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

Chemistry

Mathematics

1. If $$\mathrm{f}(x)=3^x ; \mathrm{g}(x)=4^x$$, then $$\frac{\mathrm{f}^{\prime}(0)-\mathrm{g}^{\prime}(0)}{1+\mathrm{f}^{ 2. If $$x=\frac{5}{1-2 \mathrm{i}}, \mathrm{i}=\sqrt{-1}$$, then the value of $$x^3+x^2-x+22$$ is 3. Two cards are drawn successively with replacement from a well-shuffled pack of 52 cards. Then mean of number of tens is 4. $$\int x \sqrt{\frac{2 \sin \left(x^2+1\right)-\sin 2\left(x^2+1\right)}{2 \sin \left(x^2+1\right)+\sin 2\left(x^2+1\rig 5. If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $x-3=\frac{y-\mathrm{k}}{2}=\mathrm{z}$ intersect, then the 6. $$\text { For all real } x \text {, the minimum value of } \frac{1-x+x^2}{1+x+x^2} \text { is }$$ 7. If $$\bar{a}=\hat{i}+4 \hat{j}+2 \hat{k}, \bar{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}, \bar{c}=2 \hat{i}-\hat{j}+4 \hat{k}$$, 8. If the vertices of a triangle are $$(-2,3),(6,-1)$$ and $$(4,3)$$, then the co-ordinates of the circumcentre of the tria 9. The solution of $$\frac{\mathrm{d} x}{\mathrm{~d} y}+\frac{x}{y}=x^2$$ is 10. If $$\int \frac{\cos 8 x+1}{\cot 2 x-\tan 2 x} \mathrm{~d} x=\mathrm{A} \cos 8 x+\mathrm{c}$$, where $$\mathrm{c}$$ is a 11. The set of all points, where the derivative of the functions $$\mathrm{f}(x)=\frac{x}{1+|x|}$$ exists, is 12. In triangle $$\mathrm{ABC}$$ with usual notations $$\mathrm{b}=\sqrt{3}, \mathrm{c}=1, \mathrm{~m} \angle \mathrm{A}=30^ 13. A fair die is tossed twice in succession. If $$\mathrm{X}$$ denotes the number of fours in two tosses, then the probabil 14. If $$\mathrm{f}(x)=\frac{3 x+4}{5 x-7}$$ and $$\mathrm{g}(x)=\frac{7 x+4}{5 x-3}$$, then $$\mathrm{f}(\mathrm{g}(x))=$$ 15. If the function $$f$$ is given by $$f(x)=x^3-3(a-2) x^2+3 a x+7$$, for some $$\mathrm{a} \in \mathbb{R}$$, is increasing 16. The unit vector perpendicular to each of the vectors $$\bar{a}+\bar{b}$$ and $$\bar{a}-\bar{b}$$, where $$\bar{a}=\hat{i 17. The logical statement $$(\sim(\sim \mathrm{p} \vee \mathrm{q}) \vee(\mathrm{p} \wedge \mathrm{r})) \wedge(\sim \mathrm{q 18. Let $$\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}, \bar{b}=\hat{i}+\hat{j}$$ and $$\bar{c}$$ be a vector such that $$|\bar{c}-\b 19. If $$a$$ and $$b$$ are positive number such that $$a>b$$, then the minimum value of $$a \sec \theta-b \tan \theta\left(0 20. $$\text { If } l=\lim _\limits{x \rightarrow 0} \frac{x}{|x|+x^2} \text {, then the value of } l \text { is }$$ 21. If $$y=[(x+1)(2 x+1)(3 x+1) \ldots(\mathrm{n} x+1)]^{\frac{3}{2}}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x= 22. If $$\cos x+\cos y-\cos (x+y)=\frac{3}{2}$$, then 23. The joint equation of the lines pair of lines passing through the point $$(3,-2)$$ and perpendicular to the lines $$5 x^ 24. If the line $$\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{4}$$ meets the plane $$x+2 y+3 z=15$$ at the point $$P$$, then the 25. If $$\mathrm{A}$$ and $$\mathrm{B}$$ are two events such that $$\mathrm{P}(\mathrm{A})=\frac{1}{3}, \mathrm{P}(\mathrm{B 26. If the general solution of the equation $$\frac{\tan 3 x-1}{\tan 3 x+1}=\sqrt{3}$$ is $$x=\frac{\mathrm{n} \pi}{\mathrm{ 27. If the area of the parallelogram with $$\bar{a}$$ and $$\bar{b}$$ as two adjacent sides is $$16 \mathrm{sq}$$. units, th 28. The value of $$\int(1-\cos x) \cdot \operatorname{cosec}^2 x d x$$ is 29. If $$\cos ^{-1} \sqrt{\mathrm{p}}+\cos ^{-1} \sqrt{1-\mathrm{p}}+\cos ^{-1} \sqrt{1-\mathrm{q}}=\frac{3 \pi}{4}$$, then 30. The slope of the tangent to a curve $$y=\mathrm{f}(x)$$ at $$(x, \mathrm{f}(x))$$ is $$2 x+1$$. If the curve passes thro 31. $$A$$ rod $$A B, 13$$ feet long moves with its ends $$A$$ and $$B$$ on two perpendicular lines $$O X$$ and $$O Y$$ respe 32. If $$\mathrm{f}(x)=\left\{\begin{array}{cc}\frac{x-3}{|x-3|}+\mathrm{a} & , \quad x 3\end{array}\right.$$ Is continuous 33. The equation of the tangent to the curve $$y=\sqrt{9-2 x^2}$$, at the point where the ordinate and abscissa are equal, i 34. If $$\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=2 \hat{\mathr 35. If a circle passes through points $$(4,0)$$ and $$(0,2)$$ and its centre lies on $$\mathrm{Y}$$-axis. If the radius of t 36. If $$\mathrm{A}=\left[\begin{array}{ll}\mathrm{i} & 1 \\ 1 & 0\end{array}\right]$$ where $$\mathrm{i}=\sqrt{-1}$$ and $$ 37. The solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}+\frac{y}{x}=\sin x$$ is 38. Let $$f:[-1,2] \rightarrow[0, \infty)$$ be a continuous function such that $$\mathrm{f}(x)=\mathrm{f}(1-x), \forall x \i 39. The equation of line passing through the point $$(1,2,3)$$ and perpendicular to the lines $$\frac{x-2}{3}=\frac{y-1}{2}= 40. Let a random variable $$\mathrm{X}$$ have a Binomial distribution with mean 8 and variance 4. If $$\mathrm{P}(\mathrm{X} 41. $$\pi+\left(\sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{16}{65}\right)$$ is equal to 42. If the angles of a triangle are in the ratio $$4: 1: 1$$, then the ratio of the longest side to its perimeter is 43. If truth value of logical statement $$(p \leftrightarrow \sim q) \rightarrow(\sim p \wedge q)$$ is false, then the truth 44. The teacher wants to arrange 5 students on the platform such that the boy $$B_1$$ occupies second position and the girls 45. If $$\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{b}}=4 \hat{\mathrm{i}}+ 46. At present a firm is manufacturing 1000 items. It is estimated that the rate of change of production $$\mathrm{P}$$ w.r. 47. The maximum value of $$z=3 x+5 y$$ subject to the constraints $$3 x+2 y \leq 18, x \leq 4, y \leq 6, x, y \geq 0$$, is 48. If $$\mathrm{I}=\int \sin (\log (x)) \mathrm{d} x$$, then $$\mathrm{I}$$ is given by 49. If both mean and variance of 50 observations $$x_1, x_2, \ldots \ldots, x_{50}$$ are equal to 16 and 256 respectively, t 50. The angle between the line $$\frac{x+1}{2}=\frac{y-2}{1}=\frac{z-3}{-2}$$ and plane $$x-2 y-\lambda z=3$$ is $$\cos ^{-1

