MHT CET 2023 10th May Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Identify the compound with highest acidic strength from following. 2. Which of the following species is NOT isoelectronic with neon? 3. Conductivity of a solution is $$1.26 \times 10^{-2} \Omega^{-1} \mathrm{~cm}^{-1}$$ Calculate molar conductivity for $$0 4. Identify the molecule from following that does NOT involve $$\mathrm{sp}^3$$ hybridisation. 5. Which among the following compounds is hemiacetal? 6. Calculate the concentration of $$\mathrm{H}^{+}$$ ions in a solution if pOH is 11. 7. Identify the name of compound from following. 8. Identify the physical quantity that is measured in Candela. 9. Calculate the edge length of unit cell of metal which crystallises to bcc structure. (Radius of metal atom $$=173 \mathr 10. What is new temperature of a gas when its initial volume $$3 \mathrm{~dm}^3$$ at $$300 \mathrm{~K}$$ is doubled at const 11. Which among the following phenols does NOT correctly match with their IUPAC names? 12. Which among following statements is NOT true according to principles of green chemistry? 13. What is the value of effective atomic number of cobalt in $$\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$$ 14. For the reaction, $$3 \mathrm{~I}+\mathrm{S}_2 \mathrm{O}_8^{2-} \rightarrow \mathrm{I}_3^{-}+2 \mathrm{SO}_4^{2-}$$, at 15. What is the total number of Bravais lattices present for different crystal systems? 16. Identify compound $$\mathrm{Y}$$ in the following reaction. $$\mathrm{C}_2 \mathrm{H}_5 \mathrm{Cl}+\mathrm{Y} \stackrel 17. Aniline is treated with $$\mathrm{NaNO}_2+\mathrm{HCl}$$ at low temperature to form: 18. Which of the following is NOT a difficulty in setting SHE? 19. Lewis acid is a substance that : 20. Which among the following $$\alpha$$-amino acids does NOT have chiral carbon atom? 21. The difference between $$\Delta \mathrm{H}$$ and $$\Delta \mathrm{U}$$ is usually significant for systems consisting of 22. Which of the following elements is doped with to obtain fibre amplifiers for optical fibre communication system? 23. What is the half life of a first order reaction if rate constant is $$4.2 \times 10^{-2}$$ per day? 24. What type of solution is the ethyl alcohol in water? 25. Which among the following colours is obtained in Schiff test of aldehydes? 26. Which from following monomers is used to prepare thermocol? 27. Which of the following is character of lyophilic colloid? 28. Find the depression in freezing point of solution when 3.2 gram non volatile solute with molar mass $$128 \mathrm{~gram} 29. What is the value of $$x$$ in order to balance following redox reaction? $$\mathrm{Mn}_{(\mathrm{aq})}^{2+}+x \mathrm{Cl 30. The reaction, $$3 \mathrm{ClO}^{-} \rightarrow \mathrm{ClO}_3^{-}+2 \mathrm{Cl}^{-}$$ occurs in two steps: i. $$\quad 2 31. Acetic acid dissociated to $$1.20 \%$$ in its $$0.01 \mathrm{~M}$$ solution. What is the value of its dissociation const 32. The structure of functional group of secondary amide is : 33. Which of the following solutions exhibits lowest value of boiling point elevation assuming complete dissociation? 34. Identify heteroleptic complex from following. 35. Which among the following statements of group-1 elements is NOT true? 36. Identify glycosidic linkage present in lactose. 37. Which of the following compounds reacts with $$\mathrm{HBr}$$ to form 1-Bromo-1-methylcyclohexane? 38. Identify degenerate orbitals from following for hydrogen atom. 39. Identify the product P obtained in following reaction. Benzene + ozone (excess) $$\stackrel{\mathrm{CCl}_4}{\longrightar 40. Identify strongest oxoacid of halogen from following. 41. Identify the reagent $$\mathrm{R}$$ used in the reaction stated below. Benzene diazonium chloride $$+\mathrm{R} \rightar 42. Identify lanthanoid element from following. 43. What is change in internal energy when system releases $$8 \mathrm{~kJ}$$ of heat and performs $$660 \mathrm{~J}$$ of wo 44. Identify the method used to obtain $$\mathrm{SO}_2$$ gas in industry. 45. Which among the following compounds reacts fastly with $$\mathrm{HBr}$$ ? 46. Identify biodegradable polymer from following. 47. What mass of $$\mathrm{Mg}$$ is produced during electrolysis of molten $$\mathrm{MgCl}_2$$ by passing $$2 \mathrm{~amp}$ 48. Calculate the final volume when 2 moles of an ideal gas expand from $$3 \mathrm{~dm}^3$$ at constant external pressure 1 49. Calculate the molar mass of an element with density $$2.7 \mathrm{~g} \mathrm{~cm}^{-3}$$ that forms fcc structure. $$\l 50. Identify ketone from the following.

