MHT CET 2021 20th September Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Which of the following solutions does not flow in either direction, when separated by semipermeable membrane? (Molar mas 2. For the reaction, $$3 \mathrm{I}_{(\mathrm{aq})}^{-}+\mathrm{S}_2 \mathrm{O}_{8(\mathrm{aq})}^{2-} \longrightarrow \math 3. When alcoholic solution of an organic compound is treated with few drops of Schiff's reagent, pink colour appears. This 4. What is O$$-$$O bond length in resonance hybrid of ozone? 5. What is the number of unit cells present in 3.9 g of potassium if it crystallizes in BCC structure? 6. When 2-Methylbut-2-ene is treated with hydrogen chloride, the major product obtained is 7. Which among the following elements has completely filled 4d-orbital? 8. Which of the following compounds on reaction with Grignard reagent followed by hydrolysis forms secondary alcohol? 9. How many water molecules are present in formula of crystalline chloride of lithium? 10. The solubility of AgCl in it's solution is 1.25 $$\times$$ 10$$^{-5}$$ mol dm$$^{-3}$$. What is solubility product of Ag 11. The reagent used in Gatterman-Koch formylation of arene is 12. Which among the following statements is true for Pt[(NH$$_3$$)$$_2$$Cl$$_2$$] ? 13. What type of crystal structure from following has 52.36% packing efficiency? 14. The molar conductivity of 0.1 M BaCl$$_2$$ solution is 106 $$\Omega^{-1}$$ cm$$^2$$ mol$$^{-1}$$ at 25$$^\circ$$C. What 15. Identify the compound obtained in following reaction? 16. A gas occupies 11.2 dm$$^3$$ at 105 kPa. What is it's volume if pressure is increased to 210 kPa? 17. Identify the use of Buna-N from following. 18. Which from following compounds accepts proton from water molecule according to Bronsted-Lowry theory? 19. What amount of oxygen is used at S.T.P. to obtain 9 g water from sufficient amount of hydrogen gas? 20. A solution of 6 g of solute in 100 g of water boils at 100.52$$^\circ$$C. The molal elevation constant of water is 0.52 21. Which among the following compounds has highest melting point? 22. Instantaneous rate of a reaction is $$ - {1 \over 2}{{d[x]} \over {dt}} = - {{d[y]} \over {dt}} = {1 \over 2}{{d[z]} \o 23. Which of the following reactions shows work of compression? 24. Identify total number carbon atoms present in undecane. 25. What is value of percent atom economy if formula weight of product is 46 u and sum of formula weight of all reactants is 26. Half life for a first order reaction is 6.93 hour. What is the time required for 80% completion of the reaction? 27. What is the number of moles of H atoms required to prepare one mole ethylamine from one mole acetamide? 28. If vapour pressure of pure solvent and solution are 240 and 216 mm Hg respectively then mole fraction of solvent in solu 29. Identify an orbital with the quantum numbers n = 4, $$l$$ = 3, m = 0. 30. The pH of 0.1 M solution of monobasic acid is 2.34. Calculate the degree of dissociation of the acid. 31. Calculate change in enthalpy when 39 g acetylene is completely burnt with oxygen and enthalpy of combustion of acetylene 32. Which from following is NOT correct regarding electrolysis? 33. A conductivity cell shows resistance of 600 ohm. If conductivity of 0.01 M KCl is 0.0015 $$\Omega^{-1}$$ cm$$^{-1}$$, wh 34. An element (molar mass 180 ) has BCC crystal structure with density $$18 \mathrm{~g} \mathrm{~cm}^{-3}$$. What is the ed 35. What is the number of allotropes of selenium? 36. Which among the following is a multi-molecular colloid? 