MHT CET 2022 11th August Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. For the reaction $$\mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NH}_{3(\mathrm{~g})}$ 2. Identify the products obtained when chlorine reacts with hot and conc. $$\mathrm{NaOH}$$. 3. Which from following elements does NOT react with water? 4. Identify the type of hybridization involved in hexaaminecobalt (III) complex ion. 5. Calculate the solubility of a gas in water at $$0.8 \mathrm{~atm}$$ and $$25^{\circ} \mathrm{C}$$. [Henry's law constant 6. What is the value of temperature in degree Celsius at absolute zero ? 7. Which among the following reactions does NOT correctly match with its reagent? 8. Which among the following compounds is NOT prepared by Sandmeyer's reaction ? 9. Which among the following compounds undergoes SN$$^2$$ reaction fastly ? 10. Which of the following molecules possesses highest dipole-dipole interactions ? 11. What is the total volume occupied by atoms in bcc unit cell ? 12. Which among the following metals is involved in preparation of Grignard reagent ? 13. Which among the following properties of lanthanoids is NOT true? 14. Which of the following is a Lewis acid but NOT a Bronsted acid? 15. Which of the following aqueous solutions of salts will have highest $$\mathrm{pH}$$ value? 16. Which among the following compounds represents a soap molecule? 17. How long will it take to produce $$5.4 \mathrm{~g}$$ of $$\mathrm{Ag}$$ from molten $$\mathrm{AgCl}$$ by passing $$5 \ma 18. Which of the following is NOT an example of secondary voltaic cell? 19. What is the number of unpaired electrons in $$\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$$ complex? 20. Which among the following methods is used to prepare Grignard reagent? 21. Calculate the density of metal having volume of unit cell $$64 \times 10^{-24} \mathrm{~cm}^3$$ and molar mass of metal 22. Calculate the work done when 2 moles of an ideal gas expand from a volume of $$5 \mathrm{~dm}^3$$ to $$7 \times 10^{-3} 23. Which among the following pair of monomers does not generate polyamide polymer? 24. What type of following phenomena is NOT exhibited by adsorption? 25. Find the rate constant of first order reaction in second having half life of 2.5 hours. 26. Which nitrogen atom of pyrimidine base numbered from 1 to 6 is bonded with furanose sugar ? 27. Identify the element with smallest ionic radius in +3 oxidation state from following. 28. Identify the product in the following reaction. 29. Which among following compounds possesses highest number of N atoms in it ? 30. What is the bond order of CO molecule? 31. Which of the following is NOT hydrogen like species? 32. What is the intermediate compound formed when chlorobenzene is treated with fused $$\mathrm{NaOH}$$ under pressure? 33. If rate of reaction is given as $$\frac{1}{3} \frac{\mathrm{d}[\mathrm{x}]}{\mathrm{dt}}=-\frac{1}{2} \frac{\mathrm{d}[\ 34. Which among the following compounds contains highest number of chlorine atoms in their single molecule ? 35. What is the heat of formation of $$\mathrm{HCl}_{(\mathrm{g})}$$ from following equation? $$\mathrm{H}_{2(\mathrm{~g})}+ 36. Identify the concentration of the solution from following so that values of ,$$\Delta \mathrm{T}_{\mathrm{f}}$$ and $$\m 37. What is the product formed when cumene is air oxidised in presence of Co-naphthenate and further treated with dilute aci 38. Identify the use of polystyrene for household purposes. 39. Identify compound $$\mathrm{A}$$ in following reaction Benzene + Ozone (excess) $$\rightarrow$$ Benzenetriozonide $$\xri 40. Which from following pairs of compounds is an example of metamerism? 41. If $$\mathrm{Q}$$ is the heat liberated from the system and $$\mathrm{W}$$ is the work done on the system then first law 42. Calculate the number of atoms in 5 gram metal that crystallises to form simple cubic unit cell structure having edge len 43. Identify the molecule in which central atom undergoes $$\mathrm{sp}^3$$ hybridisation? 44. Which one of the following conversions does NOT involve either oxidation or reduction? 45. Calculate $$\wedge_0$$ of $$\mathrm{CH}_2 \mathrm{ClCOOH}$$ if $$\wedge_0$$ for $$\mathrm{HCl}, \mathrm{KCl}$$ and $$\ma 46. Identify the product A in the following reaction. 47. Calculate the amount of solute dissolved in 160 gram solvent that boils at $$85^{\circ} \mathrm{C}$$, the molar mass of 48. Identify ether from the following compounds. 49. Which from following polymers is used to obtain bristles for brushes? 50. What is the $$\mathrm{pH}$$ of $$2 \times 10^{-3} \mathrm{M}$$ solution of monoacidic weak base if it ionises to the ext