Mathematics

1. A group consists of 8 boys and 5 girls, then the number of committees of 5 persons that can be formed, if committee cons 2. Scalar projection of the line segment joining the points $$\mathrm{A}(-2,0,3), \mathrm{B}(1,4,2)$$ on the line whose dir 3. For a binomial variate $$\mathrm{X}$$ with $$\mathrm{n}=6$$ if $$P(X=4)=\frac{135}{2^{12}}$$, then its variance is 4. If $$\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=2 \hat{\mathr 5. The number of integral values of $$\mathrm{p}$$ in the domain $$[-5,5]$$, such that the equation $$2 x^2+4 x y-p y^2+4 x 6. An open metallic tank is to be constructed, with a square base and vertical sides, having volume 500 cubic meter. Then t 7. The p.d.f. of a discrete random variable is defined as $$\mathrm{f}(x)=\left\{\begin{array}{l} \mathrm{k} x^2, 0 \leq x 8. The variance, for first six prime numbers greater than 5, is 9. The value of $$\lim _\limits{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}$$ is 10. The points $$(1,3),(5,1)$$ are opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line 11. Considering only the principal values of an inverse function, the set $$\mathrm{A}=\left\{x \geq 0 / \tan ^{-1} x+\tan ^ 12. The line $$\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$$ lies in the plane $$x+3 y-\alpha z+\beta=0$$, then the value of 13. The vector projection of $$\overline{\mathrm{AB}}$$ on $$\overline{\mathrm{CD}}$$, where $$A \equiv(2,-3,0), B \equiv(1, 14. If the circles $$x^2+y^2=9$$ and $$x^2+y^2+2 \alpha x+2 y+1=0$$ touch each other internally, then the value of $$\alpha^ 15. If $$y=\cos ^{-1}\left(\frac{\mathrm{a}^2}{\sqrt{x^4+\mathrm{a}^4}}\right)$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$ 16. The population $$\mathrm{P}=\mathrm{P}(\mathrm{t})$$ at time $$\mathrm{t}$$ of certain species follows the differential 17. The vertices of the feasible region for the constraints $$x+y \leq 4, x \leq 2, y \leq 1, x+y \geq 1, x, y \geq 0$$ are 18. The value of $$\tan \frac{\pi}{8}$$ is 19. If $$B=\left[\begin{array}{lll}1 & \alpha & 2 \\ 1 & 2 & 2 \\ 2 & 3 & 3\end{array}\right]$$ is the adjoint of a $$3 \tim 20. The logical statement $$[\sim(\sim p \vee q) \vee(p \wedge r)] \wedge(\sim q \wedge r)$$ is equivalent to 21. If $$w=\frac{z}{z-\frac{1}{3} i}$$ and $$|w|=1, i=\sqrt{-1}$$, then $$z$$ lies on 22. If one side of a triangle is double the other and the angles opposite to these sides differ by $$60^{\circ}$$, then the 23. If $$\int \sqrt{\frac{x-7}{x-9}} d x=A \sqrt{x^2-16 x+63}+\log \left|(x-8)+\sqrt{x^2-16 x+63}\right|+c,$$ (where $$\math 24. A player tosses 2 fair coins. He wins ₹5 if 2 heads appear, ₹ 2 if one head appears and ₹ 1 if no head appears. Then the 25. Area of the region bounded by the curve $$y=\sqrt{49-x^2}$$ and $$\mathrm{X}$$-axis is 26. The solution of the equation $$\tan ^{-1}(1+x)+\tan ^{-1}(1-x)=\frac{\pi}{2}$$ is 27. The differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{\sqrt{1-y^2}}{y}$$ determines a family of circles w 28. A square plate is contracting at the uniform rate $$4 \mathrm{~cm}^2 / \mathrm{sec}$$, then the rate at which the perime 29. If the function $$\mathrm{f}(x)$$ is continuous in $$0 \leq x \leq \pi$$, then the value of $$2 a+3 b$$ is where $$f(x)= 30. For $$x>1$$, if $$(2 x)^{2 y}=4 \mathrm{e}^{2 x-2 y}$$, then $$(1+\log 2 x)^2 \frac{\mathrm{d} y}{\mathrm{~d} x}$$ is eq 31. The vectors are $$\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}, \bar{b}=\hat{i}+\hat{j}$$. If $$\bar{c}$$ is a vector such that $ 32. $$\int \frac{1}{7-6 x-x^2} d x=$$ 33. $$\int \frac{d x}{\sin x+\cos x}=$$ 34. A ladder of length $$17 \mathrm{~m}$$ rests with one end against a vertical wall and the other on the level ground. If t 35. Let $$\mathrm{P}$$ be a plane passing through the points $$(2,1,0),(4,1,1)$$ and $$(5,0,1)$$ and $$R$$ be the point $$(2 36. The co-ordinates of the point, where the line through $$A(3,4,1)$$ and $$B(5,1,6)$$ crosses the $$\mathrm{XZ}$$-plane, a 37. The number of possible solutions of $$\sin \theta+\sin 4 \theta+\sin 7 \theta=0, \theta \in(0, \pi)$$ are 38. If $$\mathrm{I}=\int \frac{\mathrm{d} x}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$$, then $$\mathrm{I}$$ is 39. If $$\bar{a}=\hat{i}+2 \hat{j}+\hat{k}, \bar{b}=\hat{i}-\hat{j}+\hat{k}, \bar{c}=\hat{i}+\hat{j}-\hat{k}$$, then a vecto 40. The number of solutions of $$\tan x+\sec x=2 \cos x$$ in $$[0,2 \pi]$$ are 41. If $$\int_\limits0^{\frac{1}{2}} \frac{x^2}{\left(1-x^2\right)^{\frac{3}{2}}} \mathrm{~d} x=\frac{\mathrm{k}}{6}$$, then 42. General solution of the differential equation $$\cos x(1+\cos y) \mathrm{d} x-\sin y(1+\sin x) \mathrm{d} y=0$$ is 43. If the line $$a x+b y+c=0$$ is a normal to the curve $$x y=1$$, then 44. Let $$\bar{a}, \bar{b}, \bar{c}$$ be three non-zero vectors, such that no two of them are collinear and $$(\bar{a} \time 45. If $$\mathrm{f}(x)=\mathrm{e}^x, \mathrm{~g}(x)=\sin ^{-1} x$$ and $$\mathrm{h}(x)=\mathrm{f}(\mathrm{g}(x))$$, then $$\ 46. The given circuit is equivalent to 47. A kite is $$120 \mathrm{~m}$$ high and $$130 \mathrm{~m}$$ of string is out. If the kite is moving away horizontally at 48. $$\mathrm{ABC}$$ is a triangle in a plane with vertices $$\mathrm{A}(2,3,5), \mathrm{B}(-1,3,2)$$ and $$\mathrm{C}(\lamb 49. Three critics review a book. For the three critics the odds in favor of the book are $$2: 5, 3: 4$$ and $$4: 3$$ respect 50. $$\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R} ; \mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}$$ are two functions such

