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

Chemistry

1. Which element from following is used in photoelectric cells? 2. What is the total number of particles present in bcc unit cell? 3. Which among the following polymers is obtained by ring opening polymerization process? 4. Identify an example of solution that consists of solid as solute and liquid as solvent. 5. Which of the following compounds is obtained when cyclohexene is oxidized using $\mathrm{KMnO}_4$ in dilute $\mathrm{H}_ 6. Which from following expressions is used to calculate $\mathrm{E}_{\text {cell }}$ for the following cell at $25^{\circ} 7. Which of the following compounds is obtained by using Swartz reaction? 8. What is the bond order in CO molecule? 9. Which of the following is an example of heterogenous catalysis? 10. Identify the monomers used for preparation of Buna-S. 11. Which among the following is NOT an intensive property? 12. How many moles of iodomethane are consumed in the following conversion? $$\mathrm{CH}_3 \mathrm{NH}_2 \xrightarrow[\Delt 13. Calculate the time required for reactant to decrease the concentration from $100 \%$ to $20 \%$, if rate constant of fir 14. Identify the number of donor atoms in EDTA molecule that form coordinate bond with central metal atom or ion in a comple 15. Which from following gases of same mass exerts highest pressure at constant temperature? 16. Calculate the volume of unit cell of an element having molar mass $27 \mathrm{~g} \mathrm{~mol}^{-1}$ that forms fcc uni 17. What is the ratio of concentration of salt to concentration of weak acid in buffer solution to maintain its pH value $7. 18. Which of the following isomers has highest boiling point? 19. Identify the product obtained when methyl bromide reacts with sodium tert-butoxide. 20. Which from following is NOT true about electrolysis of molten NaCl ? 21. Which element from following exhibits lowest number of different oxidation states? 22. Which functional group from following is considered as principal functional group if polyfunctional compound is to be na 23. Calculate the edge length of fcc unit cell if radius of metal atom is 139 pm . 24. Which from following techniques is used for preliminary confirmation of nanoparticles? 25. What is the value of pOH if a buffer solution is prepared by mixing equal volumes of $0.4 \mathrm{~M} \mathrm{~NH}_4 \ma 26. In a process 605 J heat is absorbed by the system and 380 J work is done by the system on surrounding. What is the value 27. Identify false statement from following. 28. The resistance of decimolar solution of NaCl is 30 ohms. Calculate the conductivity of solution if the cell constant is 29. What is the total number of unpaired electrons in an element placed at period-4 and group-12 either in excited or at gro 30. Which of the following is NOT obtained when a mixture of bromoethane and 1-bromopropane is treated with sodium metal in 31. What is the oxidation number of underlined species in $\mathrm{PF}_6^{-}$and $\mathrm{V}_2 \mathrm{O}_7^{-4}$ ions respe 32. Calculate the molality of solution of non volatile solute having depression in freezing point 0.93 K and cryoscopic cons 33. Which of the following salt solutions turns red litmus blue? 34. Which from following compounds is obtained when acyl chloride is hydrolysed with water? 35. What is the rate of formation of $\mathrm{O}_2$ for the reaction stated below? $$\begin{aligned} & 2 \mathrm{~N}_2 \math 36. Which from following complexes contains only neutral ligands in it? 37. What is the number of moles of carbon atoms present in n mole molecules of an alkane if it exhibits five structural isom 38. Identify the product ' B ' in the following sequence of reactions. $$\mathrm{CH}_3 \mathrm{MgBr} \xrightarrow{\mathrm{Cd 39. Rate law for the reaction $2 \mathrm{NO}+\mathrm{Cl}_2 \rightarrow 2 \mathrm{NOCl}$ is rate $=\mathrm{k}[\mathrm{NO}]^2\ 40. Which among the following is haloarene? 41. What is energy associated with fourth orbit of hydrogen atom? $$\left(\mathrm{R}_{\mathrm{H}}=2.18 \times 10^{-18} \math 42. Identify glycosidic linkages for formation of chain and branches respectively in amylopectin. 43. Which from following species does not have number of electrons similar to other three species? 44. What is the name of tert-butyl alcohol according to carbinol system? 45. Identify the element having outer electronic configuration $\mathrm{ns}^2 \mathrm{np}^5$. 46. What is the mass in kg of 5 mole of acetic acid $\left(\mathrm{mol}\right.$. mass $\left.=60 \mathrm{~g} \mathrm{~mol}^{ 47. A solution of non volatile solute is obtained by dissolving 2 g in 50 g benzene. Calculate the vapour pressure of soluti 48. A gas absorbs certain amount of heat and expands by $200 \mathrm{~cm}^3$ against a constant external pressure of $2 \tim 49. Which of the following is primary allylic alcohol? 50. Identify elements present in copper pyrites.

