MHT CET 2020 16th October Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

Mathematics

1. If the equation $$a x^2+2 h x y+b y^2+2 g x+2 f y=0$$ has one line as the bisector of the angle between co-ordinate axes 2. $$\left[\sin \left(\tan ^{-1} \frac{3}{4}\right)\right]^2+\left[\sin \left(\tan ^{-1} \frac{4}{3}\right)\right]^2=$$ 3. If the plane $$2 x+3 y+5 z=1$$ intersects the co-ordinate axes at the points $$A, B, C$$, then the centroid of $$\triang 4. The eccentricity of the ellipse $$y^2+4 x^2-12 x+6 y+14=0$$ is 5. For $$f(x)=[x]$$, where $$[x]$$ is the greatest integer function, which of the following is true, for every $$x \in \mat 6. The value of $$\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+ 7. The integrating factor of the differential equation $$\sin y\left(\frac{d y}{d x}\right)=\cos y(1-x \cos y)$$ is 8. The direction co-sines of the line which bisects the angle between positive direction of $$Y$$ and $$Z$$ axes are 9. The equation of normal to the curve $$y=\sin \left(\frac{\pi x}{4}\right)$$ at the point $$(2,5)$$ is 10. The negation of the statement ' He is poor but happy' is 11. The matrix $$A=\left[\begin{array}{rrr}a & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2\end{array}\right]$$ is not invertible only 12. The maximum value of $$Z=3 x+5 y$$, subject to $$3 x+2 y \leq 18, x \leq 4, y \leq 6, x, y \geq 0$$ is 13. $$\int\left[-\frac{\log x-1}{1+(\log x)^2}\right]^2 d x=$$ 14. $$\int \frac{d x}{\cos 2 x-\cos ^2 x}=$$ 15. The area included between the parabolas $$y^2=5 x$$ and $$x^2=5 y$$ is 16. The straight lines represented by the equation $$9 x^2-12 x y+4 y^2=0$$ are 17. The odds in favour of drawing a king from a pack of 52 playing cards is 18. $$\int_{\frac{\pi}{5}}^{\frac{3 \pi}{10}}\left[\frac{\tan x}{\tan x+\cot x}\right] d x=$$ 19. The angle between the lines $$\frac{x-1}{4}=\frac{y-3}{1}=\frac{z}{8}$$ and $$\frac{x-2}{2}=\frac{y+1}{2}=\frac{z-4}{1}$ 20. In a $$\triangle A B C$$ if $$2 \cos C=\sin B \cdot \operatorname{cosec} A$$, then 21. The order and degree of the differential equation $$\left[1+\left[\frac{d y}{d x}\right]^3\right]^{\frac{7}{3}}=7 \frac{ 22. The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and 23. If $$A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right], \quad B=\left[\begin{array}{ll}1 & 0 \\ 3 & 1\end{array} 24. The domain of the function $$f(x)=\sqrt{x}$$ is 25. $$\text { If } \sin (x+y)+\cos (x+y)=\sin \left[\cos ^{-1}\left(\frac{1}{3}\right)\right] \text {, then } \frac{dy}{dx}= 26. The micro-organisms double themselves in 3 h. Assuming that the quantity increases at a rate proportional to it self, th 27. Out of 100 people selected at random, 10 have common cold. If five persons selected at random from the group, then the p 28. If the line $$r=(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})+\lambda(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \ 29. Let $$G$$ be the centroid of a $$\triangle A B C$$ and $$\mathrm{O}_{b_\theta}$$ other point in that plane, then $$\math 30. The points $$A(-a,-b), B(0,0), C(a, b)$$ and $$D\left(a^2, a b\right)$$ are 31. The particular solution of the differential equation $$y\left(\frac{d x}{d y}\right)=x \log x$$ at $$x=e$$ and $$y=1$$ i 32. $$\tan A+2 \tan 2 A+4 \tan 4 A+8 \cot 8 A=$$ 33. $$\begin{aligned} & \cos \left(36^{\circ}-A\right) \cos \left(36^{\circ}+A\right)+\cos \left(54^{\circ}+A\right) \cos \\ 34. The pdf of a continuous r.v. $$X$$ is given by $$f(x)=\frac{x}{8}, 0 35. If $$f(x)=\frac{|x|}{x}$$, for $$x \neq 0$$ $$=1$$, for $$x=0$$, then tre function is 36. If $$p, q$$ are true statement and $$r$$ is false statement, then which of the following statements is a true statement. 37. The cosine of the angle included between the lines $$\mathbf{r}=(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}) 38. $$\int \frac{1+2 e^{-x}}{1-2 e^{-x}} d x=$$ 39. If the volume of the parallelopiped whose conterminus edges are along the vectors $$\mathbf{a}, \mathbf{b}, \mathbf{c}$$ 40. The function $$f(x)=\frac{x+1}{9 x+x^3}$$ is 41. For any non-zero vectors $$\mathbf{a}$$ and $$\mathbf{b}$$, 42. If $$f(x)=\sin ^{-1}\left(\sqrt{\frac{1-x}{2}}\right)$$, then $$f^{\prime}(x)=$$ 43. The rational form of a number 1.41 is 44. The length of latus-rectum of the parabola $$x^2+2 y=8 x-7$$ is 45. If $$x+y=\frac{\pi}{2}$$, then the maximum value of $$\sin x \cdot \sin y$$ is 46. $$\int_\limits0^1\left(\frac{x^2-2}{x^2+1}\right) d x=$$ 47. If $$a=\sin 175^{\circ}+\cos 175^{\circ}$$, then 48. $$\int_\limits{-5}^5 \log \left(\frac{7-x}{7+x}\right) d x=$$ 49. For every value of $$x$$, the function $$f(x)=\frac{1}{a^x}, a>$$ 0 is, 50. If a die is thrown at random, then the expectation of the number on it is