Mathematics

1. $$\int_\limits{\frac{\pi}{4}}^{\frac{3 \pi}{4}} \frac{\mathrm{d} x}{1+\cos x}$$ is equal to 2. If $$\tan ^{-1}\left(\frac{1-x}{1+x}\right)=\frac{1}{2} \tan ^{-1} x$$, then $$x$$ has the value 3. If $$p: \forall n \in I N, n^2+n$$ is an even number $$q: \forall n \in I N, n^2-n$$ is an odd numer, then the truth val 4. If the function $$f(x)=x^3-3(a-2) x^2+3 a x+7$$, for some $$a \in I R$$ is increasing in $$(0,1]$$ and decreasing in $$[ 5. If $$\bar{a}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{k}}, \bar{b}=x \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+(1-x) \hat{\ 6. If $$\cot (A+B)=0$$, then $$\sin (A+2 B)$$ is equal to 7. The joint equation of pair of lines through the origin and making an equilateral triangle with the line $$y = 5$$ is 8. If $$f(x)=\sqrt{\tan x}$$ and $$g(x)=\sin x \cdot \cos x$$ then $$\int \frac{f(x)}{g(x)} \mathrm{d} x$$ is equal to (whe 9. The general solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{3 x+y}{x-y}$$ is (where $$C 10. If $$A=\left[\begin{array}{lll}1 & 2 & 1 \\ 3 & 1 & 3\end{array}\right]$$ and $$B=\left[\begin{array}{ll}2 & 3 \\ 1 & 2 11. The distance between parallel lines $$\frac{x-1}{2}=\frac{y-2}{-2}=\frac{z-3}{1}$$ and $$\frac{x}{2}=\frac{y}{-2}=\frac{ 12. Maximum value of $$Z=5 x+2 y$$, subject to $$2 x-y \geq 2, x+2 y \leq 8$$ and $$x, y \geq 0$$ is 13. The value of $$\sin \left(2 \sin ^{-1} 0.8\right)$$ is equal to 14. A line makes the same angle '$$\alpha$$' with each of the $$x$$ and $$y$$ axes. If the angle '$$\theta$$', which it make 15. The negation of the statement pattern $$p \vee(q \rightarrow \sim r)$$ is 16. Let $$\bar{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\bar{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\ha 17. The incidence of occupational disease in an industry is such that the workmen have a $$10 \%$$ chance of suffering from 18. If $$y=\log \sqrt{\frac{1+\sin x}{1-\sin x}}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=\frac{\pi}{3}$$ is 19. The variance and mean of 15 observations are respectively 6 and 10 . If each observation is increased by 8 then the new 20. If $$y=\sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right)$$ then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ is equal to 21. The magnitude of the projection of the vector $$2 \hat{\mathbf{i}}+ 3\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ on the vector p 22. $$\matrix{ {f(x) = a{x^2} + bx + 1,} & {if} & {\left| {2x - 3} \right| \ge 2} \cr { = 3x + 2,} & {if} & {{1 \ove 23. If $$\bar{a}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \bar{b}=\hat{\boldsymbol{i}}-\hat{\boldsymb 24. A tetrahedron has verticles $$P(1,2,1), Q(2,1,3), R(-1,1,2)$$ and $$O(0,0,0)$$. Then the angle between the faces $$O P Q 25. The principal value of $$\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)$$ is 26. The differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{\sqrt{1-y^2}}{y}$$ determines a family of circles w 27. The value of the integral $$\int_\limits0^1 \sqrt{\frac{1-x}{1+x}} \mathrm{~d} x$$ is 28. If a question paper consists of 11 questions divided into two sections I and II. Section I consists of 6 questions and s 29. The area (in sq. units) of the region described by $$A=\left\{(x, y) / x^2+y^2 \leq 1\right.$$ and $$\left.y^2 \leq 1-x\ 30. A firm is manufacturing 2000 items. It is estimated that the rate of change of production $$P$$ with respect to addition 31. $$\int \frac{3 x-2}{(x+1)(x-2)^2} \mathrm{~d} x=$$ (where $$C$$ is a constant of integration) 32. If the normal to the curve $$y=f(x)$$ at the point $$(3,4)$$ makes an angle $$\left(\frac{3 \pi}{4}\right)^c$$ with posi 33. If $$P(A \cup B)=0.7, P(A \cap B)=0.2$$, then $$P\left(A^{\prime}\right)+P\left(B^{\prime}\right)$$ is 34. If $$\lim _\limits{x \rightarrow 1} \frac{x^2-a x+b}{(x-1)}=5$$, then $$(a+b)$$ is equal to 35. If $$y=\cos \left(\sin x^2\right)$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=\sqrt{\frac{\pi}{2}}$$ is 36. Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then mean of number of kings is 37. The polar co-ordinates of the point, whose Cartesian coordinates are $$(-2 \sqrt{3}, 2)$$, are 38. Let $$z$$ be a complex number such that $$|z|+z=3+i, i=\sqrt{-1}$$, then $$|z|$$ is equal to 39. Given $$A=\left[\begin{array}{ccc}x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z\end{array}\right]$$, if $$x y z=60$$ and $$8 x+4 y 40. If $$y^{\frac{1}{m}}+y^{\frac{-1}{m}}=2 x, x \neq 1$$, then $$\left(x^2-1\right)\left(\frac{\mathrm{d} y}{\mathrm{~d} x} 41. $$\int_\limits0^2[x] \mathrm{d} x+\int_\limits0^2|x-1| \mathrm{d} x=$$ (where $$[x]$$ denotes the greatest integer funct 42. The equations of the lines passing through the point $$(3,2)$$ and making an acute angle of $$45^{\circ}$$ with the line 43. If $$[x]$$ is greatest integer function and $$2[2 x-5]-1=7$$, then $$x$$ lies in 44. The Cartesian equation of a line passing through $$(1,2,3)$$ and parallel to $$x-y+2 z=5$$ and $$3 x+y+z=6$$ is 45. If the lines $$3 x-4 y-7=0$$ and $$2 x-3 y-5=0$$ pass through diameters of a circle of area $$49 \pi$$ square units, the 46. A spherical iron ball of $$10 \mathrm{~cm}$$ radius is coated with a layer of ice of uniform thickness that melts at the 47. $$\int \frac{\sin \frac{5 x}{2}}{\sin \frac{x}{2}} d x=$$ (where $$C$$ is a constant of integration.) 48. The equation of the plane passing through the points $$(2,3,1),(4,-5,3)$$ and parallel to $$X$$-axis is 49. $$\text { If } \int e^{x^2} \cdot x^3 \mathrm{~d} x=e^{x^2} \cdot[f(x)+C]$$ (where $$C$$ is a constant of integration.) 50. The negation of the statement, "The payment will be made if and only if the work is finished in time" is