Mathematics

1. The vector equation of a line whose Cartesian equations are $y=2,4 x-3 z+5=0$ is 2. If 3 books on Physics, 2 books on Chemistry and 4 books on Mathematics are to be arranged on a shelf so that all the Phy 3. The value of $\lim _\limits{x \rightarrow 0} \frac{x}{|x|+x^2}$ is 4. Let $\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\overline{\mathrm{b}}=\hat{\math 5. The value of $\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)$ at $x=\frac{1}{5}$ where $0 \leq \cos ^{-1} x \leq \pi$ and 6. Considering only the principal values of inverse function, the set $$A=\left\{x \geq 0 / \tan ^{-1}(2 x)+\tan ^{-1}(3 x) 7. The slopes of the lines given by $x^2+2 h x y+2 y^2=0$ are in the ratio $1: 2$, then $h$ is 8. If $y=\left[\mathrm{e}^{4 x}\left(\frac{x-4}{x+3}\right)^{\frac{3}{4}}\right]$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}= 9. $$\int 3^{3^x} \cdot 3^x d x=$$ 10. If $\mathrm{f}(x)=\frac{1+\cos \pi x}{\pi(1-x)^2}$, for $x \neq 1$ is continuous at $x=1$, then $\mathrm{f}(1)$ is equal 11. The length of the longest interval, in which the function $3 \sin x-4 \sin ^3 x$ is increasing, is 12. The scalar $\overline{\mathrm{a}} \cdot[(\overline{\mathrm{b}}+\overline{\mathrm{c}}) \times(\overline{\mathrm{a}}+\over 13. The volume of parallelopiped formed by vectors $\hat{i}+m \hat{j}+\hat{k}, \hat{j}+m \hat{k}$ and $m \hat{i}+\hat{k}$ be 14. If the vectors $\overline{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=2 \hat 15. $$\int \log (1+x)^{1+x} \mathrm{~d} x=$$ 16. $$\int\left(\frac{x+2}{x+4}\right)^2 \cdot e^x \mathrm{~d} x=$$ 17. In $\triangle A B C$, with usual notations, if $\frac{1}{b+c}+\frac{1}{c+a}=\frac{3}{a+b+c}$, then $m \angle C$ is equal 18. If $\mathrm{a}>0$ and $\mathrm{z}=\frac{(1+\mathrm{i})^2}{\mathrm{a}-\mathrm{i}}, \mathrm{i}=\sqrt{-1}$, has magnitude $ 19. A bag contains 4 Red and 6 Black balls. A ball is drawn at random from the bag, its colour is observed and this ball alo 20. Let K be the set of all real values of $x$, where the function $\mathrm{f}(x)=\sin |x|-|x|+2(x-\pi) \cos |x|$ is not dif 21. Let $f$ and $g$ be continuous functions on $[0, a]$ such that $f(x)=f(a-x)$ and $g(x)+g(a-x)=4$, then $\int_0^a f(x) g(x 22. The principal solutions, of the equation $\sqrt{3} \sec x+2=0$, are 23. The number of real solutions of $\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^2+x+1}=\frac{\pi}{2}$ is 24. If $\bar{a}=(2 \hat{i}+2 \hat{j}+3 \hat{k}), \vec{b}=(-\hat{i}+2 \hat{j}+\hat{k}) \quad$ and $\bar{c}=(3 \hat{i}+\hat{j} 25. The solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}=(x-y)^2$ when $y(1)=1$ is 26. If $x_0$ is the point of local minima of $f(x)=\overline{\mathrm{a}} \cdot(\overline{\mathrm{b}} \times \overline{\mathr 27. $\hat{a}, \hat{b}$, and $\hat{c}$ are three unit vectors such that $\hat{a} \times(\hat{b} \times \hat{c})=\frac{\sqrt{3 28. For a suitable chosen real constant a, let a function $f: \mathbb{R}-\{-\mathrm{a}\} \rightarrow \mathbb{R}$ be defined 29. If the statement $p \vee \sim(q \wedge r)$ is false, then the truth values of $p, q$ and $r$ are respectively 30. If $\left(m_i, \frac{1}{m_i}\right), m_i>0, i=1,2,3,4$ are four distinct points on a circle, then the product $\mathrm{m 31. If two lines $x+(a-1) y=1 \quad$ and $2 x+a^2 y=1(a \in R-\{0,1\})$ are perpendicular, then the distance of their point 32. If $x \frac{\mathrm{~d} y}{\mathrm{~d} x}=y(\log y-\log x+1)$, then general solution of this equation is 33. A spherical metal ball at 80$^\circ$C cools in 5 minutes to 60$^\circ$C, in surrounding temperature of 20$^\circ$C, then 34. If a discrete random variable X takes values $0,1,2,3, \ldots \ldots$. with probability $\mathrm{P}(\mathrm{X}=x)=\mathr 35. The Cartesian equation of the plane, passing through the points $(3,1,1),(1,2,3)$ and $(-1,4,2)$, is 36. The equation of the line passing through the point $(-1,3,-2)$ and perpendicular to each of the lines $\frac{x}{1}=\frac 37. If $y=a \sin x+b \cos x \quad$ (where $\mathrm{a}$ and $\mathrm{b}$ are constants), then $y^2+\left(\frac{\mathrm{d} y}{ 38. If Rolle's theorem holds for the function $\mathrm{f}(x)=x^3+\mathrm{bx}{ }^2+\mathrm{ax}+5$ on $[1,3]$ with $\mathrm{c} 39. Ten bulbs are drawn successively, with replacement, from a lot containing $10 \%$ defective bulbs, then the probability 40. If statement I : If the work is not finished on time, the contractor is in trouble. statement II : Either the work is fi 41. The value of $\sin \left(2 \cos ^{-1}\left(-\frac{3}{5}\right)\right)$ is 42. If $y=\sqrt{\frac{1-\sin ^{-1} x}{1+\sin ^{-1} x}}$, then $\left(\frac{d y}{d x}\right)$ at $x=0$ is 43. The point, at which the maximum value of $10 x+6 y$ subject to the constraints $x+y \leq 12$, $2 x+y \leq 20, x \geq 0, 44. If the line $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}$ lies in the plane $\ell x+m y-z=9$, then $\ell^2+m^2$ is 45. The mean of 100 observations is 50 and their standard deviation is 5 , then the sum of all squares of all the observatio 46. The area of the region bounded by hyperbola $x^2-y^2=9$ and its latus rectum is 47. $\int \frac{\mathrm{d} x}{3-2 \cos 2 x}=\frac{\tan ^{-1}(\mathrm{f}(x))}{\sqrt{5}}+\mathrm{c}$, (where c is a constant o 48. The normal to the curve, $y(x-2)(x-3)=x+6$ at the point, where the curve intersects the Y-axis, passes through the point 49. For all real $x$, the vectors $C x \hat{i}-6 \hat{j}-3 \hat{k}$ and $x \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \mathrm{C} 50. If $A=\left[\begin{array}{cc}3 & -1 \\ -4 & 2\end{array}\right]$, then $A^{-1}$ is

