MHT CET 2019 2nd May Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

Mathematics

1. If $P\left(x_1, y_1\right)$ is a point on the hyperbola $x^2-y^2=a^2$, then $S P$. S'P $=$ ............. 2. If $f(x)=\cos ^{-1}\left[\frac{1-(\log x)^2}{1+(\log x)^2}\right]$, then $f^{\prime}(e)=\ldots$ 3. The order of the differential equation of all circles whose radius is 4 , is ........... 4. If $A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right]$ and $A=A^{-1}$, then $x=\ldots \ldots$ 5. Which of the following function is not continuous at $x=0$ ? 6. It is observed that $25 \%$ of the cases related to child labour reported to the police station are solved. If 6 new cas 7. For a GP, if $S_n=\frac{4^n-3^n}{3^n}$, then $t_2=$ ........... 8. The area of the region bounded by the curve $y=2 x-x^2$ and the line $y=x$ is ........... units. square 9. The general solution of $x \frac{d y}{d x}=y-x \tan \left(\frac{y}{x}\right)$ is ............. 10. The statement pattern $(p \wedge q) \wedge[\sim r \vee(p \wedge q)] \vee(\sim p \wedge q)$ is equivalent to ........... 11. A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colou 12. $$\int \frac{\cos x+x \sin x}{x^2+x \cos x} d x=$$ ........... 13. A stone is dropped into a pond. Waves in the form of circles are generated and radius of outermost ripple increases at t 14. If $f(x)=3 x-2$ and $g(x)=x^2$, then $(f \circ g)(x)=$ 15. Which of the following is not equivalent to $p \rightarrow q$. 16. The value of $\int_{-3}^3\left(a x^5+b x^3+c x+k\right) d x$, where $a, b, c, k$ are constants, depends only on 17. The general solution of the differential equation of all circles having centre at $A(-1,2)$ is ........ 18. If $A$ is non-singular matrix such that $(A-2 l)(A-4 I)=0$ then $A+8 A^{-1}=$ .......... 19. If $G(3,-5, r)$ is centroid of triangle $A B C$ where $A(7,-8,1), B(p, q, 5)$ and $C(q+1,5 p, 0)$ are vertices of a tria 20. $$\int \frac{1}{\left(x^2+1\right)^2} d x=\ldots$$ 21. If $\theta=\frac{17 \pi}{3}$ then, $\tan \theta-\cot \theta=\ldots$ 22. Derivative of $\log _{e^2}(\log x)$ with respect to $x$ is 23. In $\triangle A B C$; with usual notations, if $\cos A=\frac{\sin B}{\sin C}$ then the triangle is ............ 24. For a GP, if $(m+n)^{\text {th }}$ term is $p$ and $(m-n)^{\mathrm{th}}$ term is $q$, then $m^{\text {th }}$ term is ... 25. A random variable X has following probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{bor 26. The equation of normal to the curve $y=\log _\theta x$ at the point $P(1,0)$ is ............ 27. The values of $x$ in $\left(0, \frac{\pi}{2}\right)$ satisfying the equation $\sin x \cos x=\frac{1}{4}$ are .......... 28. If $\mathbf{a}+\mathbf{b}, \mathbf{b}+\mathbf{c}$ anc $\mathbf{c}+\mathbf{a}$ are coterminous edges of a parallel opiped 29. If the c.d.f (cumulative distribution function) is given by $F(x)=\frac{x-25}{10}$, then $P(27 \leq x \leq 33)=\ldots \l 30. The joint equation of pair of straight lines passing through origin and having slopes $(1+\sqrt{2})$ and $\left(\frac{1 31. The angle between lines $\frac{x-2}{2}=\frac{y-3}{-2}=\frac{z-5}{1}$ and $\frac{x-2}{1}=\frac{y-3}{2}=\frac{z-5}{2}$ is 32. If the line passes through the points $P(6,-1,2), Q(8,-7,2 \lambda)$ and $R(5,2,4)$ then value of $\lambda$ is ......... 33. The equivalent form of the statement $\sim(p \rightarrow \sim q)$ is $\ldots$ 34. If $A=\left(x \in R: x^2-5|x|+6=0\right\}$, then $n(A)=\ldots \ldots$ 35. If the function $f(x)=\frac{\log (1+a x)-\log (1-b x)}{x}$ $x \neq 0$ is continuous at $x=0$ then, $f(0)=\ldots \ldots$ 36. The co-ordinates of the foot of perpendicular drawn from origin to the plane $2 x-y+5 z-3=0$ are $\ldots \ldots$ 37. $$\int \frac{\sqrt{x^2-a^2}}{x} d x=\ldots \ldots$$ 38. The maximum value of $z=9 x+11 y$ subject to $3 x+2 y \leq 12,2 x+3 y \leq 12, x \geq 0, y \geq 0$ is $\ldots \ldots$. 39. $$\int_0^4 \frac{1}{1+\sqrt{x}} d x=\ldots \ldots$$ 40. The number of solutions of $\sin ^2 \theta=\frac{1}{2}$ in $[0, \pi]$ is .......... 41. If $\mathbf{p}, \mathbf{q}$ and $\mathbf{r}$ are non-zero, non-coplanar vectors 42. Which of the following equations has no solution? 43. The minimum value of $z=10 x+25 y$ subject to $0 \leq x \leq 3,0 \leq y \leq 3, x+y \geq 5$ is $\ldots$ 44. If $f(x)=3 x^3-9 x^2-27 x+15$, then the maximum value of $f(x)$ is ........... 45. The equation of the plane passing through the point $(-1,2,1)$ and perpendicular to the line joining the points $(-3,1,2 46. If the lengths of the transverse axis and the latusrectum of a hyperbola are 6 and $\frac{8}{3}$ respectively, then the 47. The value of $\tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{7}+\tan ^{-1} \frac{1}{8}$ is .......... 48. The joint equation of the lines passing through the origin and trisecting the first quadrant is 49. If $P(2,2), Q(-2,4)$ and $R(3,4)$ are the vertices of $\triangle P Q R$ then the equation of the median through vertex $ 50. If $x=\sqrt{a^{\sin ^{-1} t}}, y=\sqrt{a^{\cos ^{-1} t}}$, then $\frac{d y}{d x}=\ldots .$.