37. Which among following statements is NOT true about Gabriel phthalimide synthesis? 38. Identify the reagent R used in following reaction? 39. Identify highest field strength ligand from following. 40. Which among the following compounds is NOT a carbocyclic compound? 41. Identify the glycosidic linkage present in lactose. 42. Which from following elements of halogen family is in liquid state at room temperature? 43. Which of the following compounds on reaction with ammonical silver nitrate solution forms precipitate of silver? 44. Which of the following polymers is used in electrophoresis in the form of gel? 45. An ideal gas on isothermal reversible compression from 10L to 5L performs 1730J of work at 300 K. Calculate number of mo 46. Identify the correct statement about properties of interstitial compounds. 47. Which of the following sugar is found in milk? 48. How many chiral carbon atoms are present in 2 - Bromo - 3, 4, 5 - trimethylhexane? 49. Which among the following is NOT correct statement about $$\mathrm{S_N1}$$ reaction? 50. Identify reductant in following reaction. $$\mathrm{{C_2}O_4^{2 - } + MnO_4^ - + {H^ + } \longrightarrow M{n^{2 + }} +

Mathematics

1. $$\int \tan ^{-1}(\sec x+\tan x) d x=$$ 2. $$A(\propto)=\left[\begin{array}{cc}\cos \propto & \sin \propto \\ -\sin \propto & \cos \propto\end{array}\right]$$, the 3. Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number, is 4. If the acute angle between the lines given by $$\mathrm{a x^2+2 h x y+b y^2=0}$$ is $$\frac{\pi}{4}$$, then $$\mathrm{4 5. A wire of length 20 units is divided into two parts such that the product of one part and cube of the other part is maxi 6. The shaded part of the given figure indicates the feasible region. Then the constraints are 7. If the volume of a tetrahedron whose conterminous edges are $$\vec{\mathrm{a}}+\vec{\mathrm{b}}, \vec{\mathrm{b}}+\vec{\ 8. The joint equation of the pair of lines through the origin and making an equilateral triangle with the line $$x=3$$ is 9. If 1 is added to first 10 natural numbers, then variance of the numbers so obtained is 10. A random variable X has the following probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td 11. A differential equation for the temperature 'T' of a hot body as a function of time, when it is placed in a bath which i 12. $$\int_\limits0^{\pi / 4} \log (1+\tan x) d x=$$ 13. A particle is moving on a straight line. The distance $$\mathrm{S}$$ travelled in time $$\mathrm{t}$$ is given by $$\mat 14. The negation of a statement 'x $$\in$$ A $$\cap$$ B $$\to$$ (x $$\in$$ A and x $$\in$$ B)' is 15. The Cartesian equation of the plane passing through the point $$(0,7,-7)$$ and containing the line $$\frac{x+1}{-3}=\fra 16. If $$\overline{\mathrm{e}}_1, \overline{\mathrm{e}}_2$$ and $$\overline{\mathrm{e}}_1+\overline{\mathrm{e}}_2$$ are unit 17. If $$y=\log \tan \left(\frac{x}{2}\right)+\sin ^{-1}(\cos x)$$, then $$\frac{d y}{d x}=$$ 18. If $$\overline{\mathrm{a}}, \overline{\mathrm{b}} , \overline{\mathrm{c}}$$ are three vectors which are perpendicular to 19. If the lines $$\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$$ and $$\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$$ intersect, th 20. If inverse of $$\left[\begin{array}{ccc}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$$ does not exist, then $ 21. The general solution of the differential equation $$\frac{d y}{d x}=\frac{x+y+1}{x+y-1}$$ is given by 22. The logical expression $$\mathrm{p} \wedge(\sim \mathrm{p} \vee \sim \mathrm{q}) \equiv$$ 23. The parametric equations of a line passing through