Physics

1. In semiconductors at room temperature, 2. A particle at rest starts moving with a constant angular acceleration of $4 \mathrm{~rad} / \mathrm{s}^2$ in a circular 3. The logic circuit in figure is equivalent to 4. The intensity of light coming from one of the slits in Young's double slit experiment is double the intensity from the o 5. A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The rati 6. The height above the earth's surface at which the acceleration due to gravity becomes $\left(\frac{1}{n}\right)$ times t 7. A streamline flow of a liquid of density ' $\rho$ ' is passing through a horizontal pipe of crosssectional area $A_1$ an 8. In an a.c. circuit $\mathrm{I}=100 \sin 200 \pi \mathrm{t}$. The time required for the current to achieve its peak value 9. 90 J of work is done to move an electric charge of magnitude 3 C from a place A , where potential is -10 V to another pl 10. A particle is performing simple harmonic motion and if the oscillations are Camped oscillations then the angular frequen 11. The magnetic energy stored in an inductor of inductance $5 \mu \mathrm{H}$ carrying a current of 2 A is 12. Two identical blocks each of mass ' M ' attached to the ends of a massless inextensible string which passes over a pulle 13. The radius of innermost orbit of hydrogen atom is $5.3 \times 10^{-11} \mathrm{~m}$. The radius of fourth allowed orbit 14. Two thin lenses have a combined power of +9D. When they are separated by a distance of 20 cm , their equivalent power be 15. Two simple harmonic progressive waves have displacements $\rightarrow \mathrm{y}_1=\mathrm{a}_1 \sin \left(\frac{2 \pi \ 16. The pressure inside a soap bubble A is 1.01 atmosphere and that in a soap bubble B is 1.02 atmosphere. The ratio of volu 17. A bicycle wheel of radius ' $R$ ' has ' $n$ ' spokes. It is rotating at the rate of ' $F$ ' r.p.m. perpendicular to the 18. Choose the correct answer. When a point of suspension of pendulum is moved vertically upward with acceleration ' $a$ ', 19. When a metallic surface is illuminated with a radiation of wavelength ' $\lambda$ ', the stopping potential is ' $V$ '. 20. The magnetic field at the centre of a current carrying circular coil of area ' $A$ ' is ' $B$ '. The magnetic moment of 21. The P-V graph of an ideal gas, cycle is shown. The adiabatic process is described by the region 22. A galvanometer of resistance ' $G$ ' is shunted by resistance of 'S' ohm. To keep the main current in the circuit unchan 23. In an A.C. circuit, the potential difference ' $V$ ' and current 'I' are given respectively by $\mathrm{V}=100 \sin (100 24. An annular ring has mass 10 kg and inner and outer radii are 10 m and 5 m respectively. Its moment of inertia about an a 25. Railway track is made of steel segments separated by small gaps to allow for linear expansion. The segment of track is 1 26. A wire under tension 225 N produces 6 beats per second when it is tuned with a fork. When the tension changes to 256 N , 27. In the third orbit of hydrogen atom the energy of an electron ' $E$ '. In the fifth orbit of helium $(Z=2)$ the energy o 28. At S.T.P., the mean free path of gas molecule is 1500 d , where ' $d$ ' is diameter of molecule. What will be the mean f 29. Three charges are placed at the vertices of an equilateral triangle as shown in the figure. For what value of charge ' $ 30. One mole of an ideal gas at an initial temperature of ' $T$ ' $K$ does ' $6 R$ ' of work adiabatically. If the ratio of 31. In a Young's double slit experiment, the source is white light. One of the holes is covered by a red filter and another 32. Glycerine of density $1.25 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$ is flowing in conical shaped horizontal pipe. Crosss 33. In an NPN transistor $10^{10}$ electrons enter the emitter in $10^{-6} \mathrm{~s}$ and $2 \%$ electrons recombine with 34. Velocity of sound waves in air is $330 \mathrm{~m} / \mathrm{s}$. For a particular sound wave in air, path difference of 35. A particle is performing uniform circular motion along the circumference of the circle of diameter 1 m with frequency 4 36. A uniformly charged conducting sphere of diameter 14 cm has surface charge density of $40 \mu \mathrm{Cm}^{-2}$. The tot 37. The acceleration of a moving body can be found from 38. Two identical current carrying coils with same centre are placed with their planes perpendicular to each other. If curre 39. The frequency ' $v_{\mathrm{m}}$ ' corresponding to which the energy emitted by a black body is maximum may vary with th 40. The resistances in the left and right gap of a metre bridge are $40 \Omega$ and $60 \Omega$ respectively. When the bridg 41. The magnitude of gravitational field at distance ' $r_1$ ' and ' $r_2$ ' from the centre of a uniform sphere of radius ' 42. Three masses $500 \mathrm{~g}, 300 \mathrm{~g}$ and 100 g are suspended at the end of spring as shown in figure and are 43. The electrostatic potential inside a charged spherical ball is given by $\mathrm{V}=\mathrm{ar}^2+\mathrm{b}$ where ' r 44. In the given circuit, when $S_1$ is closed, the capacitor gets fully charged. Now $\mathrm{S}_1$ is open and $\mathrm{S} 45. A plane mirror produces a magnification of 46. The work function of metal ' $A$ ' and ' $B$ ' are in the ratio $1: 2$. If light of frequency ' $f$ ' and ' $2 f$ ' is i 47. The telescopes, for a given wavelength, the objectives with large aperture are used for 48. A circuit having a self inductance of 1 henry carries a current of 1 A . To prevent the sparking when the circuit is bro 49. An air column in a closed organ pipe vibrating in unison with a fork, produces second overtone. The vibrating air column 50. At certain place a magnet makes 30 oscillations per minute. At another place if the magnetic induction is increased by t

