MHT CET 2023 9th May Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Which of the following molecules has no lone pair of electrons on central atom? 2. Calculate $$\Delta \mathrm{G}^{\circ}$$ for the cell: $$\mathrm{Sn}_{(\mathrm{s})}\left|\mathrm{Sn}_{(\mathrm{1M})}^{2+} 3. Which from following statements is NOT correct? 4. A compound made of elements $$\mathrm{A}$$ and $$\mathrm{B}$$ form fcc structure. Atoms of A are at the corners and atom 5. What are different possible oxidation states exhibited by scandium? 6. Which from following is the slope of the graph of rate versus concentration of the reactant for first order reaction? 7. What is the packing efficiency of silver metal in its unit cell? 8. Which from following polymers is obtained from $$\mathrm{C}_2 \mathrm{~F}_4$$ ? 9. Calculate current in ampere required to deposit $$4.8 \mathrm{~g} ~\mathrm{Cu}$$ from it's salt solution in 30 minutes. 10. Identify number of moles of donor atoms in $$2 \mathrm{n}$$ mole of $$\mathrm{SCN}^{-}$$. 11. $$0.2 ~\mathrm{M}$$ aqueous solution of glucose has osmotic pressure 4.9 atm at $$300 \mathrm{~K}$$. What is the concent 12. Identify the product when phenol is heated with zinc dust. 13. Identify the product '$$\mathrm{B}$$' in the following reaction. Dry ice $$\mathrm{\mathrel{\mathop{\kern0pt\longrightar 14. Which among the following reactions exhibits $$\Delta \mathrm{H}=\Delta \mathrm{U}$$ ? 15. A buffer solution is prepared by mixing 0.2 M sodium acetate and 0.1 M acetic acid. If pK$$_a$$ for acetic acid is 4.7, 16. A solution of nonvolatile solute is obtained by dissolving $$3.5 \mathrm{~g}$$ in $$100 \mathrm{~g}$$ solvent has boilin 17. At $$0{ }^{\circ} \mathrm{C}$$ a gas occupies 22.4 liters. What is the temperature in Kelvin to reach the volume of 224 18. Which from following rule / principle states that "No two electrons in an atom can have the same set of four quantum num 19. Which from following molecules exhibits highest acidic nature? 20. What is the number of moles of $$\mathrm{sp}^2$$ hybrid carbon atoms in one mole of hexa-1,4-diyne? 21. Which of the following is NOT obtained when a mixture of methyl chloride and n-propyl chloride is treated with sodium me 22. Which carbon atoms (numbered from $$C_1$$ to $$C_6$$ ) are involved in the formation of ring structure of glucose? 23. Calculate the amount of reactant in percent that remains after 60 minutes involved in first order reaction. $$\left(\mat 24. Which salt from following forms aqueous solution having $$\mathrm{pH}$$ less than 7 ? 25. Identify neutral ligand from following 26. Identify the product 'B' in following reaction. Ethyl phenyl ketone $$\mathrm{\buildrel {{H_2}N - N{H_2}} \over \longri 27. Which of the following amines undergoes acylation reaction? 28. What is the IUPAC name of following compound? 29. What is the number of unit cells when one mole atom of a metal that forms simple cubic structure? 30. Identify the gas produced due to reduction of $$\mathrm{NH}_4^{+}$$ ions at cathode during working of dry cell. 31. Which of the following is secondary benzylic alcohol? 32. Find the value of spin only magnetic moment for chromium cation in +2 state. 33. An ideal gas expands by performing $$200 \mathrm{~J}$$ of work, during this internal energy increases by $$432 \mathrm{~ 34. Calculate the wavenumber of the photon emitted during transition from the orbit of $$n=2$$ to $$n=1$$ in hydrogen atom. 35. Calculate the value of $$\Delta G$$ for following reaction at $$300 \mathrm{~K}$$. $$\begin{aligned} & \mathrm{H}_2 \mat 36. What is the oxidation state of carbon in $$\mathrm{CaC}_2$$ and $$\mathrm{K}_2 \mathrm{C}_2 \mathrm{O}_4$$ respectively? 37. What is the number of moles of water molecules required to prepare n moles of methane from n moles of methyl magnesium i 38. Which of the following metals is used as catalyst in manufacture of sulphuric acid by contact process? 39. The rate for reaction $$\mathrm{A}+\mathrm{B} \rightarrow$$ product, is $$1.8 \times 10^{-2} \mathrm{~mol} \mathrm{~dm}^ 40. Which of the following concentration terms depends on temperature? 41. What type of reaction is the formation of aldol from aldehyde? 42. Identify homopolymer from following. 43. Identify the chiral molecule from following. 44. What is the mass in gram of 1 atom of an element if its atomic mass is $$10 ~\mathrm{u}$$ ? 45. Solubility of a salt $$\mathrm{A}_2 \mathrm{~B}_3$$ is $$1 \times 10^{-3} \mathrm{~mol} \mathrm{~dm}^{-3}$$. What is the 46. Identify the element having general electronic configuration $$\mathrm{ns}^2 \mathrm{np}^4$$ from following. 47. Identify the product $$\mathrm{A}$$ obtained in the following reaction. Phenol + Conc. Nitric acid $$\stackrel{\text { c 48. What is the value of specific rotation exhibited by glucose molecule? 49. What type of information is collected using scanning electron microscopy? 50. Identify the reagent $$\mathrm{A}$$ in the following conversion. Alkyl halide $$\stackrel{A}{\longrightarrow}$$ Alkyl ni