Physics

1. A stone of mass 1 kg is tied to a string 2 m long and it's rotated at constant speed of $40 \mathrm{~ms}^{-1}$ in a vert 2. 2. Two coils have a mutual inductance of 0.01 H . The current in the first coil changes according to equation, $I=5 \sin 3. The radius of the earth and the radius of orbit around the sun are 6371 km and $149 \times 10^6 \mathrm{~km}$ respective 4. Two open pipes of different lengths and same diameter in which the air column vibrates with fundamental frequencies ' $n 5. If ' $C_P$ ' and ' $C_V$ ' are molar specific heats of an ideal gas at constant pressure and volume respectively. If ' $ 6. In a series $L C R$ circuit $R=300 \Omega, L=0.9 \mathrm{H}$, $C=2 \mu \mathrm{~F}, \omega=1000 \mathrm{rad} / \mathrm{s 7. The quantity which does not vary periodically for a particle performing SHM is 8. Which of the following combinations of 7 identical capacitors each of $2 \mu \mathrm{~F}$ gives a resultant capacitance 9. Bohr model is applied to a particle of mass ' $m$ ' and charge ' $q$ ' is moving in a plane under the influence of a tra 10. In moving coil galvanometer, strong horse shoe magnet of concave shaped pole pieces is used to 11. 1. Two identical wires of substances ' $P$ ' and ' $Q$ ' are subjected to equal stretching force along the length. If th 12.  If $W_1, W_2$ and $W_3$ represent the work done in moving a particle from $A$ to $B$ along three different paths 1 13. Assuming that the junction diode is ideal, the current in the arrangement shown in figure is 14. The equation of simple harmonic progressive wave is given by $Y=a \sin 2 \pi(b t-c x)$. The maximum particle velocity wi 15. In a fundamental mode,the time required for the sound wave to reach upto the closed end of a pipe filled with air is ' $ 16. Two small drops of mercury each of radius ' $R$ ' coalesce to form a large single drop. The ratio of the total surface e 17. If radius of the solid sphere is doubled by keeping its mass constant, the ratio of their moment of inertia about any of 18. For a metallic wire, the ratio of voltage to corresponding current is 19. In air, a charged soap bubble of radius ' $R$ ' breaks into 27 small soap bubbles of equal radius ' $r$ '. Then the rati 20. Two parallel conductors carrying unequal currents in the same direction ............ 21. A layer of atmosphere that reflects medium frequency radio waves which is ineffective during night, is 22. A transverse wave is propagating on the string. The linear density of a vibrating string is $10^{-3} \mathrm{~kg} / \mat 23. The kinetic energy of a revolving satellite (mass $m$ ) at a height equal to thrice the radius of the earth $(R)$ is 24. A particle executes the simple harmonic motion with an amplitude ' $A$ '. The distance travelled by it in one periodic t 25. A galvanometer has resistance of $100 \Omega$ and a current of 10 mA produces full scale deflection in it. The resistanc 26. The angle made by orbital angular momentum of electron with the direction of the orbital magnetic moment is 27. The circuit in 1$$\Omega$$ resistor in the following circuit is 28. The wavelength of the first line in Balmer series in the hydrogen spectrum is ' $\lambda$ '. What is the wavelength of t 29. Work done in stretching a wire through 1 mm is 2 J . What amount of work will be done for elongating another wire of sam 30. The resultant $\mathbf{R}$ of $\mathbf{P}$ and $\mathbf{Q}$ is