ and $$\bar{b}=\hat{i}+\hat{j}$$. If $$\bar{c}$$ is a vector such that $$\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}=|\overline{\mathrm{c}}|,|\overline{\mathrm{c}}-\overline{\mathrm{a}}|=2 \sqrt{2}$$ and the angle between $$(\bar{a} \times \bar{b})$$ and $$\bar{c}$$ is $$\frac{\pi}{6}$$, then $$|(\bar{a} \times \bar{b}) \times \bar{c}|$$ is

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

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

$$\frac{3}{4}$$

MHT CET 2023 11th May Morning Shift

MCQ (Single Correct Answer)

-0

$$\int_\limits{-1}^3\left(\cot ^{-1}\left(\frac{x}{x^2+1}\right)+\cot ^{-1}\left(\frac{x^2+1}{x}\right)\right) \mathrm{d} x=$$

$$\left(\frac{\pi}{4}\right)$$

$$\pi$$

$$\left(\frac{\pi}{2}\right)$$

$$(2 \pi)$$

MHT CET 2023 11th May Morning Shift

MCQ (Single Correct Answer)

-0

If $$P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$$ is the adjoint of a $$3 \times 3$$ matrix $$A$$ and $$|A|=4$$, then value of $$\alpha$$ is

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