MHT CET 2020 19th October Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

Mathematics

1. With usual notations, if the angles $A, B, C$ of a $\triangle A B C$ are in $A P$ and $b: c=\sqrt{3}: \sqrt{2}$ 2. $$\int \sin ^{-1} x d x=$$ 3. The integrating factor of the differential equation $x \frac{d y}{d x}+y \log x=x^2$ is 4. If $\mathbf{a}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+7 \h 5. The maximum volume of a right circular cylinder if the sum of its radius and height is 6 m is 6. If the slopes of the lines given by the equation $a x^2+2 h x y+b y^2=0$ are in the ratio $5: 3$, then the ratio $h^2: a 7. The equation of a line passing through the point $(7,-4)$ and perpendicular to the line passing through the points $(2,3 8. $\int_\limits0^1 \tan ^{-1}\left(\frac{2 x-1}{1+x-x^2}\right) d x=$ 9. If $f(x)=\frac{1-\sin x+\cos x}{1+\sin x+\cos x}$, for $x \neq \pi$ is continuous at $x=\pi$, then $f(\pi)=$ 10. $\mathbf{a}$ and $\mathbf{b}$ are non-collinear vectors. If $p=(2 x+1) a-b$ and $q=(x-2) a+b$ are collinear vectors, the 11. If $A=\left[\begin{array}{ll}4 & 5 \\ 2 & 1\end{array}\right]$ and $A^2-5 A-6 I=0$, then $A^{-1}=$ 12. The quadratic equation whose roots are the numbers having arithmetic mean 34 and geometric mean 16 is 13. If $x=a \sin t-b \cos t, y=a \cos t+b \sin t$, then $y^3 \frac{d^2 y}{d x^2}+x^2+y^2=$ 14. The area of the triangle formed by the lines joining vertex of the parabola $x^2=12 y$ to the extremities of its latus r 15. If the sum of the mean and the variance of a binomial distribution for 5 trials is 1.8 , then $p=$ 16. The odds in favour of getting sum multiple of 3 , when pair of dice are thrown is 17. The rate of disintegration of a radio active element at time $t$ is proportional to its mass, at the time. Then the time 18. If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are non-coplanar vectors and $p=\frac{\mathbf{b} \times \mathbf{c}}{[a b c]}, q= 19. The negation of the statement pattern $\sim p \vee(q \rightarrow \sim r)$ is 20. The point $P$ lies on the line $A, B$ where $A=(2,4,5)$ and $B \equiv(1,2,3)$. If $z$ co-ordinate of point $P$ is 3 , th 21. If $R=\{(a, b) / b=a-1, a \in Z, 5 22. $$\int \log x \cdot(\log x+2) d x=$$ 23. The c.d.f, $F(x)$ associated with p.d.f. $f(x)=3\left(1-2 x^2\right)$. If $0 24. The range of the function $f(x)=\frac{x-3}{5-x}, x \neq 5$ is 25. If $y=\sin ^{-1}\left[\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right]$, then $\frac{d y}{d x}=$ 26. The area of the $\triangle A B C$ is $10 \sqrt{3} \mathrm{~cm}^2$, angle $B$ is $60^{\circ}$ and its perimeter is 20 cm 27. The equation of the normal to the curve $2 x^2+y^2=12$ at the point $(2,2)$ is 28. $$\frac{1-\sin \theta+\cos \theta}{1-\sin \theta-\cos \theta}=$$ 29. If $A$ and $B$ are supplementary angles, then $\sin ^2 \frac{A}{2}+\sin ^2 \frac{B}{2}=$ 30. If the equation $3 x^2+10 x y+3 y^2+16 y+k=0$ represents a pair of lines, then the value of kis 31. If $2 \cos ^2 \theta+3 \cos \theta=2$, then permissible value of $\cos \theta$ is 32. A line makes angles $\alpha, \beta, \gamma$ with the co-ordinate axes and $\alpha+\beta=90^{\circ}$, then $\gamma=$ 33. The equations of planes parallel to the plane $x+2 y+2 z+8=0$, which are at a distance of 2 units from the point $(1,1,2 34. If $X$ is a.r.v. with c.d.f $F(x)$ and its probability distribution is given by .tg {border-collapse:collapse;border-s 35. $$\int \frac{d x}{x^2+4 x+13}=$$ 36. If $x^2 y^2=\sin ^{-1} \sqrt{x^2+y^2}+\cos ^{-1} \sqrt{x^2+y^2}$ then $\frac{d y}{d x}=$ 37. $$\int_\limits0^{\frac{\pi}{2}} \frac{\sqrt[7]{\sin x}}{\sqrt[7]{\sin x}+\sqrt[7]{\cos x}} d x=$$ 38. $\int_\limits0^1\left(1-\frac{x}{1!}+\frac{x^2}{2!}-\frac{x^3}{3!}+\ldots\right.$ upto $\left.\infty\right) e^{2 x} d x= 39. The principal solutions of $\cot x=\sqrt{3}$ are 40. The statement pattern $p \wedge(q \vee \sim p)$ is equivalent to 41. The LPP to maximize $Z=x+y$, subject to $x+y \leq 1,2 x+2 y \geq 6, x \geq 0, y \geq 0$ has 42. The area of the region bounded by the curve $y=\sin x$ between $x=-\pi$ and $x=\frac{3 \pi}{2}$ is 43. The equation of a plane containing the point $(1,-1,2)$ and perpendicular to the planes $2 x+3 y-2 z=5$ and $x+2 y-3 z=8 44. The general solution of the differential equation $\left(1+y^2\right)+\left(x-e^{\tan ^{-1} y}\right) \frac{d y}{d x}=0$ 45. The equation of the line passing through $(1,2,3)$ and perpendicular to the lines $x-1=\frac{y+2}{2}=\frac{z+4}{4}$ and 46. The cofactors of the elements of the first column of the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 47. The equation of the directrix of the parabola $3 x^2=16 y$ is 48. The order and degree of the differential equation $\left[1+\frac{1}{\left(\frac{d y}{d x}\right)^2}\right]^{\frac{5}{3}} 49. If the population grows at the rate of $8 \%$ per year, then the time taken for the population to be doubled, is (Given 50. The area of the square increases at the rate of $0.5 \mathrm{~cm}^2 / \mathrm{sec}$. The rate at which its perimeter is

