MHT CET 2024 3rd May Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

Mathematics

1. If $\int \frac{\mathrm{d} x}{\cos ^3 x \sqrt{2 \sin 2 x}}=(\tan x)^A+C(\tan x)^B+K$, where K is a constant of integratio 2. $$\int \frac{2 x^2-1}{\left(x^2+4\right)\left(x^2-3\right)} d x=$$ 3. Let $\mathrm{f}(x)=\frac{1-\tan x}{4 x-\pi}, x \neq \frac{\pi}{4}, x \in\left[0, \frac{1}{2}\right], \quad \mathrm{f}(x) 4. The number of possible distinct straight lines passing through $(2,3)$ and forming a triangle with co-ordinate axes whos 5. The differential equation $\left[\frac{1+\left(\frac{d y}{d x}\right)^2}{\left(\frac{d^2 y}{d x^2}\right)}\right]^{\frac 6. A triangular park is enclosed on two sides by a fence and on the third side a straight river bank. The two sides having 7. If p and q are statements, then _________ is a contingency. 8. If $\int_\limits0^{\frac{\pi}{3}} \frac{\tan \theta}{\sqrt{2 k \sec \theta}} d \theta=1-\frac{1}{\sqrt{2}},(k>0)$, then 9. A random variable x has the following probability distribution. Then value of $k$ is _________ and $\mathrm{P}(3 .tg { 10. If $y=\log \left[\mathrm{e}^{5 x}\left(\frac{3 x-4}{x+5}\right)^{\frac{4}{3}}\right]$, then $\frac{\mathrm{d} y}{\mathrm 11. Let $f$ be a twice differentiable function such that $\mathrm{f}^{\prime \prime}(x)=-\mathrm{f}(x), \mathrm{f}^{\prime} 12. The area (in sq. units) of the parallelogram whose diagonals are along the vectors $8 \hat{\mathrm{i}}-6 \hat{\mathrm{j} 13. The line L given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line K is parallel to L and has 14. If $|\bar{a}|=\sqrt{27},|\bar{b}|=7$ and $|\bar{a} \times \bar{b}|=35$, then $\bar{a} \cdot \bar{b}$ is equal to 15. The number of real solutions of $\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^2+x+1}=\frac{\pi}{2}$ is 16. Let $S=\left\{x \in(-\pi, \pi) \mid x \neq 0, \pm \frac{\pi}{2}\right\}$. The sum of all distinct solutions of the equat 17. The number of four letter words that can be formed using letters of the word BARRACK 18. A stone is dropped into a quiet lake and waves move in circles at speed of $8 \mathrm{~cm} / \mathrm{sec}$. At the insta 19. The area (in sq. units) of the region bounded by the curve $x^2=4 y$ and the straight line $x=4 y-2$ is 20. If the half life of substance is 5 years, then the total amount of the substance left after 15 years, when initial amoun 21. Equation of the plane containing the straight line $\frac{x}{3}=\frac{y}{2}=\frac{z}{4}$ and perpendicular to the plane 22. The number of roots of the equation, $(81)^{\sin ^2 x}+(81)^{\cos ^2 x}=30$ in the interval $[0, \pi]$, is equal to 23. If $\quad \int(2 x+4) \sqrt{x-1} d x=a(x-1)^{5 / 2}+b(x-1)^{3 / 2}+c$ where $c$ is a constant of integration, then the v 24. Let $\mathrm{X} \sim \mathrm{B}\left(6, \frac{1}{2}\right)$, then $\mathrm{P}[|x-4| \leqslant 