MHT CET 2024 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

$$\int \log (1+x)^{1+x} \mathrm{~d} x=$$

$(1+x)^2 \log (1+x)-\frac{1}{2}+\mathrm{c}$, where c is a constant of integration.

$\frac{(1+x)^2}{2} \log (1+x)+\mathrm{c}$, where c is a constant of integration.

$\frac{(1+x)^2}{2}\left[\log (1+x)-\frac{1}{2}\right]+\mathrm{c}$, where c is a constant of integration.

$\frac{1+x}{2} \log (1+x)+\mathrm{c}$, where c is a constant of integration.

MHT CET 2024 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

$$\int\left(\frac{x+2}{x+4}\right)^2 \cdot e^x \mathrm{~d} x=$$

$\mathrm{e}^x\left(\frac{x}{x+4}\right)+\mathrm{c}$, where c is a constant of integration.

$\mathrm{e}^x\left(\frac{x+2}{x+4}\right)+\mathrm{c}$, where c is a constant of integration.

$\mathrm{e}^x\left(\frac{x-2}{x+4}\right)+\mathrm{c}$, where c is a constant of integration.

$\mathrm{e}^x\left(\frac{2 x}{x+4}\right)+\mathrm{c}$, where c is a constant of integration.

MHT CET 2024 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

In $\triangle A B C$, with usual notations, if $\frac{1}{b+c}+\frac{1}{c+a}=\frac{3}{a+b+c}$, then $m \angle C$ is equal to

$\frac{\pi}{3}$

$\frac{\pi}{2}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

MHT CET 2024 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

If $\mathrm{a}>0$ and $\mathrm{z}=\frac{(1+\mathrm{i})^2}{\mathrm{a}-\mathrm{i}}, \mathrm{i}=\sqrt{-1}$, has magnitude $\sqrt{\frac{2}{5}}$ then $\bar{z}$ is equal to

$\frac{1}{5}-\frac{3}{5} \mathrm{i}$

$-\frac{1}{5}-\frac{3}{5} \mathrm{i}$

$-\frac{1}{5}+\frac{3}{5} \mathrm{i}$

$-\frac{3}{5}-\frac{1}{5} \mathrm{i}$

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