MHT CET 2021 22th September Evening Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Ethers when dissolved in cold concentrated sulphuric acid forms 2. The volume of a gas at $$0^{\circ} \mathrm{C}$$ is $$2 \mathrm{~dm}^3$$. What is its volume if temperature is decreased 3. The major product obtained in the following reaction is Chlorobenzene + chlorine $$\xrightarrow[\mathrm{FeCl}_3]{\text { 4. How many moles of urea are present in 5.4 g ? (Molar mass = 60) 5. Which among the following is a double ring containing nitrogen base present in nucleic acids? 6. Identify the product '$$\mathrm{B}$$' in the following series of reactions. $$\text { Propan - 1-ol } \xrightarrow[623 \ 7. Conversion of benzene diazonium chloride to chlorobenzene in presence of $$\mathrm{CuCl} / \mathrm{HCl}$$ is known as 8. Which among the following compounds in NOT a colourless gas? 9. Solubility product of $$\mathrm{AgBr}$$ is $$4.9 \times 10^{-13}$$. What is its solubility? 10. Which element from following is radioactive? 11. Which among the following statements about $$\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$$ is $$\underline{\text { NOT 12. Formation of $$\mathrm{NO}_{2(\mathrm{g})}$$ from $$\mathrm{N}_{2(\mathrm{g})}$$ and $$\mathrm{O}_{2(\mathrm{g})}$$ is a 13. Identify reducing agent in following reaction $$\mathrm{H}_2 \mathrm{O}_{2(\mathrm{ag})}+\mathrm{ClO}_{4(\mathrm{aq})}^{ 14. Identify the type of unit cell that has particles at the centre of each face in addition to the particles at eight corne 15. Identify product '$$\mathrm{B}$$' in following reaction. Cumene $$\xrightarrow[\Delta]{\mathrm{KMnO}_4, \mathrm{KOH}} \m 16. Which of the following is NOT a correct mathematical equation for Ostwald dilution law? 17. How many Faraday of electricity is required to deposit $$0.8 \mathrm{~g}$$ of calcium at cathode by the electrolysis of 18. Identify lowest positive charge developed (indicated by $$\partial, \partial_1, \partial_2, \partial_3$$) due to inducti 19. What is rate constant of a first order reaction if 0.08 mole of reactant reduces to 0.02 mole in 23.03 minute? 20. Which element from following lanthanoids has half-filled $$\mathrm{f}$$- orbital in observed and expected electronic con 21. How many atoms of niobium are present in $$2.43 \mathrm{~g}$$ if it forms bcc structure with density $$9 \mathrm{~g} \ma 22. Identify the reagent R used in following conversion. Glucose $$\mathrm{\buildrel R \over \longrightarrow}$$ n - hexane 23. Buna-S is obtained from 24. 5 g sucrose (molar mass = 342) is dissolved in 100 g of solvent, decreases the freezing point by 2.15 K. What is cryosco 25. What is Henry's law constant if solubility of a gas in water at $$298 \mathrm{~K}$$ and 1 bar pressure is $$7\times10^{- 26. A weak monobasic acid is $$10 \%$$ dissociated in $$0.05 \mathrm{~M}$$ solution. What is its percentage dissociation in 27. What is the conductivity of $$0.02 \mathrm{~M} \mathrm{~KCl}$$ solution if cell constant is $$1.29 \mathrm{~cm}^{-1}$$ w 28. The major product obtained in the following reaction is 29. Which of the following statements is NOT true for a reaction having rate law $$\mathrm{r}=\mathrm{k}\left[\mathrm{H}_2\r 30. Identify the product '$$B$$' in following reaction. $$2 \mathrm{CH}_3 \mathrm{CHO} \xrightarrow{\text { dil. } \mathrm{N 31. Identify the correct decreasing order of precipitation power of flocculating ion added, from following. 32. Identify use of argon from following. 33. Which of the following is an example of copolymer? 34. Which of the following is likely to undergo racemization during alkaline hydrolysis? 35. What is enthalpy of formation of $$\mathrm{NH}_3$$ if bond enthalpies are as $$(\mathrm{N} \equiv \mathrm{N})=941 \mathr 36. Which of the following alkyl halide is treated with sodium metal to obtain $$2,2,3,3$$ - tetramethyl butane? 37. Electrical conductance due to all the ions in $$1 \mathrm{~cm}^3$$ of given solution is called as 38. For the reaction $$\mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NH}_{3(\mathrm{~g})}$ 39. Identify the polymer used in making floor tiles. 40. Which of the following formulae is used to obtain depression in freezing point? 41. How many tetrahedral voids are present in 0.4 mole of a compound that forms hcp structure? 42. Pure dihydrogen $$(99.5 \%)$$ is obtained by the electrolysis of 43. Which among following functional groups exhibits $$-\mathrm{R}$$ effect? 44. Which among the following compounds has highest melting point? 45. Identify compound from following having highest basic strength. 46. Which of the following alkenes on oxidation by $$\mathrm{KMnO}_4$$ in dil. $$\mathrm{H}_2 \mathrm{SO}_4$$ forms adipic a 47. What is the difference between $$\Delta H$$ and $$\Delta \mathrm{U}$$ for reaction given below at $$298 \mathrm{~K}$$ ? 48. What is the energy of an electron in stationary state corresponding to $$\mathrm{n}=2$$ ? 49. Identify the molecule having dipole moment. 50. Identify homoleptic complex from following.