2]$ is 25. The mean of $n$ observations is $\bar{x}$. If three observations $\mathrm{n}+1, \mathrm{n}-1,2 \mathrm{n}-1$ are added s 26. If $y=\sec \left(\tan ^{-1} x\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1$ is equal to 27. The equation of the concentric circle, with the circle $\mathrm{C}_1$ having equation $x^2+y^2-6 x-4 y-12=0$ and having 28. Let $\alpha(a)$ and $\beta(a)$ be the roots of the equation $$(\sqrt[3]{1+a}-1) x^2+(\sqrt{1+a}-1) x+(\sqrt[6]{1+a}-1)=0 29. Let $2 \sin ^2 x+3 \sin x-2>0$ and $x^2-x-2 30. If $\mathrm{A} \equiv(1,-1,0), \mathrm{B} \equiv(0,1,-1)$ and $\mathrm{C} \equiv(-1,0,1)$, then the unit vector $\overli 31. A bullet is shot horizontally and its distance S cm at time t second is given by $\mathrm{S}=1200 \mathrm{t}-15 \mathrm{ 32. If $|z|=1$ and $w=\frac{z-1}{z+1}$ (where $\left.z \neq-1\right)$, then $\operatorname{Re}(w)$ is 33. If $g(x)=x^2+x-1$ and (gof) $(x)=4 x^2-10 x+5$, then $\mathrm{f}(2)$ is equal to 34. The shaded area in the figure below is the solution set for a certain linear programming problem, then the linear constr 35. The equation of the normal to the curve $x=\theta+\sin \theta, y=1+\cos \theta$ at $\theta=\frac{\pi}{2}$ is 36. If $\tan x=\frac{3}{4}$ and $\pi 37. The value of $m$, such that $\frac{x-4}{1}=\frac{y-2}{1}=\frac{2 z-m}{3}$ lies in the plane $2 x-5 y+2 z=7$, is 38. The image of the line $\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}$ in the plane $2 x-y+z+3=0$ is the line 39. Let the vectors $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ be such that $|\overline{\mathrm{a 40. A person throws an unbiased die. If the number shown is even, he gains an amount equal to the number shown. If the numbe 41. Let $\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\overline{\mathrm{b}}=\hat{\math 42. If $\theta$ and $\alpha$ are not odd multiples of $\frac{\pi}{2}$ then $\tan \theta=\tan \alpha$ implies principal solut 43. The approximate value of $\cos \left(30^{\circ}, 30^{\prime}\right)$ is given that $1^{\circ}=0.0175^{\circ}$ and $\cos 44. Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Let X denote the random variabl 45. The value of $\int \frac{(x-1) \mathrm{e}^x}{(x+1)^3} \mathrm{~d} x$ is equal to 46. Let $\mathrm{P}(2,3,6)$ be a point in space and Q be a point on the line $\bar{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(-3 \ha 47. Consider the following statements p : the switch $\mathrm{S}_1$ is closed. q : the switch $\mathrm{S}_2$ is closed. $r$ 48. Let $\bar{a}, \bar{b}, \bar{c}$ be three non-coplanar vectors and $\overline{\mathrm{p}}, \overline{\mathrm{q}}, \overli 49. If $A=\left[\begin{array}{cc}2 & -2 \\ 4 & 3\end{array}\right]$, then $A^{-1}=$ 50. The differential equation of family of circles, whose centres are on the X -axis and also touch the Y -axis is