Physics

1. A tuning fork $A$ produces 5 beats per second with a tuning fork of frequency 480 Hz . When a little wax is stuck to a p 2. Two spherical rain drops reach the surface of the earth with terminal velocities having ratio $16: 9$. The ratio of thei 3. In system of two particles of masses $m_1$ and $m_2$, the first particle is moved by a distance $d$ towards the centre o 4. A graph is plotted between the fringe-width Z and the distance D between the slit and eye-piece, keeping other adjustmen 5. The graph of stopping potential $V_s$ against frequency $v$ of incident radiation is plotted for two different metals $P 6. An electron moves in a circular orbit with uniform speed $v$. It produces a magnetic field $B$ at the centre of the circ 7. If the maximum kinetic energy of emitted electrons in photoelectric effect is $3.2 \times 10^{-19} \mathrm{~J}$ and the 8. The root mean square velocity of molecules of a gas is $200 \mathrm{~m} / \mathrm{s}$. What will be the root mean square 9. Earth has mass $M_1$ and radius $R_1$. Moon has mass $M_2$ and radius $R_2$. Distance between their centre is $r$. A bod 10. Water rises upto a height $h$ in a capillary tube on the surface of the earth. The value of $h$ will increase, if the ex 11. Van de Graaff generator produces 12. A carrier wave of peak voltage 16 V is used to transmit a signal. If the modulation index is $75 \%$, the peak voltage o 13. The energy levels with transitions for the atom are shown. The transitions corresponding to emission of radiation of max 14. A milliammeter of resistance $40 \Omega$ has a range $0-30 \mathrm{~mA}$. What will be the resistance used in series to 15. A child starts running from rest along a circular track of radius $r$ with constant tangential acceleration a. After tim 16. A metal rod has length, cross-sectional area and Young's modulus as $L, A$ and $Y$, respectively. If the elongation in t 17. Two cells having unknown emfs $E_1$ and $E_2$ $\left(E_1>E_2\right)$ are connected in potentiometer circuit, so as to as 18. Three points masses, each of mass $m$ are placed at the corners of an equilateral triangle of side $\ell$. The moment of 19. Using Bohr's model, the orbital period of electron in hydrogen atom in $n$th orbit is ( $\varepsilon_0=$ permittivity of 20. Let $\sigma$ and $b$ be Stefan's constant and Wien's constant respectively, then dimensions of $\sigma b$ are 21. At the poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting 22. A steel wire of length / has a magnetic moment $M$. It is then bent into a semicircular arc. The new magnetic moment is 23. The angle subtended by the vector $A=4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+12 \hat{\mathbf{k}}$ with the $X$-axis is 24. $N$ number of balls of mass $m \mathrm{~kg}$ moving along positive direction of $X$ - axis, strike a wall per second and 25. Metal rings $P$ and $Q$ are lying in the same plane, where current I is increasing steadily. The induced current in meta 26. A 10 m long wire of resistance $20 \Omega$ is connected in series with a battery of emf 3 V and a resistance of $10 \Ome 27. A domain in a ferromagnetic substance is in the form of a cube of side $1 \mu \mathrm{~m}$. If it contains $8 \times 10^ 28. If the surface tension of a soap solution is $3 \times 10^{-2} \mathrm{~N} / \mathrm{m}$ then the work done in forming a 29. The compressibility of water is $5 \times 10^{-10} \mathrm{~m}^2 / \mathrm{N}$. Pressure of $15 \times 10^6 \mathrm{~Pa} 30. Two bodies $A$ and $B$ of equal mass