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

Chemistry

Mathematics

1. In a triangle $$A B C$$ with usual notations, if $$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$$, then area of tr 2. If $$\frac{x}{\sqrt{1+x}}+\frac{y}{\sqrt{1+y}}=0, x \neq y$$, then $$(1+x)^2 \frac{d y}{d x}=$$ 3. If $$\int \frac{\sin \theta}{\sin 3 \theta} d \theta=\frac{1}{2 k} \log \left|\frac{k+\tan \theta}{k-\tan \theta}\right| 4. The probability that bomb will miss the target is 0.2. Then, the probability that out of 10 bombs dropped exactly 2 will 5. The polar co-ordinates of the point whose cartesian co-ordinates are $$(-2,-2)$$, are given by 6. If $$\int \sqrt{x-\frac{1}{x}}\left(\frac{x^2+1}{x^2}\right) d x=\frac{2}{3}\left(x-\frac{1}{x}\right)^k+c$$, then value 7. $$\int_0^a \sqrt{\frac{x}{a-x}} d x=$$ 8. The minimum value of $$Z=5 x+8 y$$ subject to $$x+y \geq 5,0 \leq x \leq 4, y \geq 2, x \geq 0, y \geq 0$$ is 9. The sum of the cofactors of the elements of second row of the matrix $$\left[\begin{array}{rrr}1 & 3 & 2 \\ -2 & 0 & 1 \ 10. If the foot of perpendicular drawn from the origin to the plane is $$(3,2,1)$$, then the equation of plane is 11. If $$f(x)=\log (\sin x), x \in\left[\frac{\pi}{6}, \frac{5 \pi}{6}\right]$$, then value of '$$c$$' by applying LMVT is 12. The value of $$\sin ^{-1}\left(-\frac{1}{2}\right)+\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)$$ is 13. If $$p \rightarrow(\sim p \vee q)$$ is false, then the truth values of $$p$$ and $$q$$ are respectively 14. If the equation $$k x y+5 x+3 y+2=0$$ represents a pair of lines, then $$k=$$ 15. If $$(a,-2 a), a>0$$ is the mid-point of a line segment intercepted between the co-ordinate axes, then the equation of t 16. If the vectors $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$ 17. The letters of the word 'LOGARITHM' are arranged at random. The probability that arrangement starts with vowel and end w 18. If $$\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=4$$, then $$\frac{d y}{d x}=$$ 19. If $$x \cos \theta+y \sin \theta=5, x \sin \theta-y \cos \theta=3$$, then the value of $$x^2+y^2=$$ 20. The area of the region bounded by the curve $$y=4 x^3-6 x^2+4 x+1$$ and the lines $$x=1, x=5$$ and $$X$$-axis is 21. $$\int_\limits2^3 \frac{x}{x^2-1} d x=$$ 22. The angles between the lines $$\mathbf{r}=(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})+\lambda(\hat{\mathbf{ 23. The p.d.f of c.r.v $$X$$ is given by $$f(x)=\frac{x+2}{18}$$, if $$-2 24. The approximate value of the function $$f(x)=x^3-3 x+5$$ at $$x=1.99$$ is 25. If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second 26. If $$A=\left[\begin{array}{rrr}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array}\right]$$ and $$A^{-1}=\left[\begin{array} 27. The differential equation obtained from the function $$y=a(x-a)^2$$ is 28. In a quadrilateral $$ABCD, M$$ and $$N$$ are the mid-points of the sides $$A B$$ and $$C D$$ respectively. If $$\mathbf{ 29. If $$f(x)=\log (\sec x+\tan x)$$, then $$f^{\prime}\left(\frac{\pi}{4}\right)=$$ 30. If $$f(x)=\frac{2 x+3}{3 x-2}, x \neq \frac{2}{3}$$, then the function $$f$$ of is 31. $$\int \cot x \cdot \log [\log (\sin x)] d x=$$ 32. If $$\sin \theta=-\frac{12}{13}, \cos \phi=-\frac{4}{5}$$ and $$\theta, \phi$$ lie in the third quadrant, then $$\tan (\ 33. The symbolic form of the following circuit is (where $$p, q$$ represents switches $$S_1$$ and $$s_2$$ closed respectivel 34. The differential equation of all lines perpendicular to the line $$5 x+2 y+7=0$$ is 35. $$\int_\limits0^{\frac{\pi}{2}} \log \left[\sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}}\right] d x=$$ 36. If $$[\vec{a}\ \vec{b}\ \vec{c}\ ] \neq 0$$, then $$\frac{[\vec{a}\ +\vec{b}\ \vec{b}\ +\vec{c}\ \vec{c}\ +\vec{a}\ ] 37. The cartesian co-ordinates of the point on the parabola $$y^2=x$$ whose parameter is $$-\frac{4}{3}$$ are 38. The angle between the line $$r =(\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})+\lambda(3 \hat{\mathbf{i}}+\hat{\ma 39. The bacteria increases at the rate proportional to the number of bacteria present. If the original number '$$N$$' double 40. If $$A=\{x, y, z\}, B=\{1,2\}$$, then the total number of relations from set $$A$$ to set $$B$$ are : 41. The equation of tangent at $$P(-4,-4)$$ on the curve $$x^2=-4 y$$ is 42. The rate of decay of certain substance is directly proportional to the amount present at that instant. Initially, there 43. The direction cosines of a line which is perpendicular to lines whose direction ratios are $$3,-2,4$$ and $$1,3,-2$$ are 44. The points of discontinuity of the function $$\begin{aligned} f(x) & =\frac{1}{x-1}, \text { if } 0 \leq x \leq 2 \\ & = 45. If the angle between the lines given by the equation $$x^2-3 x y+\lambda y^2+3 x-5 y+2=0, \lambda \geq 0$$, is $$\tan ^{ 46. If the p.m.f of a. r.v. $$X$$ is given by $$P(X=x)=\frac{{ }^5 C_x}{2^5}$$ if $$x=0,1,2, \ldots \ldots . .5=0$$, 0 , oth 47. The radius of the circle passing through the points $$(5,7),(2,-2)$$ and $$(-2,0)$$ is 48. The integrating factor of the differential equation $$\left(1+x^2\right) d t=\left(\tan ^{-1} x-t\right) d x$$ is 49. In a triangle $$A B C$$, if $$\frac{\sin A-\sin C}{\cos C-\cos A}=\cot B$$, then $$A, B, C$$, are in 50. If the lines given by $$\frac{x-1}{2 \lambda}=\frac{y-1}{-5}=\frac{z-1}{2}$$ and $$\frac{x+2}{\lambda}=\frac{y+3}{\lambd