Physics

1. A ball ' $A$ ' is projected vertically upwards with certain initial speed. Another ball 'B' of same mass is projected at 2. A small sphere oscillates simple harmonically in a watch glass whose radius of curvature is 1.6 m . The period of oscill 3. The path difference between two waves $\mathrm{Y}_1=\mathrm{a}_1 \sin \left(\omega \mathrm{t}-\frac{2 \pi \mathrm{x}}{\l 4. Two equal point charges ' $q$ ' each exert a force ' $F$ ' on each other, when they are placed distance ' $x$ ' apart in 5. An alternating voltage $\mathrm{v}=200 \sqrt{2} \sin (100 \mathrm{t})$ is connected to a $1 \mu \mathrm{~F}$ capacitor t 6. Three charges $2 q,-q$ and $-q$ are located at the vertices of an equilateral triangle. At the centre of the triangle 7. A gardening pipe having an internal radius ' $R$ ' is connected to a water sprinkler having ' $n$ ' holes each of radius 8. A magnetic needle of magnetic moment $6 \times 10^{-2} \mathrm{Am}^2$ and moment of inertia $9.6 \times 10^{-5} \mathrm{ 9. In case of rotational dynamics, which one of the following statements is correct? [$\vec{\omega}=$ angular velocity, $\o 10. A convex lens of focal length ' $f$ ' $m$ forms a real, inverted image twice in size of the object. The object distance 11. The ratio of the wavelength of a photon of energy ' $E$ ' to that of the electron of same energy is ( $\mathrm{m}=$ mass 12. The r.m.s. velocity of hydrogen at S.T.P. is ' $u$ ' $\mathrm{m} / \mathrm{s}$. If the gas is heated at constant pressur 13. The distance of the two planets A and B from the sun are $r_A$ and $r_B$ respectively. Also $r_B$ is equal to $100 r_A$. 14. A tube of uniform bore of cross-sectional area ' $A$ ' has been set up vertically with open end facing up. Now ' $M$ ' g 15. An n-p-n transistor can be considered to be equivalent to two diodes connected. The correct figure out of the following 16. The fundamental frequency of an air column in a pipe open at both ends is ' $\mathrm{f}_1$ '. Now $80 \%$ of its length 17. Earth has mass ' $M_1$ ' radius ' $R_1$ ' and for moon mass ' $M_2$ ' and radius ' $R_2$ '. Distance between their centr 18. In an interference experiment, the $\mathrm{n}^{\text {th }}$ bright fringe for light of wavelength $\lambda_1(\mathrm{n 19. Three inductances are connected as shown in figure. The equivalent inductance is 20. There are two samples A and B of a certain gas, which are initially at the same temperature and pressure. Both are compr 21. A single slit diffraction pattern is formed with light of wavelength $6195 \mathop A\limits^o$. The second secondary max 22. Two rods, one of aluminium and the other of steel, having initial lengths ' $\mathrm{L}_1$ ' and ' $\mathrm{L}_2$ ' are 23. In an a. c. generator, when the plane of the coil is perpendicular to the magnetic field 24. Two circular metal plates each of radius ' $r$ ' are kept parallel to each other distance ' $d$ ' apart. The capacitance 25. Ratio of radius of gyration of a circular disc to that of circular ring each of same mass and radius around their respec 26. In an $A C$ circuit $E=200 \sin (50 t)$ volt and $\mathrm{I}=100 \sin \left(50 \mathrm{t}+\frac{\pi}{3}\right) \mathrm{m 27. In the following circuit, a power of 50 watt is absorbed in the section AB of the circuit. The value of resistance ' $x$ 28. A ray of light is incident at $60^{\circ}$ on one face of a prism of angle $30^{\circ}$ and the emergent ray makes $30^{ 29. Given that ' $x$ ' joule of heat is incident on a body. Out of that, total heat reflected and transmitted is ' $y$ ' jou 30. In the uranium radioactive series, the initial nucleus is ${ }_{92}^{238} \mathrm{U}$ and that the final nucleus is ${ } 31. When photons of energy hv fall on a photosensitive surface of work function $\mathrm{E}_0$, photoelectrons of maximum en 32. The pressure inside two soap bubbles, (A) is 1.01 and that of (B) is 1.02 atmosphere respectively. The ratio of their re 33. The pitch of a whistle of an engine appears to drop by $30 \%$ of original value when it passes a stationary observer. I 34. A transformer having efficiency $90 \%$ is working on 200 V and 3 kw power supply. If the current in the secondary coil 35. A diatomic ideal gas is used in Carnot engine as a working substance. If during the adiabatic expansion part of the cycl 36. The range of voltmeter of resistance ' $G$ ' $\Omega$ is ' $V$ ' volt. The resistance required to be connected in series 37. Find the magnitude of current in the given circuit. 38. An inductance coil has a resistance of $80 \Omega$. When on AC signal of frequency 480 Hz is applied to the coil, the vo 39. The displacement of a wave is given by $y=0.002 \sin (100 t+x)$ where ' $x$ 'and ' $y$ ' are in metre and ' $t$ ' is in 40. A current of 5 A flows through a toroid having a core of mean radius 20 cm . If 4000 turns of the conducting wire are wo 41. A metal ball of radius $9 \times 10^{-4} \mathrm{~m}$ and density $10^4 \mathrm{~kg} / \mathrm{m}^3$ falls freely under 42. When wavefronts pass from denser medium to rarer medium, the width of the wavefront 43. The relation between total magnetic field (B), magnetic intensity $(\mathrm{H})$, permeability of free space $\left(\mu_ 44. In common emitter transistor amplifier, load resistance is $6.5 \mathrm{k} \Omega$ and an input resistance is $1.3 \math 45. A particle having a charge 50 e is revolving in a circular path of radius 0.4 m with $1 \mathrm{r} . \mathrm{p} . \mathr 46. Two blocks of masses 6 kg and 4 kg are placed in contact with each other on a smooth surface as shown. If a force of 5 N 47. Two circular loops P and Q of radii ' r ' and ' nr ' are made respectively from a uniform wire. Moment of inertia of loo 48. Two spherical black bodies of radii ' $R_1$ ' and ' $\mathrm{R}_2$ ' and with surface temperature ' $\mathrm{T}_1$ ' and 49. If ' $\lambda_1$ ' and ' $\lambda_2$ ' are the wavelengths of the first line of the Lyman and Paschen series respectivel 50. An electric dipole of moment $\overrightarrow{\mathrm{p}}$ is lying along a uniform electric field $\overrightarrow{\mat