Physics

1. The magnetic susceptibility of the material of a rod is 349 and permeability of vacuum $$\mu_0$$ is $$4 \pi \times 10^{- 2. The magnetic flux through a coil of resistance '$$R$$' changes by an amount '$$\Delta \phi$$' in time '$$\Delta \mathrm{ 3. A body weighs $$500 \mathrm{~N}$$ on the surface of the earth. At what distance below the surface of the earth it weighs 4. Three discs $$\mathrm{x}, \mathrm{y}$$ and $$\mathrm{z}$$ having radii $$2 \mathrm{~m}, 3 \mathrm{~m}$$ and $$6 \mathrm{ 5. A stationary wave is represented by $$\mathrm{y}=10 \sin \left(\frac{\pi \mathrm{x}}{4}\right) \cos (20 \pi \mathrm{t})$ 6. When the rms velocity of a gas is denoted by '$$v$$', which one of the following relations is true? ($$\mathrm{T}=$$ Abs 7. A parallel plate air capacitor has a uniform electric field 'E' in the space between the plates. Area of each plate is A 8. Two massless springs of spring constant $$\mathrm{K}_1$$ and $$\mathrm{K}_2$$ are connected one after the other forming 9. The time taken by a particle executing simple harmonic motion of period '$$\mathrm{T}$$', to move from the mean position 10. Using Bohr's model, the orbital period of electron in hydrogen atom in the $$\mathrm{n}^{\text {th }}$$ orbit is $$\left 11. A parallel plate capacitor is charged and then disconnected from the charging battery. If the plates are now moved furth 12. If the kinetic energy of a free electron doubles, it's de Broglie wavelength ($$\lambda$$) changes by a factor 13. In the following network, the current through galvanometer will 14. In a medium, the phase difference between two particles separated by a distance '$$x$$' is $$\left(\frac{\pi}{5}\right)^ 15. The work done in blowing a soap bubble of radius $$\mathrm{R}$$ is '$$\mathrm{W}_1$$' at room temperature. Now the soap 16. A capacitor of capacitance $$50 \mu \mathrm{F}$$ is connected to a.c. source $$\mathrm{e}=220 \sin 50 \mathrm{t}$$ ($$\m 17. Two waves are superimposed whose ratio of intensities is $$9: 1$$. The ratio of maximum and minimum intensity is 18. The masses and radii of the moon and the earth are $$\mathrm{M_1, R_1}$$ and $$\mathrm{M_2, R_2}$$ respectively. Their c 19. A monoatomic gas $$\left(\gamma=\frac{5}{3}\right)$$ initially at $$27^{\circ} \mathrm{C}$$ having volume '$$\mathrm{V}$ 20. Two parallel conducting wires of equal length are placed distance 'd' apart, carry currents '$$\mathrm{I}_1$$' and '$$\m 21. Self inductance of a solenoid cannot be increased by 22. For a NAND gate, the inputs and outputs are given below. .tg {border-collapse:collapse;border-spacing:0;} .tg td{borde 23. An electron and a proton having the same momenta enter perpendicularly into a magnetic field. What are their trajectorie 24. The resistance offered by an inductor $$\left(X_L\right)$$ in an a.c. circuit is 25. The force between the plates of a parallel plate capacitor of capacitance '$$\mathrm{C}$$' and distance of separation of 26. Consider the following statements about stationary waves. A. The distance between two adjacent nodes or antinodes is equ 27. If the radius of the spherical gaussian surface is increased then the electric flux due to a point charge enclosed by th 28. The wave number of the last line of the Balmer series in hydrogen spectrum will be (Rydberg's constant $$=10^7 \mathrm{~ 29. A bucket containing water is revolved in a vertical circle of radius $$r$$. To prevent the water from falling down, the 30. Two monatomic ideal gases A and B of molecular masses '$$m_1$$' and '$$m_2$$' respectively are enclosed in separate cont 31. A particle starts oscillating simple harmonically from its mean position with time period '$$T$$'. At time $$t=\frac{T}{ 32. A hollow pipe of length $$0.8 \mathrm{~m}$$ is closed at one end. At its open end, a $$0.5 \mathrm{~m}$$ long uniform st 33. A graph of magnetic flux $$(\phi)$$ versus current (I) is drawn for four inductors A, B, C, D. Larger value of self indu 34. A parallel beam of monochromatic light falls normally on a single narrow slit. The angular width of the central maximum 35. A body moving in a circular path with a constant speed has constant 36. A steel coin of thickness '$$\mathrm{d}$$' and density '$$\rho$$' is floating on water of surface tension '$$T$$'. The r 37. A door $$1.2 \mathrm{~m}$$ wide requires a force of $$1 \mathrm{~N}$$ to be applied perpendicular at the free end to ope 38. The thermodynamic process in which no work is done on or by the gas is 39. The given circuit has two ideal diodes $$D_1$$ and $$D_2$$ connected as shown in the figure. The current flowing through 40. In a Fraunhofer diffraction at a single slit of width 'd' and incident light of wavelength $$5500 \mathop A\limits^o$$, 41. A galvanometer of resistance $$200 \Omega$$ is to be converted into an ammeter. The value of shunt resistance which allo 42. The speed of light in two media $$M_1$$ and $$M_2$$ are $$1.5 \times 10^8$$ $$\mathrm{m} / \mathrm{s}$$ and $$2 \times 1 43. The minimum distance between an object and its real image formed by a convex lens of focal length 'f' is 44. Heat given to a body, which raises its temperature by 1ºC is known as 45. A shell is fired at an angle of $$30^{\circ}$$ to the horizontal with velocity $$196 \mathrm{~m} / \mathrm{s}$$. The tim 46. Three equal charges '$$\mathrm{q}_1$$', '$$^{\prime} \mathrm{q}_2$$' and '$$\mathrm{q}_3$$' are placed on the three corn 47. A coil having an inductance of $$\frac{1}{\pi} \mathrm{H}$$ is connected in series with a resistance of $$300 \Omega$$. 48. In a full wave rectifier circuit without filter, the output current is 49. The excess pressure inside a soap bubble of radius $$2 \mathrm{~cm}$$ is 50 dyne/cm$$^2$$. The surface tension is 50. Two bodies of masses '$$\mathrm{m}$$' and '$$3 \mathrm{~m}$$' are rotating in horizontal speed of the body of mass '$$m$

