MHT CET 2024 2nd May Evening Shift | MHT CET Year Wise Previous Years Questions

Mathematics

1. Two tangents drawn from $\mathrm{P}(1,7)$ to the circle $x^2+y^2=25$, touch the circle at Q and R respectively. The area 2. Let $X=\left[\begin{array}{l}\mathrm{a} \\ \mathrm{b} \\ \mathrm{c}\end{array}\right], \mathrm{A}=\left[\begin{array}{cc 3. Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 4. The unit vector which is orthogonal to the vector $5 \hat{i}+2 \hat{j}+6 \hat{k}$ and is coplanar with the vectors $2 \h 5. The probability distribution of a random variable X is given by .tg {border-collapse:collapse;border-spacing:0;} .tg t 6. If $\int \frac{x+1}{\sqrt{2 x-1}} \mathrm{~d} x=\mathrm{f}(x) \sqrt{2 x-1}+\mathrm{c}$, (where c is a constant of integr 7. If $\alpha+\beta+\gamma=\pi$, then the expression $\sin ^2 \alpha+\sin ^2 \beta-\sin ^2 \gamma$ has the value 8. Let $\overline{\mathrm{A}}=2 \hat{\mathrm{i}}+\hat{\mathrm{k}}, \overline{\mathrm{B}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+ 9. Distance between the parallel lines $\frac{x}{3}=\frac{y-1}{-2}=\frac{z}{1}$ and $\frac{x+4}{3}=\frac{y-3}{-2}=\frac{z+2 10. If $\mathrm{f}(x)=\log _{x^2}\left(\log _{\mathrm{e}} x\right)$, then $\mathrm{f}^{\prime}(x)$ at $x=\mathrm{e}$ is 11. A body cools according to Newton's law of cooling from $100^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ in 15 minutes 12. The value of k , for which the function $$\mathrm{f}(x)= \begin{cases}\left(\frac{4}{5}\right)^{\frac{\ln 4 x}{\tan 5 x} 13. The co-ordinates of a point on the curve $y=x \log x$ at which the normal is parallel to the line $2 x-2 y=3$ are 14. The value of $\mathrm{I}=\int_\limits{\sqrt{\log _{\mathrm{e}}}}^{\sqrt{\log _{\mathrm{e}} 3}} \frac{x \sin x^2}{\sin x^ 15. The value of $\mathrm{I}=\int \frac{\mathrm{d} x}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$ is 16. Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consult 17. The value of C for which Mean value Theorem holds for the function $\mathrm{f}(x)=\log _e x$ on the interval $[1,3]$ is 18. The shaded region in the following figure is the solution set of the inequations 19. The diagonals of a parallelogram $A B C D$ are along the lines $x+3 y=4$ and $6 x-2 y=7$. Then ABCD must be a 20. If $x=\sec \theta-\cos \theta, y=\sec ^{10} \theta-\cos ^{10} \theta$ and $\left(x^2+4\right)\left(\frac{d y}{d x}\right 21. If $y=y(x)$ is the solution of the differential equation $\left(\frac{5+\mathrm{e}^x}{2+y}\right) \frac{\mathrm{d} y}{\m 22. The equation of the plane, passing through the mid point of the line segment of join of the points $\mathrm{P}(1,2,5)$ a 23. If C is a given non-zero scalar and $\overline{\mathrm{A}}$ and $\overline{\mathrm{B}}$ are given non-zero vectors such 24. If the equation $7 x^2-14 x y+p y^2-12 x+q y-4=0$ represents a pair