Physics

1. An open organ pipe having fundamental frequency (n) is in unison with a vibrating string. If the tube is dipped in water 2. A graph of magnetic flux $$(\phi)$$ versus current (I) is plotted for four inductors A, B, C, D. Larger value of self in 3. An electron accelerated through a potential difference '$$V_1$$' has a de-Broglie wavelength '$$\lambda$$'. When the pot 4. In case of a stationary wave pattern which of the following statement is CORRECT? 5. If 'I' is moment of inertia of a thin circular disc about an axis passing through the tangent of the disc and in the pla 6. A parallel plate capacitor has plate area '$$\mathrm{A}$$' and separation between plates is '$$d$$'. It is charged to a 7. The shortest wavelength in the Balmer series of hydrogen atom is equal to the shortest wavelength in the Brackett series 8. If the length of stretched string is reduced by $$40 \%$$ and tension is increased by $$44 \%$$ then the ratio of final 9. A square loop of area $$25 \mathrm{~cm}^2$$ has a resistance of $$10 \Omega$$. This loop is placed in a uniform magnetic 10. Two capacitors $$\mathrm{C}_1=3 \mu \mathrm{F}$$ and $$\mathrm{C}_2=2 \mu \mathrm{F}$$ are connected in series across d. 11. To obtain the truth-table shown, from the following logic circuit, the gate G should be 12. An electric dipole consisting of two opposite charges of $$2 \times 10^{-6} \mathrm{C}$$ separated by a distance of $$3 13. In insulators 14. Seven identical discs each of mass $$M$$ and radius $$\mathrm{R}$$ are arranged in a hexagonal plane pattern so as to to 15. A satellite moves in a stable circular orbit round the earth if (where $$\mathrm{V}_{\mathrm{H}}, \mathrm{V}_{\mathrm{c} 16. The mean electrical energy density between plates of a charged air capacitor is (where $$\mathrm{q}=$$ charge on capacit 17. A person is observing a bacteria through a compound microscope. For better observation and to improve its resolving powe 18. The inductive reactance of a coil is '$$\mathrm{X}_{\mathrm{L}}$$'. If the inductance of a coil is tripled and frequency 19. In the circuit shown the ratio of quality factor and the bandwidth is 20. Water flows through a horizontal pipe at a speed '$$\mathrm{V}$$'. Internal diameter of the pipe is '$$\mathrm{d}$$'. If 21. In Young's double slit experiment the separation between the slits is doubled without changing other setting of the expe 22. A body is released from the top of a tower '$$\mathrm{H}$$' metre high. It takes $$t$$ second to reach the ground. The h 23. There is a second's pendulum on the surface of earth. It is taken to the surface of planet whose mass and radius are twi 24. Two long parallel wires carrying currents $$8 \mathrm{~A}$$ and $$15 \mathrm{~A}$$ in opposite directions are placed at 25. A body of mass 200 gram is tied to a spring of spring constant $$12.5 \mathrm{~N} / \mathrm{m}$$, while other end of spr 26. Which of the following is NOT involved in the formation of secondary rainbow? 27. For a satellite orbiting around the earth in a circular orbit, the ratio of potential energy to kinetic energy at same h 28. Maximum kinetic energy of photon is '$$E$$' when wavelength of incident radiation is '$$\lambda$$'. If wavelength of inc 29. Consider the Doppler effect in two cases. In the first case, an observer moves towards a stationary source of sound with 30. According to Curie's law in magnetism, the correct relation is ( $$\mathrm{M}=$$ magnetization in paramagnetic sample, $ 31. A double convex air bubble in water behaves as 32. Three liquids have same surface tension and densities $$\rho_1, \rho_2$$, and $$\rho_3\left(\rho_1>\rho_2>\rho_3\right)$ 33. If a lighter body of mass '$$\mathrm{M}_1$$' and velocity '$$\mathrm{V}_1$$' and a heavy body (mass $$M_2$$ and velocity 34. Electron of mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$' is travelling with speed '$$v$$' along a circular path of 35. In a series LR circuit, $$X_L=R$$, power factor is $$P_1$$. If a capacitor of capacitance $$C$$ with $$X_C=X_L$$ is adde 36. If only $$1 \%$$ of total current is passed through a galvanometer of resistance '$$G$$' then the resistance of the shun 37. A voltmeter of resistance $$150 \Omega$$ connected across a cell of e.m.f. $$3 \mathrm{~V}$$ reads $$2.5 \mathrm{~V}$$. 38. Two conducting circular loops of radii '$$R_1$$' and '$$R_2$$' are placed in the same plane with their centres coincidin 39. The average force applied on the walls of a closed container depends on $$T^x$$ where $$T$$ is the temperature of an ide 40. A black body radiates maximum energy at wavelength '$$\lambda$$' and its emissive power is $$\mathrm{E}$$. Now due to ch 41. A Carnot engine with efficiency $$50 \%$$ takes heat from a source at $$600 \mathrm{~K}$$. To increase the efficiency to 42. The amplitude of a particle executing S.H.M. is $$3 \mathrm{~cm}$$. The displacement at which its kinetic energy will be 43. A piece of metal at $$850 \mathrm{~K}$$ is dropped in to $$1 \mathrm{~kg}$$ water at $$300 \mathrm{~K}$$. If the equilib 44. Heat energy is incident on the surface at the rate of X J/min . If '$$a$$' and '$$r$$' represent coefficient of absorpti 45. Identify the mismatch out of the following. 46. Two sources of light $$0.6 \mathrm{~mm}$$ apart and screen is placed at a distance of $$1.2 \mathrm{~m}$$ from them. A l 47. The ratio of longest to shortest wavelength emitted in Paschen series of hydrogen atom is 48. The height of liquid column raised in a capillary tube of certain radius when dipped in liquid '$$A$$' vertically is $$5 49. A particle of mass '$$\mathrm{m}$$' is rotating along a circular path of radius '$$r$$' having angular momentum '$$L$$'. 50. A sample of gas at temperature $$T$$ is adiabatically expanded to double its volume. The work done by the gas in the pro