Mathematics

1. If two vertices of a triangle are $$\mathrm{A}(3,1,4)$$ and $$\mathrm{B}(-4,5,-3)$$ and the centroid of the triangle is 2. In a Binomial distribution with $$\mathrm{n}=4$$, if $$2 \mathrm{P}(\mathrm{X}=3)=3 \mathrm{P}(\mathrm{X}=2)$$, then the 3. Let two non-collinear vectors $$\hat{a}$$ and $$\hat{b}$$ form an acute angle. A point $$\mathrm{P}$$ moves, so that at 4. The number of solutions in $$[0,2 \pi]$$ of the equation $$16^{\sin ^2 x}+16^{\cos ^2 x}=10$$ is 5. The differential equation of all parabolas, whose axes are parallel to $$\mathrm{Y}$$-axis, is 6. The value of $$c$$ of Lagrange's mean value theorem for $$f(x)=\sqrt{25-x^2}$$ on $$[1,5]$$ is 7. $$\int \frac{x+1}{x\left(1+x \mathrm{e}^x\right)^2} \mathrm{~d} x=$$ 8. If $$Z_1=4 i^{40}-5 i^{35}+6 i^{17}+2, Z_2=-1+i$$, where $$i=\sqrt{-1}$$, then $$\left|Z_1+Z_2\right|=$$ 9. The approximate value of $$\log _{10} 998$$ is (given that $$\log _{10} \mathrm{e}=0.4343$$ ) 10. If $$\sin ^{-1} x+\cos ^{-1} y=\frac{3 \pi}{10}$$, then the value of $$\cos ^{-1} x+\sin ^{-1} y$$ is 11. The area (in sq. units) of the region $$\mathrm{A}=\left\{(x, y) / \frac{y^2}{2} \leq x \leq y+4\right\}$$ is 12. $$\mathrm{A}, \mathrm{B}, \mathrm{C}$$ are three events, one of which must and only one can happen. The odds in favor of 13. The value of $$\alpha$$, so that the volume of the parallelopiped formed by $$\hat{i}+\alpha \hat{j}+\hat{k}, \hat{j}+\a 14. Two sides of a triangle are $$\sqrt{3}+1$$ and $$\sqrt{3}-1$$ and the included angle is $$60^{\circ}$$, then the differe 15. The standard deviation of the following distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-co 16. The maximum value of xy when x + 2y = 8 is 17. If truth values of statements $$\mathrm{p}, \mathrm{q}$$ are true, and $$\mathrm{r}$$, $$s$$ are false, then the truth v 18. The rate of change of $$\sqrt{x^2+16}$$ with respect to $$\frac{x}{x-1}$$ at $$x=5$$ is 19. If $$x^2+y^2=\mathrm{t}+\frac{1}{\mathrm{t}}$$ and $$x^4+y^4=\mathrm{t}^2+\frac{1}{\mathrm{t}^2}$$, then $$\frac{\mathrm 20. Two tangents to the circle $$x^2+y^2=4$$ at the points $$\mathrm{A}$$ and $$\mathrm{B}$$ meet at the point $$\mathrm{P}( 21. $$\mathrm{f}: \mathbb{R}-\left(-\frac{3}{5}\right) \rightarrow \mathbb{R}$$ is defined by $$f(x)=\frac{3 x-2}{5 x+3}$$, 22. The value of $$\cot \left(\sum_\limits{n=1}^{23} \cot ^{-1}\left(1+\sum_\limits{k=1}^n 2 k\right)\right)$$ is 23. An object is moving in the clockwise direction around the unit circle $$x^2+y^2=1$$. As it passes through the point $$\l 24. If feasible region is as shown in the figure, then the related inequalities are 25. $$\int \frac{\mathrm{e}^{\tan ^{-1} x}}{1+x^2}\left[\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+\cos ^{-1}\left(\frac{1-x^2}{ 26. If $$\mathrm{f}(x)$$ is a function satisfying $$\mathrm{f}^{\prime}(x)=\mathrm{f}(x)$$ with $$\mathrm{f}(0)=1$$ and $$\m 27. The foot of the perpendicular drawn from the origin to the plane is $$(4,-2,5)$$, then the Cartesian equation of the pla 28. $$\lim _\limits{x \rightarrow \frac{\pi}{2}} \frac{\cot x-\cos x}{(\pi-2 x)^3}$$ equals 29. If the distance between the parallel lines given by the equation $$x^2+4 x y+p y^2+3 x+q y-4=0$$ is $$\lambda$$, then $$ 30. The particular solution of the differential equation $$\left(1+y^2\right) \mathrm{d} x-x y \mathrm{~d} y=0$$ at $$x=1, y 31. If at the end of certain meeting, everyone had shaken hands with everyone else, it was found that 45 handshakes were exc 32. If $$\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}$$, then $$\cos ^2 48^{\circ}-\sin ^2 12^{\circ}$$ has the value 33. If $$A=\left[\begin{array}{cc}2 & -1 \\ -1 & 3\end{array}\right]$$, then the inverse of $$\left(2 A^2+5 A\right)$$ is 34. If $$ I=\int \frac{\sin x+\sin ^3 x}{\cos 2 x} d x=P \cos x+Q \log \left|\frac{\sqrt{2} \cos x-1}{\sqrt{2} \cos x+1}\rig 35. The negation of the statement $$(p \wedge q) \rightarrow(\sim p \vee r)$$ is 36. The probability mass function of random variable X is given by $$P[X=r]=\left\{\begin{array}{ll} \frac{{ }^n C_r}{32}, 37. The distance of a point $$(2,5)$$ from the line $$3 x+y+4=0$$ measured along the line $$L_1$$ and $$L_1$$ are same. If s 38. The distance of the point having position vector $$\hat{i}-2 \hat{j}-6 \hat{k}$$, from the straight line passing through 39. A vector $$\overrightarrow{\mathrm{n}}$$ is inclined to $$\mathrm{X}$$-axis at $$45^{\circ}$$, $$\mathrm{Y}$$-axis at $$ 40. If $$\cos ^{-1} x-\cos ^{-1} \frac{y}{3}=\alpha$$, where $$-1 \leq x \leq 1, -3 \leq y \leq 3, x \leq \frac{y}{3}$$, the 41. If $$\mathrm{f}(1)=1, \mathrm{f}^{\prime}(1)=3$$, then the derivative of $$\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathr 42. Three fair coins numbered 1 and 0 are tossed simultaneously. Then variance Var (X) of the probability distribution of ra 43. $$\int \frac{1}{\sin (x-a) \sin x} d x=$$ 44. The derivative of $$\mathrm{f}(\sec x)$$ with respect to $$g(\tan x)$$ at $$x=\frac{\pi}{4}$$, where $$f^{\prime}(\sqrt{ 45. The scalar product of the vector $$\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$$ with a unit vector along the sum 46. The number of discontinuities of the greatest integer function $$\mathrm{f}(x)=[x], x \in\left(-\frac{7}{2}, 100\right)$ 47. If $$[(\bar{a}+2 \bar{b}+3 \bar{c}) \times(\bar{b}+2 \bar{c}+3 \bar{a})] \cdot(\bar{c}+2 \bar{a}+3 \bar{b})=54$$ then th 48. A spherical raindrop evaporates at a rate proportional to its surface area. If originally its radius is $$3 \mathrm{~mm} 49. If the Cartesian equation of a line is $$6 x-2=3 y+1=2 z-2$$, then the vector equation of the line is 50. The volume of parallelopiped, whose coterminous edges are given by $$\overline{\mathrm{u}}=\hat{\mathrm{i}}+\hat{\mathrm

