MHT CET 2024 4th May Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

Mathematics

1. Suppose A is any $3 \times 3$ non-singular matrix and $(\mathrm{A}-3 \mathrm{I})(\mathrm{A}-5 \mathrm{I})=0$ where $\mat 2. The lines $\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k} \quad$ and $\frac{x-1}{\mathrm{k}}=\frac{y-4}{2}=\frac{\mathrm{z}- 3. The variance of first 50 even natural numbers is 4. The statement pattern $[p \wedge(q \vee r)] \vee[\sim r \wedge \sim q \wedge p]$ is equivalent to 5. If $8 \mathrm{f}(x)+6 \mathrm{f}\left(\frac{1}{x}\right)=x+5$ and $y=x^2 \mathrm{f}(x)$, then $\frac{\mathrm{d} y}{\math 6. The number of ways in which 5 boys and 3 girls can be seated on a round table, if a particular boy $B_1$ and a particula 7. The value of $\cot \left(\operatorname{cosec}^{-1} \frac{5}{3}+\tan ^{-1} \frac{2}{3}\right)$ is 8. $\int\left(1+x-\frac{1}{x}\right) e^{x+\frac{1}{x}} d x$ equal to 9. The function $f(x)=\frac{\log _e(\pi+x)}{\log _e(e+x)}$ is 10. Let $y=y(x)$ be the solution of the differential equation $\sin x \frac{\mathrm{~d} y}{\mathrm{~d} x}+y \cos x=4 x, x \i 11. The value of $\mathrm{I}=\int \frac{x^2}{(\mathrm{a}+\mathrm{bx})^2} \mathrm{dx}$ is 12. Let $\quad \overline{\mathrm{a}}=\alpha \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}, \overline{\mathrm{b}}=3 \h 13. If $4 a b=3 h^2$, then the ratio of the slope of lines represented by $a x^2+2 \mathrm{~h} x y+\mathrm{b} y^2=0$ is 14. If $\sin \left(\cot ^{-1}(x+1)\right)=\cos \left(\tan ^{-1} x\right)$ then considering positive square roots, $x$ has th 15. A random variable has the following probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{b 16. Let A and B be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability 17. Let $\left(-2-\frac{1}{3} \mathrm{i}\right)^3=\frac{x+\mathrm{i} y}{27}, \mathrm{i}=\sqrt{-1}$, where $x$ and $y$ are re 18. The shaded region in the following figure is the solution set of the inequations 19. Let $\bar{p}$ and $\bar{q}$ be the position vectors of $P$ and $Q$ respectively, with respect to $O$ and $|\vec{p}|=p,|\ 20. The value of a for which the volume of parallelepiped formed by $\hat{i}+a \hat{j}+\hat{k}, \hat{j}+a \hat{k}$ and $a \h 21. The approximate value of $\log _{10} 1002$ is (Given $\log _{10} \mathrm{e}=0.4343$) 22. The sum of intercepts on coordinate axes made by tangent to the curve $\sqrt{x}+\sqrt{y}=\sqrt{a}$ is 23. If the angles of a triangle are in the ratio $4: 1: 1$, then the ratio of the longest side to the perimeter is 24. Considering only the Principal values of inverse functions, the set $$A=\left\{x \geq 0 \left\lvert\, \tan ^{-1}(2 x)+\t 25. The line L given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line K is parallel to line L and 26. The integral $\int_{\frac{-1}{2}}^{\frac{1}{2}}\left([x]+\log _{\mathrm{e}}\left(\frac{1+x}{1-x}\right)\right) \mathrm{d 27. If the function $\mathrm{f}(x)=x^3+\mathrm{e}^{\frac{x}{2}}$ and $\mathrm{g}(x)=\mathrm{f}^{-1}(x)$ then the value of $g 28. A wire of length 2 units is cut into two parts, which are bent respectively to form a square of side $x$ units and a cir 29. Let $\mathrm{L}_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2}$ and $\mathrm{L}_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{ 30. Let $a, b \in R$. If the mirror image of the point $\mathrm{p}(\mathrm{a}, 6,9)$ w.r.t. line $\frac{x-3}{7}=\frac{y-2}{5 31. A random variable $X$ has the following probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg 32. The number of distinct real values of $\lambda$, for which the vectors $-\lambda^2 \hat{i}+\hat{j}+\hat{k}, \hat{i}-\lam 33. If $f(x)=\log _e\left(\frac{1-x}{1+x}\right),|x| 34. Let the vectors $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ and $\overline{\mathrm{d}}$ be suc 35. If $I=\int e^{\sin \theta}\left(\log \sin \theta+\operatorname{cosec}^2 \theta\right) \cos \theta d \theta$, then $I$ is 36. The equation of the circle which has its centre at the point $(3,4)$ and touches the line $5 x+12 y-11=0$ is 37. A plane which is perpendicular to two planes $2 x-2 y+z=0$ and $x-y+2 z=4$, passes through $(1,-2,1)$. The distance of t 38. The value of the expression $\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}$ is equal to 39. Let $\bar{a}, \bar{b}$ and $\overline{\mathrm{c}}$ be three vectors having magnitude 1,1 and 2 respectively. If $\overli 40. The area bounded between the curves $y=a x^2$ and $x=a y^2(a>0)$ is 1 sq. units, then the value of a is 41. The integral $\int \sec ^{\frac{2}{3}} x \cdot \operatorname{cosec}^{\frac{4}{3}} x \mathrm{~d} x$ is equal to 42. If sum of two numbers is 3 , then the maximum value of the product of first number and square of the second number is 43. Given that the slope of the tangent to a curve $y=y(x)$ at any point $(x, y)$ is $\frac{2 y}{x^2}$. If the curve passes 44. If $y=\left((x+1)(4 x+1)(9 x+1) \ldots\left(\mathrm{n}^2 x+1\right)\right)^2$, then $\frac{\mathrm{dy}}{\mathrm{d} x}$ a 45. A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is corre 46. A wet substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet hung in th 47. $\lim _\limits{x \rightarrow 0} \frac{(1-\cos 2 x)(3+\cos x)}{x \tan 4 x}$ has the value 48. Let $a, b \in(a \neq 0)$. If the function $f$ is defined as $$f(x)=\left\{\begin{array}{cc} \frac{2 x^2}{\mathrm{a}} & , 49. If $(p \wedge \sim q) \wedge(p \wedge r) \rightarrow \sim p \vee q$ is false, then the truth values of $p, q$ and $r$ ar 50. In $\triangle \mathrm{ABC}$, with usual notations, if $\mathrm{b}=3$, $c=8, \mathrm{~m} \angle \mathrm{~A}=60^{\circ}$,