of parallel lines then the value of $\sqrt{p^2+q^2-p 25. If $\mathrm{P}(x, y)$ denotes $\mathrm{z}=x+\mathrm{i} y x, y \in \mathbb{R}$ and $\mathrm{i}=\sqrt{-1}$ in Argand's pla 26. The general solution of $2 \sqrt{3} \cos ^2 \theta=\sin \theta$ is 27. If $(2+\sin x) \frac{\mathrm{d} y}{\mathrm{~d} x}+(y+1) \cos x=0$ and $y(0)=1$ then $y\left(\frac{\pi}{2}\right)$ is equ 28. The area of the triangle, whose vertices are $A \equiv(1,-1,2), B \equiv(2,1,-1)$ and $C \equiv(3,-1,2)$, is 29. The maximum value of the function $$f(x)=3 x^3-18 x^2+27 x-40$$ on the set $\mathrm{S}=\left\{x \in \mathbb{R} / x^2+30 30. $\tan \left(\frac{\pi}{4}+\frac{1}{2} \cos ^{-1}\left(\frac{\mathrm{a}}{\mathrm{b}}\right)\right)+\tan \left(\frac{\pi}{ 31. Consider three observations $\mathrm{a}, \mathrm{b}$ and c such that $b=a+c$. If the standard deviation of $\mathrm{a}+2 32. The area (in sq. units) bounded by the curves $y=\sqrt{x}, 2 y-x+3=0, X$-axis and lying in the first quadrant is 33. If the lengths of the sides of triangle are 3,5,7, then the largest angle of the triangle is 34. If $\mathrm{f}(x)=\sin ^{-1}\left(\frac{2 \cdot 3^x}{1+9^x}\right)$, then $\mathrm{f}^{\prime}\left(\frac{1}{2}\right)$ 35. $\int\left(\mathrm{f}(x) \mathrm{g}^{\prime \prime}(x)-\mathrm{f}^{\prime \prime}(x) \mathrm{g}(x)\right) \mathrm{d} x$ 36. The value of $\tan \left(2 \tan ^{-1}\left(\frac{\sqrt{5}-1}{2}\right)\right)$ is 37. Number of different nine digit numbers, that can be formed from the digits in the number 223355888 by rearranging its di 38. If $\overline{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ and $\bar{b}=\hat{i} \times(\bar{a} \t 39. The equation of normal to the curve $x=\theta+\sin \theta, y=1+\cos \theta$ at $\theta=\frac{\pi}{2}$ is 40. The equation of the line, through $\mathrm{A}(1,2,3)$ and perpendicular to the vector $2 \hat{\mathrm{i}}+\hat{\mathrm{j 41. $\int \frac{\log \sqrt{x}}{3 x} \mathrm{dx}$ is equal to 42. The negation of contrapositive of the statement $\mathrm{p} \rightarrow(\sim \mathrm{q} \wedge \mathrm{r})$ is 43. If $\mathrm{F}(x)=\left(\mathrm{f}\left(\frac{x}{2}\right)\right)^2+\left(\mathrm{g}\left(\frac{x}{2}\right)\right)^2$, 44. Let $P$ be the image of the point $(3,1,7)$ with respect to the plane $x-y+z=3$. Then the equation of the plane passing 45. Let $f(\theta)=\sin \left(\tan ^{-1}\left(\frac{\sin \theta}{\sqrt{\cos 2 \theta}}\right)\right)$, where $\frac{-\pi}{4} 46. The approximate value of $\sqrt[3]{0.026}$ is 47. The incentre of the triangle whose vertices are $P(0,3,0), Q(0,0,4)$ and $R(0,3,4)$ is 48. A random variable $X$ has the following probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg 49. $\lim _\limits{x \rightarrow 0} \frac{\sin \left(\pi \cos ^2 x\right)}{x^2}$ is equal to 50. Which one of the following is the pair of equivalent circuits?