perpendicular to $\mathbf{P}$. Also $|\mathbf{P}|=|\mathb 31. A telescope has large diameter of the objective. Then its resolving power is 32. A uniform rod of length ' 6 L ' and mass ' 8 m ' is pivoted at its centre ' $C$ '. Two masses ' $m$ ' and ' $2 m^{\prime 33. If $\sqrt{A^2+B^2}$ represents the magnitude of resultant of two vectors $(\mathbf{A}+\mathbf{B})$ and $(\mathbf{A}-\mat 34. A thin metal wire of length 'L' and uniform linear mass density '$\rho$' is bent into a circular coil with 'O' as centre 35. The dimensions of torque are same as that of 36. . For a transistor, the current ratio ' $\beta_{d c}$ ' is defined as the ratio of 37. A clock pendulum having coefficient of linear expansion. $\alpha=9 \times 10^{-7} /{ }^{\circ} \mathrm{C}^{-1}$ has a pe 38. Two capillary tubes of different diameters are dipped in water. The rise of water is 39. A thin hollow prism of refracting angle $3^{\circ}$, filled with water gives a deviation of $1^{\circ}$. The refractive 40. A body is projected vertically from the surface of the earth of radius ' $R$ ' with velocity equal to half of the escape 41. In biprism experiment, the distance between source and eyepiece is 1.2 m, the distance between two virtual sources is 0. 42. When photons of energy $h v$ fall on a metal plate of work function ' $W_0$ ', photoelectrons of maximum kinetic energy 43. If a star emitting yellow light is accelerated towards earth, then to an observer on earth it will appear 44. The magnitude of the magnetic induction at a point on the axis at a large distance ( $r$ ) from the centre of a circular 45. A metal sphere of radius ' $R$ ' and density ' $\rho_1$ ' is dropped in a liquid of density ' $\sigma$ ' moves with term 46. If $\alpha$ is the coefficient of performance of a refrigerator and ' $Q$ ' is heat released to the hot reservoir, then 47. The real force ' $F$ ' acting on a particle of mass $m$ ' performing circular motion acts along the radius of circle ' $ 48. Dimensions of Gyromagnetic ratio are 49. The maximum velocity of the photoelectron emitted by the metal surface is ' $v$ '. Charge and mass of the photoelectron 50. The equi-convex lens has a focal length ' $f$ '. If the lens is cut along the line perpendicular to the principal axis a

MHT CET 2019 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

If $A=\left(x \in R: x^2-5|x|+6=0\right\}$, then $n(A)=\ldots \ldots$

MHT CET 2019 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

If the function $f(x)=\frac{\log (1+a x)-\log (1-b x)}{x}$ $x \neq 0$ is continuous at $x=0$ then, $f(0)=\ldots \ldots$

$\log a-\log b$

$a+b$

$\log a+\log b$

$a-b$

MHT CET 2019 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

The co-ordinates of the foot of perpendicular drawn from origin to the plane $2 x-y+5 z-3=0$ are $\ldots \ldots$

$\left(\frac{2}{\sqrt{30}}, \frac{-1}{\sqrt{30}}, \frac{5}{\sqrt{30}}\right)$

$(2,-1,5)$

$\left(\frac{2}{3}, \frac{-1}{3}, \frac{5}{3}\right)$

$\left(\frac{1}{5}, \frac{-1}{10}, \frac{1}{2}\right)$

MHT CET 2019 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{\sqrt{x^2-a^2}}{x} d x=\ldots \ldots$$

$\sqrt{x^2-a^2}-a \cos ^{-1}\left(\frac{a}{x}\right)+c$

$x \sqrt{x^2-a^2}-\frac{1}{a} \tan ^{-1}\left(\frac{x}{a}\right)+c$

$\sqrt{x^2-a^2}+a \sec ^{-1}\left(\frac{x}{a}\right)+c$

$\sqrt{x^2-a^2}+\frac{1}{x} \sec ^{-1}(x)+c$

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