Physics

1. An ammeter of resistance $$20 \Omega$$ gives full scale deflection, when $$1 \mathrm{~mA}$$ current flows through it. Wh 2. An alternating emf of $$0.2 \mathrm{~V}$$ is applied across an L-C-R series circuit having $$R=4 \Omega, C=80 \mu \mathr 3. An electron $$(e)$$ is revolving in a circular orbit of radius $$r$$ in hydrogen atom. The angular momentum of the elect 4. In non-uniform circular motion, the ratio of tangential to radial acceleration is ($$r=$$ radius, $$\alpha=$$ angular ac 5. In common emitter amplifier, input resistance is $$1000 \Omega$$, peak value of input signal voltage is $$5 \mathrm{~mV} 6. A simple pendulum of length $$L$$ has mass $$m$$ and it oscillates freely with amplitude $$A$$. At extreme position, its 7. The extension in a wire obeying Hooke's law is $$x$$. The speed of sound in the stretched wire is $$v$$. If the extensio 8. Let force $$F=A \sin (C t)+B \cos (D x)$$, where $$x$$ and $$t$$ are displacement and time, respectively. The dimensions 9. Two vectors of same magnitude have a resultant equal to either of the two vectors. The angle between two vectors is 10. If there is a change of angular momentum from $$1 \mathrm{j}$$-$$\mathrm{s}$$ to $$4 \mathrm{j}$$-$$\mathrm{s}$$ in $$4 11. For a gas, $$\frac{R}{C_V}=0.4$$, where $$R$$ is universal gas constant and $$C_V$$ is the molar specific heat at consta 12. The maximum velocity of the photoelectron emitted by the metal surface is $$v$$. Charge and mass of the photoelectron is 13. Energy of the incident photon on the metal surface is $$3 W$$ and then $$5 W$$, where $$W$$ is the work function for tha 14. Water rises in a capillary tube of radius $$r$$ upto a height $$h$$. The mass of water in a capillary is $$m$$. The mass 15. Two waves $$Y_1=0.25 \sin 316 t$$ and $$Y_2=0.25 \sin 310 t$$ are propagating along the same direction. The number of be 16. A small metal sphere of mass $$M$$ and density $$d_1$$ when dropped in a jar filled with liquid moves with terminal velo 17. The capacitance of a parallel plate capacitor with air as medium is $$3 \mu \mathrm{F}$$. With the introduction of a die 18. The mass of earth is 81 times the mass of the moon and the distance between their centres is $$R$$. The distance from th 19. A coil of $$n$$ turns and resistance $$R \Omega$$ is connected in series with a resistance $$\frac{R}{2}$$. The combinat 20. Two identical bar magnets each of magnetic moment $$M$$, separated by some distance are kept perpendicular to each other 21. A bullet of mass $$m$$ moving with velocity $$v$$ is fired into a wooden block of mass $$M$$, If the bullet remains embe 22. In diffraction experiment, from a single slit, the angular width of the central maxima does not depend upon 23. A vehicle of mass $$m$$ is moving with momentum $$p$$ on a rough horizontal road. The coefficient of friction between th 24. In Young's double slit experiment green light is incident on the two slits. The interference pattern is observed on a sc 25. Two identical strings of length $$l$$ and $$2l$$ vibrate with fundamental frequencies $$\mathrm{N} \mathrm{~Hz}$$ and $$ 26. In amplitude modulation, 27. When a photon enters glass from air, which one of the following quantity does not change? 