MHT CET 2021 21th September Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

Mathematics

1. If $$\mathrm{(m+3 n)(3 m+n)=4 h^2}$$, then the acute angle between the lines represented by $$\mathrm{m x^2+2 h x y+n y^ 2. $$\text{I} : y^{\prime}=\frac{y+x}{x} ; \quad \text { II }: y^{\prime}=\frac{x^2+y}{x^3} ; \quad \text { III }: y^{\prim 3. The differential equation of the family of circles touching $$y$$-axis at the origin is 4. The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the ot 5. If $$\overline{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}, \overline{\mathrm{b}}=3 \hat{\mathrm{ 6. If $$\mathrm{p}$$ is the length of the perpendicular from origin to the line whose intercepts on the axes are a and $$b$ 7. The abscissa of the points, where the tangent to the curve $$y=x^3-3 x^2-9 x+5$$ is parallel to $$X$$ axis are 8. $$\int \frac{1}{x^{\frac{1}{2}}+x^{\frac{1}{3}}} d x=$$ 9. If $$A=\left[\begin{array}{ccc}\cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\r 10. $$\int[\sin |\log x|+\cos |\log x|] d x=$$ 11. $$\int\limits_5^{10} \frac{d x}{(x-1)(x-2)}=$$ 12. The direction cosines $$\ell, \mathrm{m}, \mathrm{n}$$ of the line $$\frac{\mathrm{x}+2}{2}=\frac{2 \mathrm{y}-5}{3} ; \ 13. an urn contains 9 balls of which 3 are red, 4 are blue and 2 are green. Three balls are drawn at random from the urn. Th 14. If $${\pi \over 2} 15. Equation of the plane passing through the point (2, 0, 5) and parallel to the vectors $$\widehat i - \widehat j + \wideh 16. If $$A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1\end{array}\right]$$ and $$A^{-1}=\frac{1}{2}\left[\be 17. For all real $$x$$, the minimum value of the function $$f(x)=\frac{1-x+x^2}{1+x+x^2}$$ is 18. The objective function $$z=4 x+5 y$$ subjective to $$2 x+y \geq 7 ; 2 x+3 y \leq 15 ; y \leq 3, x \geq 0 ; y \geq 0$$ ha 19. The co-ordinates of the point $$\mathrm{P} \equiv(1,2,3)$$ and $$\mathrm{O} \equiv(0,0,0)$$, then the direction cosines 20. $$\int\limits_{{{ - \pi } \over 2}}^{{\pi \over 2}} {{{\cos x} \over {1 + {e^x}}}dx = } $$ 21. The equation of the plane containing the line $$\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$$ and the point $$(0,7,-7)$$ 22. If the lines $$x^2-4xy+y^2=0$$ make angles $$\alpha$$ and $$\beta$$ with positive direction X-axis, then $$\cot^2\alpha+ 23. It is observed that $$25 \%$$ of the cases related to child labour reported to the police station are solved. If 6 new c 24. For X ~ B(n, p), if p = 0.6, E(X) = 6, then Var(X) = 25. The equation of a line passing through $$(3,-1,2)$$ and perpendicular to the lines $$\bar{r}=(\hat{i}+\hat{j}-\hat{k})+\ 26. $$\begin{aligned} & \text { } f(x)=\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x} \text {, if } 1 \leq x is continuous in the inter 27. The function $$f(x)=\log (1+x)-\frac{2 x}{2+x}$$ is increasing on 28. If $$A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right]$$, then $$A^{-1}=$$ 29. The equation of circle with centre at $$(2,-3)$$ and the circumference $$10 \pi$$ units is 30. If y = 2 sin x + 3 cos x and y + A$$\mathrm{\frac{d^2y}{dx^2}}$$ = B, then the values of A, B are respectively 31. The number of solutions of cos2$$\theta$$ = sin$$\theta$$ in (0, 2$$\pi$$) are 32. If $$y=\tan ^{-1}\left[\frac{1}{1+x+x^2}\right]+\tan ^{-1}\left[\frac{1}{x^2+3 x+3}\right], x>0$$, then $$\frac{d y}{d x 33. If $$z(2-i)=(3+i)$$, then $$z^{38}=$$, ( where $$z=x+i y$$) 34. The area bounded by the parabola $$y^2=x$$, the straight line $$y=4$$ and $$Y$$ axis is 35. If $$\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)=\sin ^{-1} \alpha$$, then $$\alpha=$$ 36. If $$\lim _\limits{x \rightarrow 5} \frac{x^k-5^k}{x-5}=500$$, then the value of $$k$$, where $$k \in N$$ is 37. The logical statement (p $$\to$$ q) $$\wedge$$ (q $$\to$$ ~p) is equivalent to 38. For a set of five true or false questions, no student has written the all correct answers and no two students have given 39. The general solution of the differential equation. $$\left(\frac{y}{x}\right) \cos \left(\frac{y}{x}\right) d x-\left[\l 40. If the half life period of a substance is 5 years, then the total amount of the substance left after 15 years, when init 41. A bakerman sells 5 types of cakes. Profit due to sale of each type of cake is respectively ₹ 2.5, ₹ 3 , ₹ 1.5 and ₹ 1. T 42. If $$m$$ is order and $$n$$ is degree of the differential equation $$\left(\frac{d^2 y}{d x^2}\right)^5+4 \frac{\left(\f 43. If $$\theta+\phi=\alpha$$ and $$\tan \theta=k \tan \phi($$ where $$K>1)$$, then the value of $$\sin (\theta-\phi)$$ is 44. With usual notations, perimeter of a triangle $$A B C$$ is 6 times the arithmetic mean of sine of its angles. If $$\math 45. If p $$\to$$ (~p $$\vee$$ q) is false, then the truth values of p and q are, respectively 46. If $$|\bar{a} \times \bar{b}|^2+(\bar{a} \cdot \bar{b})^2=144$$ and $$|\bar{a}|=4$$, then $$|\bar{b}|=$$ 47. Let A = {10, 11, 12, 14, 26} and let f : A $$\to$$ N be such that f(a) = highest prime factor of a, where a $$\in$$ A, t 48. If $$\int {{{5\tan x} \over {\tan x - 2}}dx = x + a\log |\sin x - 2\cos x| + c} $$, then a = (Where c is constant of int 49. The area of the parallelogram with vertices A(1, 2, 3), B(1, 3, a), C(3, 8, 6) and D(3, 7, 3) is $$\sqrt{265}$$ sq. unit 50. If $$y = {\tan ^{ - 1}}\left\{ {{{a\cos x - b\sin x} \over {b\cos x + a\sin x}}} \right\}$$, then $${{dy} \over {dx}}$$