Physics

1. The magnetic flux through a circuit of resistance '$$R$$' changes by an amount $$\Delta \phi$$ in the time $$\Delta t$$. 2. A beam of light of wavelength $$600 \mathrm{~nm}$$ from a distant source falls on a single slit $$1 \mathrm{~mm}$$ wide 3. An electron of mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$' is accelerated from rest in a uniform electric field of 4. Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies o 5. A ball kept at $$20 \mathrm{~m}$$ height falls freely in vertically downward direction and hits the ground. The coeffici 6. Two long conductors separated by a distance '$$\mathrm{d}$$' carry currents $$I_1$$ and $$I_2$$ in the same direction. T 7. The a.c. source is connected to series LCR circuit. If voltage across $$R$$ is $$40 \mathrm{~V}$$, that across $$\mathrm 8. In the study of transistor as an amplifier if $$\alpha=\frac{I_C}{I_E}=0.98$$ and $$\beta=\frac{I_C}{I_B}=49$$, where $$ 9. A liquid drop of radius '$$R$$' is broken into '$$n$$' identical small droplets. The work done is [T = surface tension o 10. For a gas, $$\frac{\mathrm{R}}{\mathrm{C}_{\mathrm{v}}}=0 \cdot 4$$, where $$\mathrm{R}$$ is universal gas constant and 11. Two bodies $$\mathrm{A}$$ and $$\mathrm{B}$$ at temperatures '$$\mathrm{T}_1$$' $$\mathrm{K}$$ and '$$\mathrm{T}_2$$' $$ 12. In a conical pendulum the bob of mass '$$\mathrm{m}$$' moves in a horizontal circle of radius '$$r$$' with uniform speed 13. A fluid of density '$$\rho$$' is flowing through a uniform tube of diameter '$$d$$'. The coefficient of viscosity of the 14. The self inductance '$$L$$' of a solenoid of length '$$l$$' and area of cross-section '$$\mathrm{A}$$', with a fixed num 15. A transverse wave in a medium is given by $$y=A \sin 2(\omega t-k x)$$. It is found that the magnitude of the maximum ve 16. The radius of the orbit of a geostationary satellite is (mean radius of earth is '$$R$$', angular velocity about own axi 17. According to Bohr's theory of hydrogen atom, the total energy of the electron in the $$\mathrm{n}^{\text {th }}$$ statio 18. In a series LCR circuit, $$\mathrm{C}=2 \mu \mathrm{F}, \mathrm{L}=1 \mathrm{mH}$$ and $$\mathrm{R}=10 \Omega$$. The rat 19. In Young's double slit experiment, the fifth maximum with wavelength '$$\lambda_1$$' is at a distance '$$y_1$$' and the 20. Bohr model is applied to a particle of mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$' moving in a plane under the inf 21. A rectangular block of mass '$$\mathrm{m}$$' and crosssectional area A, floats on a liquid of density '$$\rho$$'. It is 22. Two spherical conductors of capacities $$3 \mu \mathrm{F}$$ and $$2 \mu \mathrm{F}$$ are charged to same potential havin 23. A circular arc of radius '$$r$$' carrying current '$$\mathrm{I}$$' subtends an angle $$\frac{\pi}{16}$$ at its centre. T 24. A sound of frequency $$480 \mathrm{~Hz}$$ is emitted from the stringed instrument. The velocity of sound in air is $$320 25. A sonometer wire '$$A$$' of diameter '$$\mathrm{d}$$' under tension '$$T$$' having density '$$\rho_1$$' vibrates with fu 26. The upper end of the spring is fixed and a mass '$$m$$' is attached to its lower end. When mass is slightly pulled down 27. What should be the diameter of a soap bubble, in order that the excess pressure inside it is $$25.6 \mathrm{~Nm}^{-2}$$ 28. If temperature of gas molecules is raised from $$127^{\circ} \mathrm{C}$$ to $$527^{\circ} \mathrm{C}$$, the ratio of r. 29. The ratio of energy required to raise a satellite to a height '$$h$$' above the earth's surface to that required to put 30. According to Boyle's law, the product PV remains constant. The unit of $$\mathrm{PV}$$ is same as that of 31. When a metallic surface is illuminated with radiation of wavelength '$$\lambda$$', the stopping potential is '$$\mathrm{ 32. Three identical capacitors of capacitance '$$\mathrm{C}$$' each are connected in series and this connection is connected 33. In Young's double slit experiment, green light is incident on two slits. The interference pattern is observed on a scree 34. Two batteries, one of e.m.f. $$12 \mathrm{~V}$$ and internal resistance $$2 \Omega$$ and other of e.m.f. $$6 \mathrm{~V} 35. Potential difference between the points P and Q is nearly 36. A coil having effective area '$$A$$' is held with its plane normal to a magnitude field of induction '$$\mathrm{B}$$'. T 37. The path difference between two waves, represented by $$\mathrm{y}_1=\mathrm{a}_1 \sin \left(\omega \mathrm{t}-\frac{2 \ 38. An electromagnetic wave, whose wave normal makes an angle of $$45^{\circ}$$ with the vertical, travelling in air strikes 39. The difference in length between two rods $$\mathrm{A}$$ and $$\mathrm{B}$$ is $$60 \mathrm{~cm}$$ at all temperatures. 40. A parallel plate capacitor is charged by a battery and battery remains connected. The dielectric slab of constant '$$\ma 41. From a disc of mass '$$M$$' and radius '$$R$$', a circular hole of diameter '$$R$$' is cut whose rim passes through the 42. If $$p$$-$$n$$ junction diode is in forward bias then 43. The orbital magnetic moment associated with orbiting electron of charge '$$e$$' is 44. An ideal gas expands adiabatically. $$(\gamma=1 \cdot 5)$$ To reduce the r.m.s. velocity of the molecules 3 times, the g 45. A metal surface of work function $$1 \cdot 13 \mathrm{~eV}$$ is irradiated with light of wavelength $$310 \mathrm{~nm}$$ 46. Two cars A and B start from a point at the same time in a straight line and their positions are represented by $$\mathrm 47. The a.c. source of e.m.f. with instantaneous value '$$e$$' is given by $$e=200 \sin (50 t)$$ volt. The r.m.s. value of c 48. In the digital circuit the inputs are as shown in figure. The Boolean expression for output $$\mathrm{Y}$$ is 49. A double convex lens of focal length '$$F$$' is cut into two equal parts along the vertical axis. The focal length of ea 50. Two progressive waves are travelling towards each other with velocity $$50 \mathrm{~m} / \mathrm{s}$$ and frequency $$20

