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

Calculate the entropy change for melting 1 g ice at $0^{\circ} \mathrm{C}$ in $\mathrm{Jg}^{-1} \mathrm{~K}^{-1}$ if heat of fusion of ice at $0^{\circ} \mathrm{C}$ is $80 \mathrm{~J} \mathrm{~K}^{-1}$.

0.039

0.293

8.0

27.3

MHT CET 2024 4th May Morning Shift

MCQ (Single Correct Answer)

-0

Which pair of elements from following has halt filled d-orbital in observed electronic configuration?

Cu and Mn

Mn and Cr

Zn and Co

Cu and Zn

MHT CET 2024 4th May Morning Shift

MCQ (Single Correct Answer)

-0

Calculate the radius of metal atom if it forms bec unit cell having edge length 530 pm.

229.5 pm

187.4 pm

459.0 pm

265.2 pm

MHT CET 2024 4th May Morning Shift

MCQ (Single Correct Answer)

-0

Calculate the concentration of weak monobasic acid if its degree of dissociation and dissociation constant are $5.0 \times 10^{-4}$ and $5.0 \times 10^{-9}$ respectively.

0.1 M

0.02 M

0.03 M

0.04 M

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