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

If a circle passes through points $$(4,0)$$ and $$(0,2)$$ and its centre lies on $$\mathrm{Y}$$-axis. If the radius of the circle is $$r$$, then the value of $$r^2-r+1$$ is

MHT CET 2023 11th May Evening Shift

MCQ (Single Correct Answer)

-0

If $$\mathrm{A}=\left[\begin{array}{ll}\mathrm{i} & 1 \\ 1 & 0\end{array}\right]$$ where $$\mathrm{i}=\sqrt{-1}$$ and $$\mathrm{B}=\mathrm{A}^{2029}$$, then $$\mathrm{B}^{-1}=$$

$$-\mathrm{A}$$

$$\operatorname{adj} \mathrm{A}$$

$$\mathrm{-I}$$

$$-\operatorname{adj} \mathrm{A}$$

MHT CET 2023 11th May Evening Shift

MCQ (Single Correct Answer)

-0

The solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}+\frac{y}{x}=\sin x$$ is

$$x y+\cos x=\sin x+\mathrm{c}$$, where c is a constant of integration.

$$x(y+\cos x)=\sin x+\mathrm{c}$$, where c is a constant of integration.

$$y(x+\cos x)=\sin x+c$$, where c is a constant of integration.

$$x y+\sin x=\cos x+\mathrm{c}$$, where c is a constant of integration.

MHT CET 2023 11th May Evening Shift

MCQ (Single Correct Answer)

-0

Let $$f:[-1,2] \rightarrow[0, \infty)$$ be a continuous function such that $$\mathrm{f}(x)=\mathrm{f}(1-x), \forall x \in[-1,2]$$

Let $$\mathrm{R}_1=\int_{-1}^2 x \mathrm{f}(x) \mathrm{d} x$$ and $$\mathrm{R}_2$$ be the area of the region bounded by $$y=\mathrm{f}(x), x=-1, x=2$$ and the $$\mathrm{X}$$-axis, then $$\mathrm{R}_2$$ is

$$\frac{1}{2} R_1$$

$$2 R_1$$

$$3 R_1$$

$$\frac{1}{3} R_1$$

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