MHT CET 2023 11th May Evening Shift

MCQ (Single Correct Answer)

-0

An electromagnetic wave, whose wave normal makes an angle of $$45^{\circ}$$ with the vertical, travelling in air strikes a horizontal liquid surface. While travelling through the liquid it gets deviated through $$15^{\circ}$$. What is the speed of the electromagnetic wave in the liquid, if the speed of electromagnetic wave in air is $$3 \times 10^8 \mathrm{~m} / \mathrm{s}$$ ? $$\left(\sin 30^{\circ}=0.5, \sin 45^{\circ}=\frac{1}{\sqrt{2}}\right)$$

$$\frac{\sqrt{2}}{3} \times 10^8 \mathrm{~m} / \mathrm{s}$$

$$1.5 \times 10^8 \mathrm{~m} / \mathrm{s}$$

$$2.1 \times 10^8 \mathrm{~m} / \mathrm{s}$$

$$2.5 \times 10^8 \mathrm{~m} / \mathrm{s}$$

MHT CET 2023 11th May Evening Shift

MCQ (Single Correct Answer)

-0

The difference in length between two rods $$\mathrm{A}$$ and $$\mathrm{B}$$ is $$60 \mathrm{~cm}$$ at all temperatures. If $$\alpha_{\mathrm{A}}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C}$$ and $$\beta_{\mathrm{B}}=27 \times 10^{-6} /{ }^{\circ} \mathrm{C}$$, the lengths of the two rods are

$$l_{\mathrm{A}}=200 \mathrm{~cm}, l_{\mathrm{B}}=140 \mathrm{~cm}$$

$$l_{\mathrm{A}}=180 \mathrm{~cm}, l_{\mathrm{B}}=120 \mathrm{~cm}$$

$$l_{\mathrm{A}}=160 \mathrm{~cm}, l_{\mathrm{B}}=100 \mathrm{~cm}$$

$$l_{\mathrm{A}}=120 \mathrm{~cm}, l_{\mathrm{B}}=60 \mathrm{~cm}$$

MHT CET 2023 11th May Evening Shift

MCQ (Single Correct Answer)

-0

A parallel plate capacitor is charged by a battery and battery remains connected. The dielectric slab of constant '$$\mathrm{K}$$' is inserted between the plates and then taken out. Then electric field between the plates

remains the same

increases

decreases

becomes zero

MHT CET 2023 11th May Evening Shift

MCQ (Single Correct Answer)

-0

From a disc of mass '$$M$$' and radius '$$R$$', a circular hole of diameter '$$R$$' is cut whose rim passes through the centre. The moment of inertia of the remaining part of the disc about perpendicular axis passing through the centre is

$$\frac{13 \mathrm{MR}^2}{32}$$

$$\frac{11 \mathrm{MR}^2}{32}$$

$$\frac{9 \mathrm{MR}^2}{32}$$

$$\frac{7 \mathrm{MR}^2}{32}$$

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