Physics

1. Under isothermal conditions, two soap bubbles of radii '$$r_1$$' and '$$r_2$$' combine to form a single soap bubble of 2. Two identical parallel plate air capacitors are connected in series to a battery of emf '$$\mathrm{V}$$'. If one of the 3. In LCR series resonant circuit, at resonance, voltage across 'L' and 'C' will cancel each other because they are 4. Two coherent sources of wavelength '$$\lambda$$' produce steady interference pattern. The path difference corresponding 5. In a capillary tube having area of cross-section A, water rises to a height 'h'. If cross-sectional area is reduced to $ 6. Water rises upto a height $$10 \mathrm{~cm}$$ in a capillary tube. It will rise to a height which is much more than $$10 7. A moving coil galvanometer is converted into an ammeter, reading upto $$0.04 \mathrm{~A}$$ by connecting a shunt of resi 8. The inductive reactance of a coil is R$$\Omega$$. If the inductance of a coil is doubled and frequency of a.c. supply is 9. For a body of mass '$$m$$', the acceleration due to gravity at a distance '$$R$$' from the surface of the earth is $$\le 10. What is the ratio of the velocity of sound in hydrogen $$\left(\gamma=\frac{7}{5}\right)$$ to that in helium $$\left(\ga 11. A particle performs rotational motion with an angular momentum 'L'. If frequency of rotation is doubled and its kinetic 12. Equation of two simple harmonic waves are given by $${Y_1} = 2\sin 8\pi \left( {{t \over {0.2}} - {x \over 2}} \right)m$ 13. A current through 1 $$\Omega$$ resistance in the following circuit is 14. Three bodies P, Q and R have masses 'm' kg, '2m' kg and '3m' kg respectively. If all the bodies have equal kinetic energ 15. Equal volumes of two gases are kept in different containers having densities in the ratio 1 : 16. They exert equal press 16. In Young's experiment, fringes are obtained on a screen placed at a distance $$75 \mathrm{~cm}$$ from the slits. When th 17. Combination of NAND gates is shown in the figure. It is equivalent to 18. A molecule of mass 'm' moving with velocity 'v' makes 5 elastic collisions with a wall of container per second. The chan 19. In thermodynamics, for an isochoric process, which one of the following statement is INCORRECT? 20. The ratio of energy required to raise a satellite of mass '$$m$$' to height '$$h$$' above the earth's surface to that re 21. When a piece of polythene is rubbed with wool, a negative charge of $$4 \times 10^{-7} \mathrm{C}$$ is developed on the 22. Ratio centripetal acceleration for an electron revolving in 3rd and 5th Bohr orbit of hydrogen atom is 23. In an ideal junction diode, the current flowing through PQ is 24. LED is manufactured using zinc selenide then it emits. 25. If '$$\mathrm{E}$$' is the kinetic energy per mole of an ideal gas and '$$\mathrm{T}$$' is the absolute temperature, the 26. A child is sitting on a swing which performs S.H.M. It has minimum and maximum heights from ground $$0.75 \mathrm{~cm}$$ 27. The north pole of a long horizontal bar magnet is being brought towards closed circuit consisting of a coil. The directi 28. The wave number of the last line of the Balmer series in the hydrogen spectrum will be $$\left(\right.