MHT CET 2022 11th August Evening Shift

MCQ (Single Correct Answer)

-0

The general solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{3 x+y}{x-y}$$ is (where $$C$$ is a constant of integration.)

$$\tan ^{-1}\left(\frac{y}{x}\right)+\log \left(\frac{y^2+3 x^2}{x^2}\right)=\log (x)+C$$

$$\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{y}{x \sqrt{3}}\right)+\log \left(\frac{y^2+3 x^2}{x^2}\right)^{\frac{1}{2}}=\log (x)+C$$

$$\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{y}{x \sqrt{3}}\right)-\log \left(\frac{y^2+3 x^2}{x^2}\right)^{\frac{1}{2}}=\log (x)+C$$

$$\tan ^{-1}\left(\frac{x}{y}\right)+\log \left(\frac{y^2+3 x^2}{x^2}\right)=\log (x)+C$$

MHT CET 2022 11th August Evening Shift

MCQ (Single Correct Answer)

-0

If $$A=\left[\begin{array}{lll}1 & 2 & 1 \\ 3 & 1 & 3\end{array}\right]$$ and $$B=\left[\begin{array}{ll}2 & 3 \\ 1 & 2 \\ 1 & 2\end{array}\right]$$, then $$(A B)^{-1}=$$

$$\left[\begin{array}{ll}\frac{17}{5} & \frac{9}{5} \\ 2 & 1\end{array}\right]$$

$$\left[\begin{array}{cc}\frac{-17}{5} & \frac{9}{5} \\ 2 & -1\end{array}\right]$$

$$\left[\begin{array}{ll}\frac{17}{5} & 2 \\ \frac{9}{5} & 1\end{array}\right]$$

$$\left[\begin{array}{cc}\frac{-17}{5} & 2 \\ \frac{-9}{5} & -1\end{array}\right]$$

MHT CET 2022 11th August Evening Shift

MCQ (Single Correct Answer)

-0

The distance between parallel lines

$$\frac{x-1}{2}=\frac{y-2}{-2}=\frac{z-3}{1}$$ and

$$\frac{x}{2}=\frac{y}{-2}=\frac{z}{1}$$ is :

$$\frac{2 \sqrt{5}}{3}$$ units

$$\frac{\sqrt{5}}{3}$$ units

$$\frac{5 \sqrt{5}}{3}$$ units

$$\frac{4 \sqrt{5}}{3}$$ units

MHT CET 2022 11th August Evening Shift

MCQ (Single Correct Answer)

-0

Maximum value of $$Z=5 x+2 y$$, subject to $$2 x-y \geq 2, x+2 y \leq 8$$ and $$x, y \geq 0$$ is

17.6

25.6

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