Physics

1. According to the law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the m 2. A parallel plate air capacitor, with plate separation ' d ' has a capacitance of 9 pF . The space between the plates is 3. The collector supply voltage is 6 V and a voltage drop across a resistor of $600 \Omega$ in the collector circuit is 0.6 4. The velocity of particle executing S.H.M. varies with displacement $(\mathrm{x})$ as $4 \mathrm{~V}^2=50-\mathrm{x}^2$. 5. For a projectile, the maximum height and horizontal range are same. The angle of projection ' $\theta$ ' of the projecti 6. For the given figure, choose the correct option. 7. A disc and a ring both have same mass and radius. The ratio of moment of inertia of the disc about its diameter to that 8. Two waves $\mathrm{Y}_1=0.25 \sin 316 \mathrm{t} \quad$ and $\mathrm{Y}_2=0.25 \sin 310 \mathrm{t}$ are propagating alon 9. In a meter bridge experiment, the balance point is obtained if the gaps are closed by $2 \Omega$ and $3 \Omega$. A shunt 10. Water rises up to height ' $X$ ' in a capillary tube immersed vertically in water. When the whole arrangement is taken t 11. In an equilateral prism the ray undergoes minimum deviation when it is incident at an angle of $50^{\circ}$. The angle o 12. A rotating body has angular momentum ' $L$ '. If its frequency is doubled and kinetic energy is halved, its angular mome 13. The distance between two consecutive points with phase difference of $60^{\circ}$ in wave of frequency 500 Hz is 0.6 m . 14. A square loop of area $25 \mathrm{~cm}^2$ has a resistance of $10 \Omega$. The loop is placed in uniform magnetic field 15. The electric potential at the centre of two concentric half rings of radii $R_1$ and $R_2$, having same linear charge de 16. Which of the following person is in an inertial frame of reference? 17. A charged particle of charge ' $q$ ' is accelerated by a potential difference ' $V$ ' enters a region of uniform magneti 18. A simple pendulum of length $l_1$ has time period $\mathrm{T}_1$. Another simple pendulum of length $l_2\left(l_1>l_2\ri 19. A zener diode, having breakdown voltage 15 V is used in a voltage regulator circuit as shown. The current through the ze 20. If ' $R$ ' is the radius of earth \& ' $g$ ' is acceleration due to gravity on earth's surface, then mean density of ear 21. In LCR series circuit if the frequency is increased, the impedance of the circuit 22. A potentiometer wire of length 1 m is connected in series with $495 \Omega$ resistance and 2 V battery. If $0.2 \mathrm{ 23. A carnot engine, whose efficiency is $40 \%$ takes heat from a source maintained at temperature 600 K . It is desired to 24. A person is observing a bacteria through a compound microscope. For better analysis and to improve the resolving power h 25. Two rods of same length \& material transfer a given amount of heat in 12 s when they are joined end to end. But when th 26. A graph of magnetic flux $(\phi)$ versus current ( 1 ) is shown for four inductors A, B, C, D. Smaller value of self ind 27. An insulated container contains a monoatomic gas of molar mass ' $m$ '. The container is moving with velocity ' $V$ '. I 28. A ray of light is incident normally on a glass slab to thickness 5 cm and refractive index 1.6. The time taken to travel 29. The magnetic moments associated with two closely wound circular coils A and B of radius $r_A=10 \mathrm{~cm}$ and $r_B=2 30. Focal length of objective of an astronomical telescope is 1.5 m . Under normal adjustment, length of telescope is 1.56 m 31. The surface of water in a water tank of cross section area $750 \mathrm{~cm}^2$ on the top of a house is ' $h$ ' $m$ abo 32. A string A has twice the length, twice the diameter, twice the tension and twice the density of another string B. The ov 33. An inductor of inductance $2 \mu \mathrm{H}$ is connected in series with a resistance, a variable capacitor and an a.c. 34. Three identical polaroids $P_1, P_2$ and $P_3$ are placed one after another. The pass axis of $P_2$ and $P_3$ are inclin 35. A semiconductor device X is connected in series with a battery and a resistor. The current of 10 mA is found to pass thr 36. A solid cylinder of mass M and radius R is rotating about its geometrical axis. A solid sphere of the same mass and same 37. A circular coil of resistance $R$, area $A$, number of turns ' $N$ ' is rotated about its vertical diameter with angular 38. The excess pressure inside a spherical drop of water A is four times that of another drop B. Then the ratio of mass of d 39. A parallel plate capacitor has plate area $40 \mathrm{~cm}^2$ and plate separation 2 mm . The space between the plates i 40. The height ' $h$ ' above the earth's surface at which the value of acceleration due to gravity $(\mathrm{g})$ becomes $\ 41. In an isobaric process of an ideal gas, the ratio of work done by the system to the heat supplied $\left(\frac{W}{Q}\rig 42. The threshold frequency of a metal is ' $F_0$ '. When light of frequency $2 F_0$ is incident on the metal plate, the max 43. A charged particle is moving in a uniform magnetic field in a circular path with radius ' $R$ '. When the energy of the 44. A massless square loop of wire of resistance ' $R$ ' supporting a mass ' M ' hangs vertically with one of its sides in a 45. A sphere is at temperature 600 K . In an external environment of 200 K , its cooling rate is ' $R$ ' When the temperatur 46. A progressive wave of frequency 400 Hz is travelling with a velocity $336 \mathrm{~m} / \mathrm{s}$. How far apart are t 47. Two bodies A and B of equal mass are suspended from two separate massless springs of spring constants $\mathrm{K}_1$ and 48. For hydrogen atom, ' $\lambda_1$ ' and ' $\lambda_2$ ' are the wavelengths corresponding to the transitions 1 and 2 resp 49. A metallic sphere ' A ' isolated from ground is charged to $+50 \mu \mathrm{C}$. This sphere is brought in contact with 50. For a photosensitive material, work function is ' $\mathrm{W}_0$ ' and stopping potential is ' V '. The wavelength of in