MHT CET 2023 10th May Morning Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{1}{7-6 x-x^2} d x=$$

$$\frac{1}{4} \log \left(\frac{7+x}{1-x}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$\frac{1}{8} \log \left(\frac{7+x}{1-x}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$\frac{1}{16} \log \left(\frac{7+x}{1-x}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$\frac{1}{32} \log \left(\frac{7+x}{1-x}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

MHT CET 2023 10th May Morning Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{d x}{\sin x+\cos x}=$$

$$\sqrt{2} \log \tan \left(x+\frac{\pi}{4}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$\frac{1}{\sqrt{2}} \log \tan \left(\frac{x}{2}+\frac{\pi}{8}\right)+c$$, where c is a constant of integration.

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

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

MHT CET 2023 10th May Morning Shift

MCQ (Single Correct Answer)

-0

A ladder of length $$17 \mathrm{~m}$$ rests with one end against a vertical wall and the other on the level ground. If the lower end slips away at the rate of $$1 \mathrm{~m} / \mathrm{sec}$$., then when it is $$8 \mathrm{~m}$$ away from the wall, its upper end is coming down at the rate of

$$\frac{5}{8} \mathrm{~m} / \mathrm{sec}$$.

$$\frac{8}{15} \mathrm{~m} / \mathrm{sec}$$.

$$\frac{-8}{15} \mathrm{~m} / \mathrm{sec}$$.

$$\frac{15}{8} \mathrm{~m} / \mathrm{sec}$$.

MHT CET 2023 10th May Morning Shift

MCQ (Single Correct Answer)

-0

Let $$\mathrm{P}$$ be a plane passing through the points $$(2,1,0),(4,1,1)$$ and $$(5,0,1)$$ and $$R$$ be the point $$(2,1,6)$$. Then image of $$R$$ in the plane $$P$$ is

$$(6,5,2)$$

$$(4,3,2)$$

$$(6,5,-2)$$

$$(3,4,-2)$$

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