Physics

1. A body slides down a smooth inclined plane having angle $$\theta$$ and reaches the bottom with velocity $$v$$. If a body 2. A light wave of wavelength $$\lambda$$ is incident on a slit of width $$d$$. The resulting diffraction pattern is observ 3. The damping force of an oscillator is directly proportional to the velocity. The unit of constant of proportionality is 4. The magnetic susceptibility of a paramagnetic material at $$-73^{\circ} \mathrm{C}$$ is 0.0075. Its value at $$-173^{\ci 5. A particle performs simple harmonic motion with period of 3 s . The time taken by it to cover a distance equal to half t 6. A sonometer wire under suitable tension having specific gravity $$\rho$$, vibrates with frequency $$n$$ in air. If the l 7. A radioactive nucleus emits $$4 \alpha$$-particles and $$7 \beta$$-particles in succession. The ratio of number of neutr 8. A thin uniform rod has mass $$M$$ and length $$L$$ The moment of inertia about an axis perpendicular to it and passing t 9. An obstacle is moving towards the source with velocity $$v$$. The sound is reflected from the obstacle. If $$c$$ is the 10. If the angle of dip at places $$A$$ and $$B$$ are $$30^{\circ}$$ and $$45^{\circ}$$ respectively, then the ratio of hori 11. The ratio of energy required to raise a satellite of mass $$m$$ to a height $$h$$ above the earth's surface of that requ 12. A circular coil of radius $$R$$ is carrying a current $$I_1$$ in anti-clockwise sense. A long straight wire is carrying 13. A circular coil of radius $$R$$ has a resistance of $$40 \Omega$$. Figure shows two points $$P$$ and $$Q$$ on the circum 14. An $$\alpha$$-particle of energy 10 eV is moving in a circular path in uniform magnetic field. The energy of proton movi 15. In communication system, a repeater is used to extend the range to transmission. It is the combination of 16. Two wires of different materials have same length $$L$$ and same diameter $$d$$. The second wire is connected at the end 17. When wavelength of light used in optical instruments A and B are 4500$$\mathop A\limits^o $$ and 6000$$\mathop A\limits^ 18. The light of wavelength $$\lambda$$ incident on the surface of metal having work function $$\phi$$ emits the electrons. 19. A thin light weight rod of diamagnetic substance such as silver is suspended in uniform external magnetic field. It will 20. A batsman hits a ball of mass 0.2 kg straight towards the bowler without changing its initial speed of $$6 \mathrm{~m} / 21. There are four convex lenses $$L_1, L_2, L_3$$ and $$L_4$$ of focal length $$2,4,6$$ and 8 cm, respectively. Two of thes 22. The ratio of radii of gyration of a ring to a disc (both circular) of same radii and mass, about a tangential axis perpe 23. An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of 24. A particle starting from rest moves along the circumference of a circle of radius $$r$$ with angular acceleration $$\alp 25. Two spherical black bodies of radius $$r_1$$ and $$r_2$$ with surface temperature $$T_1$$ and $$T_2$$ respectively, radi 26. Which of the following instruments is not a direct reading instrument? 