MHT CET 2024 4th May Morning Shift

MCQ (Single Correct Answer)

-0

The integral $\int_{\frac{-1}{2}}^{\frac{1}{2}}\left([x]+\log _{\mathrm{e}}\left(\frac{1+x}{1-x}\right)\right) \mathrm{d} x$, where $[x]$ represent greatest integer function, equals

$-\frac{1}{2}$

$\log _{\mathrm{c}}\left(\frac{1}{2}\right)$

$\frac{1}{2}$

$ 2 \log _{\mathrm{e}}\left(\frac{1}{2}\right)$

MHT CET 2024 4th May Morning Shift

MCQ (Single Correct Answer)

-0

If the function $\mathrm{f}(x)=x^3+\mathrm{e}^{\frac{x}{2}}$ and $\mathrm{g}(x)=\mathrm{f}^{-1}(x)$ then the value of $g^{\prime}(1)$ is

$\frac{1}{2}$

MHT CET 2024 4th May Morning Shift

MCQ (Single Correct Answer)

-0

A wire of length 2 units is cut into two parts, which are bent respectively to form a square of side $x$ units and a circle of radius of r units. If the sum of the areas of square and the circle so formed is minimum, then

$2 x=(\pi+4) \mathrm{r}$

$(4-\pi) x=\pi \mathrm{r}$

$x=2 \mathrm{r}$

$2 x=\mathrm{r}$

MHT CET 2024 4th May Morning Shift

MCQ (Single Correct Answer)

-0

Let $\mathrm{L}_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2}$ and $\mathrm{L}_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3}$ be two given lines. Then the unit vector perpendicular to $L_1$ and $L_2$ is

$\frac{-\hat{\mathrm{i}}+7 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}}{\sqrt{99}}$

$\frac{-\hat{\mathrm{i}}-7 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}}{5 \sqrt{3}}$

$\frac{-\hat{i}+7 \hat{j}+5 \hat{k}}{5 \sqrt{3}}$

$\frac{7 \hat{\mathrm{i}}-7 \hat{\mathrm{j}}-7 \hat{\mathrm{k}}}{\sqrt{99}}$

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