Physics

1. A rubber ball filled with water, having a small hole is used as the bob of a simple pendulum. The time period of such a 2. The ratio of wavelengths for transition of electrons from $$2^{\text {nd }}$$ orbit to $$1^{\text {st }}$$ orbit of Heli 3. For an intrinsic semiconductor $$\left(\mathrm{n}_{\mathrm{h}}\right.$$ and $$\mathrm{n}_{\mathrm{e}}$$ are the number o 4. A $$5.0 \mathrm{~V}$$ stabilized power supply is required to be designed using a $$12 \mathrm{~V}$$ DC power supply as i 5. A jar '$$\mathrm{P}$$' is filled with gas having pressure, volume and temperature $$\mathrm{P}, \mathrm{V}, \mathrm{T}$$ 6. The magnetic flux through a loop of resistance $$10 ~\Omega$$ varying according to the relation $$\phi=6 \mathrm{t}^2+7 7. A thin rod of length '$$L$$' is bent in the form of a circle. Its mass is '$$M$$'. What force will act on mass '$$m$$' p 8. The coil of an a.c. generator has 100 turns, each of cross-sectional area $$2 \mathrm{~m}^2$$. It is rotating at constan 9. A beam of unpolarized light passes through a tourmaline crystal A and then it passes through a second tourmaline crystal 10. The materials suitable for making electromagnets should have 11. A body falls on a surface of coefficient of restitution 0.6 from a height of $$1 \mathrm{~m}$$. Then the body rebounds t 12. In a diffraction pattern due to single slit of width '$$a$$', the first minimum is observed at an angle of $$30^{\circ}$ 13. A stone is projected vertically upwards with speed '$$v$$'. Another stone of same mass is projected at an angle of $$60^ 14. An electron (mass $$\mathrm{m}$$ ) is accelerated through a potential difference of '$$V$$' and then it enters in a magn 15. A capacitor, an inductor and an electric bulb are connected in series to an a.c. supply of variable frequency. As the fr 16. When both source and listener are approaching each other the observed frequency of sound is given by $$\left(V_L\right.$ 17. Water is flowing through a horizontal pipe in stream line flow. At the narrowest part of the pipe 18. The angle of prism is $$A$$ and one of its refracting surface is silvered. Light rays falling at an angle of incidence ' 19. The maximum velocity of a particle performing S.H.M. is '$$\mathrm{V}$$'. If the periodic time is made $$\left(\frac{1}{ 20. A conducting wire of length $$2500 \mathrm{~m}$$ is kept in east-west direction, at a height of $$10 \mathrm{~m}$$ from 21. For an electron moving in the $$\mathrm{n}^{\text {th }}$$ Bohr orbit the deBroglie wavelength of an electron is 22. A square lamina of side '$$b$$' has same mass as a disc of radius '$$R$$' the moment of inertia of the two objects about 23. A body weighs $$300 \mathrm{~N}$$ on the surface of the earth. How much will it weigh at a distance $$\frac{R}{2}$$ belo 24. To get the truth table shown, from the following logic circuit, the Gate G should be 25. For a gas having '$$\mathrm{X}$$' degrees of freedom, '$$\gamma$$' is ($$\gamma=$$ ratio of specific heats $$=\mathrm{C_ 26. A galvanometer of resistance $$\mathrm{G}$$ is shunted with a resistance of $$10 \%$$ of $$\mathrm{G}$$. The part of the 27. If an electron in a hydrogen atom jumps from an orbit of level $$n=3$$ to orbit of level $$n=2$$, then the emitted radia 28. Self inductance of solenoid is 29. The capacitance of a parallel plate capacitor is $$2.5 ~\mu \mathrm{F}$$. When it is half filled with a dielectric as sh 30. Equation of simple harmonic progressive wave is given by $$y=\frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \co 31. Two uniform brass rods $$A$$ and $$B$$ of length '$$l$$' and '$$2 l$$' and their radii '$$2 r$$' and '$$r$$' respectivel 32. In a single slit experiment, the width of the slit is doubled. Which one of the following statements is correct? 33. A gas at N.T.P. is suddenly compressed to $$\left(\frac{1}{4}\right)^{\text {th }}$$ of its original volume. The final p 34. The excess of pressure in a first soap bubble is three times that of other soap bubble. Then the ratio of the volume of 35. In a meter bridge experiment null point is obtained at $$l \mathrm{~cm}$$ from the left end. If the meter bridge wire is 36. A long straight wire carrying a current of $$25 \mathrm{~A}$$ rests on the table. Another wire PQ of length $$1 \mathrm{ 37. In a thermodynamic process, there is no exchange of heat between the system and surroundings. Then the thermodynamic pro 38. According to kinetic theory of gases, which one of the following statements is wrong? 39. The radii of two soap bubbles are $$r_1$$ and $$r_2$$. In isothermal condition they combine with each other to form a si 40. The rays of different colours fail to converge at a point after passing through a thick converging lens. This defect is 41. The ratio of potential difference that must be applied across parallel and series combination of two capacitors $$C_1$$ 42. The potential energy of charged parallel plate capacitor is $$v_0$$. If a slab of dielectric constant $$\mathrm{K}$$ is 43. A solid sphere rolls without slipping on an inclined plane at an angle $$\theta$$. The ratio of total kinetic energy to 44. Two discs of same mass and same thickness (t) are made from two different materials of densities '$$d_1$$' and '$$d_2$$' 45. When a string of length '$$l$$' is divided into three segments of length $$l_1, l_2$$ and $$l_3$$. The fundamental frequ 46. A seconds pendulum is placed in a space laboratory orbiting round the earth at a height '$$3 \mathrm{R}$$' from the eart 47. A solid metallic sphere has a charge $$+3 Q$$. Concentric with this sphere is a conducting spherical shell having charge 48. A closed organ pipe of length '$$L_1$$' and an open organ pipe contain diatomic gases of densities '$$\rho_1$$' and '$$\ 49. From a metallic surface photoelectric emission is observed for frequencies $$v_1$$ and $$v_2\left(v_1 > v_2\right)$$ of 50. In an $$\mathrm{AC}$$ circuit, the current is $$\mathrm{i}=5 \sin \left(100 \mathrm{t}-\frac{\pi}{2}\right) \mathrm{A}$$