MHT CET 2024 3rd May Morning Shift

MCQ (Single Correct Answer)

-0

Let $\alpha(a)$ and $\beta(a)$ be the roots of the equation $$(\sqrt[3]{1+a}-1) x^2+(\sqrt{1+a}-1) x+(\sqrt[6]{1+a}-1)=0$$ where $a>-1$ then $\lim _\limits{a \rightarrow 0^{+}} \alpha(a)$ and $\lim _\limits{a \rightarrow 0^{+}} \beta(a)$ respectively are

1 and $-\frac{5}{2}$

$-$1 and $-\frac{1}{2}$

2 and $-\frac{7}{2}$

3 and $-\frac{9}{2}$

MHT CET 2024 3rd May Morning Shift

MCQ (Single Correct Answer)

-0

Let $2 \sin ^2 x+3 \sin x-2>0$ and $x^2-x-2<0$. ( $x$ is measured in radians). The $x$ lies in the interval

$\left(\frac{\pi}{6}, \frac{5 \pi}{6}\right)$

$\left(-1, \frac{5 \pi}{6}\right)$

$(-1,2)$

$\left(\frac{\pi}{6}, 2\right)$

MHT CET 2024 3rd May Morning Shift

MCQ (Single Correct Answer)

-0

If $\mathrm{A} \equiv(1,-1,0), \mathrm{B} \equiv(0,1,-1)$ and $\mathrm{C} \equiv(-1,0,1)$, then the unit vector $\overline{\mathrm{d}}$ such that $\overline{\mathrm{a}}$ and $\overline{\mathrm{d}}$ are perpendiculars and $\overline{\mathrm{b}}, \overline{\mathrm{c}}, \overline{\mathrm{d}}$ are coplanar is

$+\frac{1}{\sqrt{3}}(1,1,1)$

$+\frac{1}{\sqrt{3}}(-1,-1,1)$

$+\frac{1}{\sqrt{6}}(1,1,-2)$

$+\frac{1}{\sqrt{2}}(1,1,0)$

MHT CET 2024 3rd May Morning Shift

MCQ (Single Correct Answer)

-0

A bullet is shot horizontally and its distance S cm at time t second is given by $\mathrm{S}=1200 \mathrm{t}-15 \mathrm{t}^2$, then the distance covered by the bullet when it comes to the rest, is

12000 cm

24000 cm

1200 cm

2400 cm

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