Physics

1. A ferromagnetic material is heated above its curie temperature. The correct statement from the following is that 2. The number of photoelectrons emitted for light of frequency $v$ (higher than the threshold frequency $\left(v_0\right)$ 3. The amount of work done in increasing the voltage across the plates of a capacitor form 5 V to 10 V is ' W '. The work d 4. Liquid drops are falling slowly one by one from vertical glass tube. The relation between the weight of a drop ' $w$ ', 5. A solid sphere of mass ' $m$ ', radius ' $R$ ', having moment of inertia about an axis passing through center of mass as 6. Rate of flow of heat through a cylindrical rod is ' $\mathrm{H}_1$ '. The temperature at the ends of the rod are ' $T_1$ 7. A ball rises to surface at a constant velocity in liquid whose density is 4 times greater than that of the material of t 8. An air cored coil has self inductance of 0.1 H . A soft iron core of relative permeability 1000 is introduced and the nu 9. $\mathrm{L}=2 \mathrm{H}, \mathrm{C}=5 \mathrm{mF}$ and $\mathrm{R}=12 \Omega$ are connected in series to an a.c. genera 10. An electron of stationary Hydrogen atom passes from fifth energy level to ground level. The velocity that the atom acqui 11. A diffraction pattern is obtained using a beam of red light. If red light is replaced by blue light then 12. The magnetic energy in an inductor changes from maximum value to minimum value in 5 ms . When connected to an a.c. sourc 13. Which of the following statement is correct? 14. The potential barrier in p-n junction diode is due to 15. An inclined plane makes an angle of $30^{\circ}$ with the horizontal. A solid sphere rolling down this inclined plane fr 16. A fixed mass of gas at constant pressure occupies a volume ' V '. The gas undergoes a rise in temperature so that the r. 17. When cell of E.M.F. ' $E_1$ ' is connected to potentiometer wire, the balancing length is $l_1$. Another cell of E.M.F. 18. The logic gate combination circuit shown in the figure performs the logic function of 19. In an isobaric process 20. A concave mirror of focal length ' $f$ ' produces an image ' $n$ ' time the size of the object. If the image is real, th 21. A drum of radius ' $R$ ' full of liquid of density ' $d$ ' is rotated at angular velocity ' $\omega$ ' $\mathrm{rad} / \ 22. In a vibrating string with fixed ends the waves are of type 23. The focal length of combination of lenses formed with lenses having power of +2.50 D and $-3.75$ D will be 24. The current flowing in a coil is 3 A and the power consumed is 108 W . If the a.c. source is of $120 \mathrm{~V}, 50 \ma 25. In the following circuit, the current flowing through zener diode is 26. The mass of the lift is 200 kg , when it ascends with an acceleration of $4 \mathrm{~m} / \mathrm{s}^2$ then the tension 27. The average translational kinetic energy of nitrogen (molar mass 28) molecules at a particular temperature is 0.042 eV . 28. A spring has a certain mass suspended from it and its period of vertical oscillations is $T_1$. The spring is now cut in 29. The intensity ratio of the maxima and minima in an interference pattern produced by two coherent sources of light is $9: 30. The coil and magnet are moved in the same direction with same speed (V). The induced e.m.f. is 31. A driver applies the brakes on seeing the red traffic signal 400 m ahead. At the time of applying brakes, the vehicle wa 32. The driver of a car travelling with a speed ' $V_1$ ' $\mathrm{m} / \mathrm{s}$ towards a wall sounds a siren of frequen 33. A stretched string is fixed at both ends. It is made to vibrate so that the total number of nodes formed in it is ' $x$ 34. Three long, straight parallel wires carrying currents are arranged as shown. The wire C which carries a current of 5.0 A 35. Which of the following statements about the Bohr model of the hydrogen atom is false? 36. Two points separated by a distance of 0.1 mm can just be seen in microscope when light of wavelength $6000 \mathop A\lim 37. In the following circuit, the current $\mathrm{I_2}$ is 38. The first operation involved in a carnot cycle is 39. The gravitational potential energy required to raise a satellite of mass ' $m$ ' to height ' $h$ ' above the earth's sur 40. The core used in transformer and other electromagnetic devices is laminated to 41. The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at $47^{\circ} \m 42. A sonometer wire is stretched by hanging a metal bob. The fundamental frequency of vibration of wire is ' $n_1$ '. When 43. For a body performing simple harmonic motion, its potential energy is $\mathrm{E}_{\mathrm{x}}$ at displacement x and $\ 44. Charge on a parallel plate capacitor of capacity C is Q , the electric field intensity between its two plates separated 45. Four point charges each +q is placed on the circumference of a circle of diameter 2 d in such a way that they form a squ 46. A meter scale is supported on a wedge at its centre of gravity. A body of weight ' $w$ ' is suspended from the 20 cm mar 47. The stopping potential for a photelectric emission process is 10 V . The maximum kinetic energy of the electrons ejected 48. Cyclotron is used to 49. The displacement of a particle performing S.H.M. is given by $Y=A \cos [\pi(t+\phi)]$. If at $\mathrm{t}=0$, the displac 50. The string of pendulum of length ' $L$ ' is displaced through $90^{\circ}$ from the vertical and released. Then the maxi

Mathematics

Physics

MHT CET 2024 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

The string of pendulum of length ' $L$ ' is displaced through $90^{\circ}$ from the vertical and released. Then the maximum strength of the string in order to withstand the tension, as the pendulum passes through the mean position is ( $\mathrm{m}=$ mass of pendulum, $\mathrm{g}=$ acceleration due to gravity)

3 mg

5 mg

6 mg