are suspended from two separate massles springs of force constant $k_1$ and $k_2$, 31. Two capacitors of capacities $2 \mu \mathrm{~F}$ and $4 \mu \mathrm{~F}$ are connected in parallel. A third capacitor of 32. The escape velocity of a body from any planet, whose mass is six times the mass of earth and radius is twice the radius 33. A ray of light is incident at an angle $i$ on one face of a thin angled prism. The ray emerges normally from the other f 34. What is the angle between resultant of $A+B$ and $\mathbf{A} \times \mathbf{B}$. 35. A rope is wound around a solid cylinder of mass 1 kg and radius 0.4 m . What is the angular acceleration of cylinder, if 36. A transistor having $\alpha=0.8$ is connected in common emitter configuration. When the base current changes by 6 mA , t 37. A uniform metal wire has length $L$, mass $M$ and density $\rho$. It is under tension $T$ and $v$ is the speed of transv 38. An object is clearly seen through an astronomical telescope of length 50 cm . The focal lengths of its objective and eye 39. A bob of a simple pendulum has mass $m$ and is oscillating with an amplitude $a$. If the length of the pendulum is $L$, 40. The Brewster's angle for the glass-air interface is $(54.74)^{\circ}$. If a ray of light passing from air to glass stric 41. For a paramagnetic substance, the magnetic susceptibility is 42. Let $x=\pi R\left(\frac{P^2-Q^2}{2}\right)$, where $P, Q$ and $R$ are lengths. The physical quantity $x$ is 43. The fundamental frequency of a closed pipe is 400 Hz . If $\frac{1}{3}$ rd pipe is filled with water, then the frequency 44. An AC circuit contains resistance of $12 \Omega$ and inductive reactance $5 \Omega$. The phase angle between current and 45. In an intrinsic semiconductor, at an ordinary temperature, the correct relation between the number of electrons per unit 46. By increasing the aperture of the objective lens, wavelength of light, focal length of the objective lens and the resolv 47. Two galvanometers $A$ and $B$ require currents of 4 mA and 7 mA , respectively to produce the same deflection of 20 divi 48. Two circular loop $A$ and $B$ of radii $R$ and $N R$ respectively are made from a uniform wire. Moment of inertia of $B$ 49. A body is moving along a circular track of radius 100 m with velocity $20 \mathrm{~m} / \mathrm{s}$. Its tangential acce 50. A body of mass 64 g is made to oscillate turn by turn on two different springs $A$ and $B$. Spring $A$ and $B$ has force

MHT CET 2020 19th October Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \log x \cdot(\log x+2) d x=$$

$x(\log x)^2+c$

$x \log x+c$

$e^x(\log x)^2+c$

$(\log x)^2+c$

MHT CET 2020 19th October Evening Shift

MCQ (Single Correct Answer)

-0

The c.d.f, $F(x)$ associated with p.d.f. $f(x)=3\left(1-2 x^2\right)$. If $0< x<1$ is $k\left(x-\frac{2 x^3}{k}\right)$, then value of $k$ is

$\frac{1}{3}$

$\frac{1}{6}$

MHT CET 2020 19th October Evening Shift

MCQ (Single Correct Answer)

-0

The range of the function $f(x)=\frac{x-3}{5-x}, x \neq 5$ is

$R-\{-5\}$

$R-\{-1\}$

$R-\{1\}$

$R-\{5\}$

MHT CET 2020 19th October Evening Shift

MCQ (Single Correct Answer)

-0

If $y=\sin ^{-1}\left[\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right]$, then $\frac{d y}{d x}=$

$\left(\frac{1}{4}\right) \frac{1}{\sqrt{x^2-1}}$

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

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

$\left(\frac{1}{4}\right) \frac{1}{\sqrt{1-x^2}}$

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