Mathematics

1. Let $$\begin{aligned} f(x) & =x+a \sqrt{2} \sin x & & , 0 \leq x If $$\mathrm{f}(\mathrm{x})$$ is continuous for $$0 \le 2. The area of triangle with vertices $$(1,2,0),(1,0, a)$$ and $$(0,3,1)$$ is $$\sqrt{6}$$ sq. units, then the values of '$ 3. If $$A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]$$ and $$A$$ adj $$A=A A^T$$, then $$5 a+b=$$ 4. The numbers can be formed using the digits $$1,2,3,4,3,2,1$$ so that odd digits always occupy odd places in __________ w 5. If $$y=\tan ^{-1} \sqrt{\frac{1+\cos x}{1-\cos x}}$$, then $$\frac{d y}{d x}=$$ 6. Following data shows the information about marks obtained in Physics, Chemistry, Mathematics and Biology by 100 students 7. If $$\mathrm{G}(4,3,3)$$ is the centroid of the triangle $$\mathrm{ABC}$$ whose vertices are $$\mathrm{A}(\mathrm{a}, 3, 8. The d.r.s. of the normal to the plane passing through the origin and the line of intersection of the planes $$x+2 y+3 z= 9. The degree of the differential equation whose solution is $$y^2=8 a(x+a)$$, is 10. If the sum of slopes of lines represented by $$\mathrm{ax^2+8xy+5y^2=0}$$ is twice their product, then a = 11. In $$\Delta ABC$$, with usual notations $$\mathrm{\frac{b\sin B-c\sin C}{\sin(B-C)}}=$$ 12. Two circles centred at $$(2,3)$$ and $$(4,5)$$ intersects each other. If their radii are equal, then the equation of the 13. The function $$f(x)=\frac{\lambda \sin x+6 \cos x}{2 \sin x+3 \cos x}$$ is increasing, if 14. If $$f(x)=x^2+a x+b$$ has minima at $$x=3$$ whose value is 5 , then the values of $$a$$ and $$b$$ are respectively. 15. The area bounded by the parabola $$y^2=x$$ and the line $$x+y=2$$ in the first quadrant is 16. If $$2 \cos \theta=x+\frac{1}{x}$$, then $$2 \cos 3 \theta=$$ 17. For an invertible matrix $$A$$, if $$A(\operatorname{adj} A)=\left[\begin{array}{cc}20 & 0 \\ 0 & 20\end{array}\right]$$ 18. $$\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{2}} \frac{\operatorname{cosec} x \cdot \cot x}{1+\operatorname{cosec}^2 x} d x 19. A spherical raindrop evaporates at a rate proportional to its surface area. If its radius originally is 3 mm. and 1 hour 20. The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is 21. If the vectors $$2 \hat{i}-\hat{j}-\hat{k} ; \hat{i}+2 \hat{j}-3 \hat{k}$$ and $$3 \hat{i}+\lambda \hat{j}+5 \hat{k}$$ a 22. $$\lim _\limits{x \rightarrow 2}(x-1)^{ \frac{1}{3 x-6}}=$$ 23. Given $$\mathrm{p}$$ : A man is a judge, $$\mathrm{q}$$ : A man is honest If $$\mathrm{S} 1$$ : If a man is a judge, the 24. If $$2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x)$$, then the value of $$x$$ is 25. $$\int \frac{\tan ^4 \sqrt{x} \cdot \sec ^2 \sqrt{x}}{\sqrt{x}} d x=$$ 26. The line $$\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$$ lies in the plane $$x+3 y-\alpha z+\beta=0$$, then value of $$\a 27. The statement pattern $$(p \wedge q) \wedge[(p \wedge q) \vee(\sim p \wedge q)]$$ is equivalent to 28. If the points $$P(4,5, x), Q(3, y, 4)$$ and $$R(5,8,0)$$ are collinear, then the value of $$x+y$$ is 29. The particular solution of the differential equation $$\frac{d y}{d x}=\frac{y+1}{x^2-x}$$, when $$x=2$$ and $$y=1$$ is 30. The distribution function $$F(X)$$ of discrete random variable $$X$$ is given by .tg {border-collapse:collapse;border- 31. The general solution of $$\frac{d y}{d x}=\frac{x+y}{x-y}$$ is 32. A line drawn from a point $$A(-2,-2,3)$$ and parallel to the line $$\frac{x}{-2}=\frac{y}{2}=\frac{z}{-1}$$ meets the $$ 33. First bag contains 3 red and 5 black balls and second bag contains 6 red and 4 black balls. A ball is drawn from each ba 34. If $$A=\left[\begin{array}{ccc}1 & 2 & 1 \\ -1 & 1 & 3\end{array}\right]$$ and $$B=\left[\begin{array}{cc}1 & 2 \\ -3 & 35. With usual notations, in any $$\triangle A B C$$, if $$a\cos B=b \cos A$$, then the triangle is 36. A fair coin is tossed 4 times. If $$X$$ is a random variable which indicates number of heads, then $$\mathrm{P}[\mathrm{ 37. If the line joining two points $$\mathrm{A}(2,0)$$ and $$\mathrm{B}(3,1)$$ is rotated about $$\mathrm{A}$$ in anticlockw 38. The common region of the solution of the inequations $$x+y \geq 5, y \leq 4, x \geq 2, x, y \geq 0$$ is 39. If the mean and variance of a binomial distribution are 4 and 2 respectively, then probability of getting 2 heads is 40. The vector equation of the line whose Cartesian equations are $$y=2$$ and $$4 x-3 z+5=0$$ is 41. If $$x^y \cdot y^x=16$$, then $\frac{d y}{d x}$ at $(2,2)$$ is 42. $$\int_\limits0^2|2 x-3| d x=$$ 43. $$\int \cos ^{-1} x d x=$$ 44. $$\int \frac{1}{\cos x+\sqrt{3} \sin x} d x=$$ 45. If $$f(x)=[8 x]-3$$, where $$[x]$$ is greatest integer function of $$x$$, then $$f(\pi)=$$ (where $$\pi=3,14$$) 46. If lines represented by the equation $$\mathrm{px}^2-\mathrm{qy^{2 }}=0$$ are distinct, then 47. The slant height of a right circular cone is $$3 \mathrm{~cm}$$. The height of the cone for maximum volume is 48. If $$\omega$$ is the complex cube root of unity, then $$\left(3+5 \omega+3 \omega^2\right)^2+\left(3+3 \omega+5 \omega^2 49. Let $$a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$$ and $$b:(p \vee s) \leftrightarrow(q \wedge r)$$. If the truth valu 50. If $$\int_\limits0^a \sqrt{\frac{a-x}{x}} d x=\frac{k}{2}$$, then $$k=$$