$$ Rydberg's cons 29. The refractive index of glass is 1.5 and that of water is 1.33 . The critical angle for a ray of light going from glass 30. A, B and C are three parallel conductors of equal lengths carrying currents $$\mathrm{I}, \mathrm{I}$$ and $$2 \mathrm{I 31. Three pure inductors each of inductance 6H are connected as shown in the figure. Their equivalent inductance between the 32. A body at rest falls through a height 'h' with velocity 'V'. If it has to fall down further for its velocity to become t 33. A convex lens is dipped in a liquid whose refractive index is equal to refractive index of lens material. Then its focal 34. Photoemission from metal surface takes place for frequencies '$$v_1$$' and '$$v_2$$' of incident rays $$\left(v_1>v_2\ri 35. The angle of banking '$$\theta$$' for a meter gauge railway line is given by $$\theta=\tan ^{-1}\left(\frac{1}{20}\right 36. Three rings each of mass 'M' and radius 'R' are arranged as shown in the figure. The moment of inertia of system about 37. The instantaneous value of an alternating current is given by $$\mathrm{i}=50 \sin (100 \pi \mathrm{t})$$. It will achie 38. A proton and alpha particle are accelerated through the same potential difference. The ratio of the de-Broglie wavelengt 39. Two rods of same length and material are joined end to end. They transfer heat in 8 second. When they are joined in para 40. A pendulum clock is running fast. To correct its time, we should 41. A pipe closed at one end has length $$0.8 \mathrm{~m}$$. At its open end $$0.5 \mathrm{~m}$$ long uniform string is vibr 42. Two coherent sources 'P' and 'Q' produce interference at point 'A' on the screen, where there is a dark band which is fo 43. The equation of simple harmonic wave produced in the string under tension $$0.4 \mathrm{~N}$$ is given by $$\mathrm{y=4 44. A condenser of capacity '$$\mathrm{C}_1$$' is charged to potential '$$\mathrm{V}_1$$' and then disconnected. Uncharged c 45. In a step up transformer, which one of the following statements is correct? 46. Magnetic moment of revolving electron of charge (e) and mass (m) in terms of angular momentum (L) of electron is : 47. A particle is performing S.H.M. with maximum velocity '$$v$$'. If the amplitude is tripled and periodic time is doubled 48. A big water drop is divided into 8 equal droplets. $$\Delta \mathrm{P}_{\mathrm{s}}$$ and $$\Delta \mathrm{P}_{\mathrm{B 49. A hollow metal sphere has a radius 'r'. The potential difference between a point on its surface and at a point at a dist 50. The magnetic flux near the axis and inside the air core solenoid of length $$60 \mathrm{~cm}$$ carrying current '$$\math

MHT CET 2021 21th September Evening Shift

MCQ (Single Correct Answer)

-0

The co-ordinates of the point $$\mathrm{P} \equiv(1,2,3)$$ and $$\mathrm{O} \equiv(0,0,0)$$, then the direction cosines of $$\overline{\mathrm{OP}}$$ are

$$\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}$$

$$\frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}}$$

$$\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}$$

$$\frac{2}{\sqrt{29}}, \frac{3}{\sqrt{29}}, \frac{4}{\sqrt{29}}$$

MHT CET 2021 21th September Evening Shift

MCQ (Single Correct Answer)

-0

$$\int\limits_{{{ - \pi } \over 2}}^{{\pi \over 2}} {{{\cos x} \over {1 + {e^x}}}dx = } $$

$$-$$1

MHT CET 2021 21th September Evening Shift

MCQ (Single Correct Answer)

-0

The equation of the plane containing the line $$\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$$ and the point $$(0,7,-7)$$ is

$$2 x+y+z=0$$

$$x+y+z=0$$

$$x+2 y-3 z=35$$

$$x+3 y+z=14$$

MHT CET 2021 21th September Evening Shift

MCQ (Single Correct Answer)

-0

If the lines $$x^2-4xy+y^2=0$$ make angles $$\alpha$$ and $$\beta$$ with positive direction X-axis, then $$\cot^2\alpha+\cot^2\beta=$$

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