MHT CET 2023 9th May Morning Shift

MCQ (Single Correct Answer)

-0

If $$\cos ^{-1} x-\cos ^{-1} \frac{y}{3}=\alpha$$, where $$-1 \leq x \leq 1, -3 \leq y \leq 3, x \leq \frac{y}{3}$$, then for all $$x, y$$ $$9 x^2-6 x y \cos \alpha+y^2$$ is equal to

$$\sin ^2 \alpha$$

$$3 \sin ^2 \alpha$$

$$9 \sin ^2 \alpha$$

$$\frac{4}{9} \sin ^2 \alpha$$

MHT CET 2023 9th May Morning Shift

MCQ (Single Correct Answer)

-0

If $$\mathrm{f}(1)=1, \mathrm{f}^{\prime}(1)=3$$, then the derivative of $$\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$$ at $$x=1$$ is

MHT CET 2023 9th May Morning Shift

MCQ (Single Correct Answer)

-0

Three fair coins numbered 1 and 0 are tossed simultaneously. Then variance Var (X) of the probability distribution of random variable $$\mathrm{X}$$, where $$\mathrm{X}$$ is the sum of numbers on the uppermost faces, is

0.7

0.75

0.65

0.62

MHT CET 2023 9th May Morning Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{1}{\sin (x-a) \sin x} d x=$$

$$ \sin \mathrm{a}(\log (\sin (x-\mathrm{a}) \cdot \operatorname{cosec} x))+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$\operatorname{cosec} a(\log (\sin (x-a) \cdot \operatorname{cosec} x))+c$$, where $$\mathrm{c}$$ is a constant of integration.

$$-\sin \mathrm{a}(\log (\sin (x-\mathrm{a}) \cdot \sin x))+\mathrm{c}$$, where c is a constant of integration.

$$-\operatorname{cosec} \mathrm{a}(\log (\sin (x-\mathrm{a}) \cdot \sin x))+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

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