Physics

1. Force is applied to a body of mass $$2 \mathrm{~kg}$$ at rest on a frictionless horizontal surface as shown in the force 2. Which of the following gates will give an output '1' for the given inputs? 3. For a common-emitter amplifier, the voltage gain is 40. Its input and output impedances are $$100 \Omega$$ and $$400 \Om 4. A tuning fork of frequency '$$n$$' is held near the open end of tube which is closed at the other end and the lengths ar 5. In parallel plate capacitor, electric field between the plates is '$$E$$'. If the charge on the plates is '$$Q$$' then t 6. A particle with position vector $$\overrightarrow{\mathrm{r}}$$ has a linear momentum $$\overrightarrow{\mathrm{P}}$$. W 7. A ball rises to the surface of a liquid with constant velocity. The density of the liquid is four times the density of t 8. A particle having a charge $$100 \mathrm{e}$$ is revolving in a circular path of radius $$0.8 \mathrm{~m}$$ with 1. r.p. 9. Two satellites of same mass are launched in circular orbits at heights '$$R$$' and '$$2 R$$' above the surface of the ea 10. The emissive power of sphere of area $$0.04 \mathrm{~m}^2$$ is $$0.7 \mathrm{~k} \mathrm{~cal} \mathrm{~s}^{-1} \mathrm{ 11. In a potentiometer experiment, the balancing length for a cell is $$240 \mathrm{~cm}$$. On shunting the cell with a resi 12. A sound wave of frequency $$160 \mathrm{~Hz}$$ has a velocity of $$320 \mathrm{~m} / \mathrm{s}$$. When it travels throu 13. In $$n^{\text {th }}$$ Bohr orbit, the ratio of the kinetic energy of an electron to the total energy of it, is 14. Two spherical conductors of radii $$4 \mathrm{~cm}$$ and $$5 \mathrm{~cm}$$ are charged to the same potential. If '$$\si 15. Kirchhoff's current and voltage law are respectively based on the conservation of 16. A glass tube of $$1 \mathrm{~m}$$ length is filled with water. The water can be drained out slowly from the bottom of th 17. The rate of flow of heat through a copper rod with temperature difference $$28^{\circ} \mathrm{C}$$ is $$1400 \mathrm{~c 18. A capacitor of capacity '$$C$$' is charged to a potential '$$V$$'. It is connected in parallel to an inductor of inducta 19. When a photon enters glass from air, which one of the following quantity does not change? 20. In Young's double slit experiment using monochromatic light of wavelength '$$\lambda$$', the maximum intensity of light 21. An electron of mass '$$m$$' and charge '$$q$$' is accelerated from rest in a uniform electric field of strength '$$E$$'. 22. If the terminal speed of a sphere A [density $$\rho_{\mathrm{A}}=7.5 \mathrm{~kg} \mathrm{~m}^{-3}$$ ] is $$0.4 \mathrm{ 23. A particle connected to the end of a spring executes S.H.M. with period '$$T_1$$'. While the corresponding period for an 24. The change in internal energy of the mass of a gas, when the volume changes from '$$\mathrm{V}$$' to '$$2 \mathrm{~V}$$' 25. An object is located on a wall, its image of equal size is to be obtained on a parallel wall with the help of a convex l 26. A child is standing with folded hands at the centre of the platform rotating about its central axis. The kinetic energy 27. If the pressure of an ideal gas is decreased by $$10 \%$$ isothermally, then its volume will 28. The critical angle for light going from medium '$$x$$' to medium '$$Y$$' is $$\theta$$. The speed of light in medium '$$ 29. A needle is $$7 \mathrm{~cm}$$ long. Assuming that the needle is not wetted by water, what is the weight of the needle, 30. A driver applies the brakes on seeing the red traffic signal $$400 \mathrm{~m}$$ ahead. At the time of applying the brak 31. An ideal gas having molar mass '$$\mathrm{M}_0$$', has r.m.s. velocity 'V' at temperature 'T'. Then 32. A step down transformer is used to reduce the main supply from '$$V_1$$' volt to '$$V_2$$' volt. The primary coil draws 33. For the circuit shown below, instantaneous current through inductor '$$\mathrm{L}$$' and capacitor '$$\mathrm{C}$$' is r 34. The light of wavelength '$$\lambda$$' is incident on the surface of metal of work function $$\phi$$ and emits the electr 35. A parallel plate capacitor having plates of radius 6 cm has capacitance 100 pF. It is connected to 230 V a.c. supply wit 36. At a height 'R' above the earth's surface the gravitational acceleration is (R = radius of earth, g = acceleration due t 37. Two rings of radius 'R' and 'nR' made of same material have the ratio of moment of inertia about an axis passing through 38. '$$n$$' waves are produced on a string in 1 second. When the radius of the string is doubled, keeping tension same, the 39. the magnetic flux (in weber) in a closed circuit of resistance $$20 \Omega$$ varies with time $$t$$ second according to 40. If '$$E$$' and '$$L$$' denote the magnitude of total energy and angular momentum of revolving electron in $$\mathrm{n}^{ 41. The magnetic field inside a current carrying toroidal solenoid is $$0.2 \mathrm{~mT}$$. What is the magnetic field insid 42. A body of mass '$$m$$' performs linear S.H.M. given by equation $$x=P \sin \omega t+Q \sin \left(\omega t+\frac{\pi}{2}\ 43. Two particles $$A$$ and $$B$$ having same mass have charge $$+q$$ and $$+4 q$$ respectively. When they are allowed to fa 44. The relative permeability of iron is 2000. Its absolute permeability in SI unit will be $$\left(\frac{\mu_0}{4 \pi}=10^{ 45. Choose the correct statement. In semiconductors valance band and conduction band 46. A step down transformer has turns ratio $$20: 1$$. If $$8 \mathrm{~V}$$ is applied across $$0.4 \mathrm{~ohm}$$ secondar 47. Photons of energy $$10 \mathrm{~eV}$$ are incident on a photosensitive surface of threshold frequency $$2 \times 10^{15} 48. Two radioactive materials $$X_1$$ and $$X_2$$ have decay constants '$$5 \lambda$$' and '$$\lambda$$' respectively. Initi 49. If two sources emit light waves of different amplitudes then 50. An ideal gas at $$27^{\circ} \mathrm{C}$$ is compressed adiabatically to $$(8 / 27)$$ of its original volume. If ratio o