27. A block of mass $$m$$ is moving on rough horizontal surface with momentum $$p$$. The coefficient of friction between the 28. A large open tank containing water has two holes to its wall. A square hole of side $a$ is made at a depth $$y$$ and a c 29. Refractive index of the medium is $$\mu$$ and wavelength is $$\lambda$$, then which of the following proportionality rel 30. $$A$$ transistor has a voltage gain $$A$$. If the amount $$\beta A$$ of its output is applied to the input of the transi 31. A spherical rubber balloon carries a charge, uniformly distributed over the surface. As the balloon is blown up and incr 32. A diatomic gas undergoes adiabatic change. Its pressure $$p$$ and temperature $$T$$ are related as $$p \propto T^x$$, wh 33. The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) second to first en 34. As we go from the equator of the earth to pole of the earth, the value of acceleration due to gravity 35. Two wires $$A$$ and $$B$$ are stretched by the same load. The radius of wire $$A$$ is double the radius of wire $$B$$. T 36. When tension $$T$$ is applied to a sonometer wire of length $$I$$, it vibrates with the fundamental frequency $$n$$. Kee 37. At absolute zero temperature, pure silicon behaves as 38. Five capacitors each of capacity $$C$$ are connected as shown in figure. If their resultant capacity is $$2 \mu \mathrm{ 39. The work done in blowing a soap bubble of radius $$R$$ is $$W$$. The work done in blowing a bubble of radius $$2 R$$ of 40. The $$x, y$$ components of vector $$\mathbf{P}$$ have magnitudes 1 and 3 and $$x, y$$ components of resultant of $$\math 41. The graph of kinetic energy against the frequency $$v$$ of incident light is as shown in the figure. The slope of the gr 42. The length of solenoid is $$I$$ whose windings are made of material of density $$D$$ and resistivity $$\rho$$. The windi 43. A step-up transformer has 300 turns of primary winding and 450 turns of secondary winding. A primary is connected to 150 44. A simple pendulum of length $$I$$ has a bob of mass $$m$$. It executes SHM of small amplitude A. The maximum tension in 45. A block of mass $$m$$ attached to one end of the vertical spring produces extension $$x$$. If the block is pulled and re 46. The resultant of two vector $$\mathbf{A}$$ and $$\mathbf{B}$$ is $$\mathbf{C}$$. If the magnitude of $$\mathbf{B}$$ is d 47. A ray of light travelling through glass of refractive index $$\sqrt{2}$$ is incident on glass-air boundary at an angle o 48. A particle of mass $$m$$ is performing UCM along a circle of radius $$r$$. The relation between centripetal acceleration 49. In conversion of moving coil galvanometer into an ammeter of required range, the resistance of ammeter, so formed is [$$ 50. A square frame of each side $$L$$ is dipped in a soap solution and taken out. The force acting on the film formed is ($$

MHT CET 2020 16th October Evening Shift

MCQ (Single Correct Answer)

-0

The eccentricity of the ellipse $$y^2+4 x^2-12 x+6 y+14=0$$ is

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

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

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

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

MHT CET 2020 16th October Evening Shift

MCQ (Single Correct Answer)

-0

For $$f(x)=[x]$$, where $$[x]$$ is the greatest integer function, which of the following is true, for every $$x \in \mathbf{R}$$

$$[x]+1=x$$

$$[x]+1 < x$$

$$[x]+1 \leq x$$

$$[x]+1>x$$

MHT CET 2020 16th October Evening Shift

MCQ (Single Correct Answer)

-0

The value of $$\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{8}\right)$$ is

$$\frac{\pi}{6}$$

$$\frac{\pi}{3}$$

$$\frac{\pi}{4}$$

$$\frac{\pi}{12}$$

MHT CET 2020 16th October Evening Shift

MCQ (Single Correct Answer)

-0

The integrating factor of the differential equation $$\sin y\left(\frac{d y}{d x}\right)=\cos y(1-x \cos y)$$ is

$$e^{\sin y}$$

$$e^{-x}$$

$$e^{-\cos y}$$

$$e^{-y}$$

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