28. Two wires $$A$$ and $$B$$ of equal lengths are connected in left and right gap of a meter bridge, null point is obtained 29. When a small amount of impurity atoms are added to a semiconductor, then generally its resistivity 30. When open pipe is closed from one end third overtone of closed pipe is higher in frequency by $$150 \mathrm{~Hz}$$, then 31. A ray of light is incident at an angle $$i$$ on one face of prism of small angle $$A$$ and emerges normally from the oth 32. Two small drops of mercury each of radius $$r$$ coalesce to form a large single drop. The ratio of the total surface ene 33. A solid cylinder of radius $$r$$ and mass $$M$$ rolls down an inclined plane of height $$h$$. When it reaches the bottom 34. A potentiometer wire is $$4 \mathrm{~m}$$ long and potential difference of $$3 \mathrm{~V}$$ is maintained between the e 35. A charged particle is moving in a uniform magnetic field in a circular path of radius $$R$$. When the energy of the part 36. The density of a metal at normal pressure $$p$$ is $$\rho$$. When it is subjected to an excess pressure, the density bec 37. For a particle performing SHM when displacement is $$x$$, the potential energy and restoring force acting on it is denot 38. Surface density of charge on a charged conducting sphere of radius $$R$$ in terms of electric field intensity $$E$$ at a 39. A body is thrown from the surface of the earth velocity $$\mathrm{v} / \mathrm{s}$$. The maximum height above the earth' 40. Using Bohr's quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? ($$I=$$ 41. A monoatomic gas of pressure $$p$$ having volume $$V$$ expands isothermally to a volume $$2V$$ and then adiabatically to 42. A particle is moving in a radius $$R$$ with constant speed $$v$$. The magnitude of average acceleration after half revol 43. The magnifying power of a telescope is high, if its objective and eyepiece have respectively 44. The ratio of speed of an electron in the ground state in the Bohr's first orbit of hydrogen atom to velocity of light $$ 45. A charge $$q$$ moves with velocity $$v$$ through electric field $$\mathrm{E}$$ as well as magnetic field (B). Then, the 46. The force acting on the electrons in hydrogen atom (Bohr's theory) is related to the principle quantum number $$n$$ as 47. A body of mass $$2 \mathrm{~kg}$$ is acted upon by two forces each of magnitude $$1 \mathrm{~N}$$ and inclined at $$60^{ 48. Two rods of same material and volume having circular cross-section are subjected to tension $$T$$. Within the elastic li 49. An iron rod is placed parallel to magnetic field of intensity $$2000 \mathrm{~A} / \mathrm{m}$$. The magnetic flux throu 50. A moving body is covering distances which are proportional to square of the time. Then, the acceleration of the body is

MHT CET 2020 16th October Morning Shift

MCQ (Single Correct Answer)

-0

If the angle between the lines given by the equation $$x^2-3 x y+\lambda y^2+3 x-5 y+2=0, \lambda \geq 0$$, is $$\tan ^{-1}\left(\frac{1}{3}\right)$$, then $$\lambda=$$

$$1, \frac{2}{5}$$

$$\frac{2}{3}, 40$$

MHT CET 2020 16th October Morning Shift

MCQ (Single Correct Answer)

-0

If the p.m.f of a. r.v. $$X$$ is given by

$$P(X=x)=\frac{{ }^5 C_x}{2^5}$$

if $$x=0,1,2, \ldots \ldots . .5=0$$,

0 , otherwise,

then which of the following is not true?

$$P(X \leq 2)=P(X \geq 3)$$

$$P(X \leq 1)=P(X \geq 4)$$

$$P(X \leq 2) \geq P(X \geq 4)$$

$$P(X \leq 3) \leq P(X \geq 3)$$

MHT CET 2020 16th October Morning Shift

MCQ (Single Correct Answer)

-0

The radius of the circle passing through the points $$(5,7),(2,-2)$$ and $$(-2,0)$$ is

2 units

5 units

3 units

4 units

MHT CET 2020 16th October Morning Shift

MCQ (Single Correct Answer)

-0

The integrating factor of the differential equation $$\left(1+x^2\right) d t=\left(\tan ^{-1} x-t\right) d x$$ is

$$e^{\tan ^{-1} x}$$

$$-e^{\frac{\left(\tan ^{-1} x\right)^2}{2}}$$

$$-e^{\tan ^{-1} x}$$

$$e^{\frac{\left(\tan ^{-1} x\right)^2}{2}}$$

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