MHT CET 2021 22th September Evening Shift

MCQ (Single Correct Answer)

-0

If $$x^y \cdot y^x=16$$, then $\frac{d y}{d x}$ at $(2,2)$$ is

$$-$$1

MHT CET 2021 22th September Evening Shift

MCQ (Single Correct Answer)

-0

$$\int_\limits0^2|2 x-3| d x=$$

$$\frac{3}{10}$$

$$\frac{5}{2}$$

$$\frac{10}{3}$$

$$\frac{2}{5}$$

MHT CET 2021 22th September Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \cos ^{-1} x d x=$$

$$x \cos ^{-1} x+\sqrt{1-x^2}+c$$

$$-x \cos ^{-1} x+\sqrt{1+x^2}+c$$

$$x \cos ^{-1} x-\sqrt{1+x^2}+c$$

$$x \cos ^{-1} x-\sqrt{1-x^2}+c$$

MHT CET 2021 22th September Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{1}{\cos x+\sqrt{3} \sin x} d x=$$

$$2 \log \left[\tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{12}\right)\right]+\mathrm{c}$$

$$\frac{1}{2} \log \left[\tan \left(\frac{\mathrm{x}}{2}-\frac{\pi}{12}\right)\right]+\mathrm{c}$$

$$\frac{1}{2} \log \left[\tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{12}\right)\right]+\mathrm{c}$$

$$2 \log \left[\tan \left(\frac{\mathrm{x}}{2}-\frac{\pi}{12}\right)\right]+\mathrm{c}$$

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