the points $$\mathrm{A}(3,4,-7)$$ and $$\mathrm{B}(1,-1,6)$$ are 24. The value of (1 + i)$$^5$$ (1 $$-$$ i)$$^7$$ is 25. Rajesh has just bought a VCR from Maharashtra Electronics and the shop offers after sales service contract for Rs. 1000 26. The area of the region bounded by the parabola x$$^2$$ = y and the line y = x is 27. If $$A = \left[ {\matrix{ 3 & 2 & 4 \cr 1 & 2 & 1 \cr 3 & 2 & 6 \cr } } \right]$$ and A$$_{ij}$$ are co 28. The general solution of the differential equation $$x+y \frac{d y}{d x}=\sec \left(x^2+y^2\right)$$ is 29. $$\mathop {\lim }\limits_{x \to \infty } \left( {\sqrt {{x^2} + 5x - 7} - x} \right) = $$ 30. The differential equation of all circles which pass through the origin and whose centre lie on Y-axis is 31. With usual notations if the angles of a triangle are in the ratio 1 : 2 : 3, then their corresponding sides are in the r 32. $$(2 \hat{\mathrm{i}}+6 \hat{\mathrm{i}}+27 \hat{\mathrm{k}}) \times(\hat{\mathrm{i}}+\lambda \hat{\mathrm{j}}+\mu \hat{ 33. If f(x) = |x|, for x $$\in$$ ($$-1,2$$), then f is discontinuous at (where [x] represents floor function) 34. The angle between a line with direction ratios 2, 2, 1 and a line joining (3, 1, 4) and (7, 2, 12) is 35. The equation of the tangent to the curve $$y = 4x{e^x}$$ at $$\left( { - 1,{{ - 4} \over e}} \right)$$ is 36. The slope of the line through the origin which makes an angle of 30$$^\circ$$ with the positive direction of Y-axis meas 37. The domain of the function $$f(x)=\frac{1}{\sqrt{x+|x|}}$$ is 38. All the letters of the word 'ABRACADABRA' are arranged in different possible ways. Then the number of such arrangements 39. If $$\int \frac{1+x^2}{1+x^4} d x=\frac{1}{\sqrt{2}} \tan ^{-1}\left[\frac{f(x)}{\sqrt{2}}\right]+c$$, then $$f(x)=$$ 40. The value of $$\sin 18^{\circ}$$ is 41. If $$4 \sin ^{-1} x+6 \cos ^{-1} x=3 \pi$$, where $$-1 \leq x \leq 1$$, then $$x=$$ 42. If $$h(x)=\sqrt{4 f(x)+3 g(x)}, f(1)=4, g(1)=3, f^{\prime}(1)=3, g^{\prime}(1)=4$$, then $$h^{\prime}(1)=$$ 43. If the line $$\frac{x+1}{2}=\frac{y-m}{3}=\frac{z-4}{6}$$ lies in the plane $$3 x-14 y+6 z+49=0$$, then the value of $$m 44. If $$x \in\left(0, \frac{\pi}{2}\right)$$ and $$x$$ satisfies the equation $$\sin x \cos x=\frac{1}{4}$$, then the value 45. If $$x=a \cos \theta, y=b \sin \theta$$, then $$\left[\frac{d^2 y}{d x^2}\right]_{\theta=\frac{\pi}{4}}=$$ 46. $$\int \frac{x+\sin x}{1+\cos x} d x=$$ 47. An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half the quantity of ice melts 48. If $$\int_\limits0^{\frac{\pi}{2}} \frac{d x}{5+4 \sin x}=A \tan ^{-1} B$$, then A + B = 49. If $$X \sim B(4, p)$$ and $$P(X=0)=\frac{16}{81}$$, then $$P(X=4)=$$ 50. If the lines $$3x - 4y + 4 = 0$$ and $$6x - 8y - 7 = 0$$ are tangents to a circle, then the radius of the circle is

Physics

1. A mass '$$\mathrm{m}_1$$' is suspended from a spring of negligible mass. A spring is pulled slightly in downward directi 2. If the charge to ratio of an electron is 'A' C/kg, then the gyromagnetic ratio of an orbital electron in C/kg is 3. A parallel plate capacitor filled with oil of a dielectric constant 3 between the plates has capacitance 'C'. If the oil 4. In Young's double slit experiment, the '$$\mathrm{n^{th}}$$' maximum of wavelength '$$\lambda_1$$' is at a distance '$$\ 5. A perfectly black body emits a radiation at temperature 'T$$_1$$' K. If it is to radiate at 16 times this power, its tem 6. Two conducting wire loops are concentric and lie in the same plane. The current in the outer loop is clockwise and incre 7. Two particles $$\mathrm{P}$$ and $$\mathrm{Q}$$ performs S.H.M. of same amplitude and frequency along the same straight 8. An electric dipole having dipole moment $$\mathrm{P}=\mathrm{q} \times 2 \ell$$ is placed in a uniform electric field '$ 9. The frequencies of three tuning forks $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ are related as $$\mathrm{n}_{\mathrm 10. The magnetic field intensity 'H' at the centre of a long solenoid having 'n' turns per unit length and carrying a curren 11. One mole of an ideal gas expands adiabatically at constant pressure such that its temperature $$T \propto {1 \over {\sqr 12. On an imaginary linear scale of temperature (called 'W' scale) the freezing and boiling points of water are 39$$^\circ$$ 13. When a d.c. voltage of $$200 \mathrm{~V}$$ is applied to a coil of self-inductance $$\left(\frac{2 \sqrt{3}}{\pi}\right) 14. When light of wavelength '$$\lambda$$' is incident on a photosensitive surface, photons of power 'P' are emitted. The nu 15. Air is pushed in a soap bubble to increase its radius from 'R' to '2R'. In this case, the pressure inside the bubble 16. The equation of wave is given by $$\mathrm{y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)$$. If the displace 17. A uniformly charged half ring of a radius ' $R$ ' has linear charge density '$$\sigma$$'. The electric potential at the 18. A sonometer wire resonates with 4 antinodes between two bridges for a given tuning fork, when 1 kg mass is suspended fro 19. Let '$$\mathrm{R_1}$$' and '$$\mathrm{R_2}$$' are radii of two mercury drops. A big mercury drop is formed from them und 20. A galvanometer of resistance $$50 \Omega$$ is converted to an ammeter. After shunting, the effective resistance of ammet 21. The electron in hydrogen atom is initially in the third excited state. When it finally moves to ground state, the maximu 22. Two different logic gates moving output '0' for the inputs (0, 1) and then for (1, 0) are 23. A straight conductor of length 0.6 M is moved with a speed of 10 ms$$^{-1}$$ perpendicular to magnetic field of inductio 24. If the electron in a hydrogen atom moves from ground state orbit to 5th orbit, then the potential energy of the electron 25. A particle of mass 5kg is executing S.H.M. with an amplitude 0.3 m and time period $$\frac{\pi}{5}$$s. The maximum value 26. The weight of a man in a lift moving upwards with an acceleration 'a' is 620 N. When the lift moves downwards with the s 27. Consider the circuit shown in the figure. The value of current 'I' is 28. Two bodies '$$\mathrm{A}$$' and '$$\mathrm{B}$$' start from the same point at the same instant and move along a straight 29. Light of wavelength '$$\lambda$$' is incident on a single slit of width 'a' and the distance between slit and screen is 30. An inductor coil wound uniformly has self inductance 'L' and resistance 'R'. The coil is broken into two identical par 31. Two wires of same material of radius 'r' and '2r' respectively are welded together end to end. The combination is then u 32. A ray of light travels from a denser medium to a rarer medium. The reflected and the refracted rays are perpendicular to 33. Specific heats of an ideal gas at constant pressure and volume are denoted by $$\mathrm{C}_{\mathrm{p}}$$ and $$\mathrm{ 34. The force required to take away a flat circular plate of radius $$2 \mathrm{~cm}$$ from the surface of water is $$\left[ 35. The frequency of a given a.c. signal is 'N' Hz. When it is connected to a half wave rectifier, the number of output puls 36. A convex lens of focal length 'F' produces a real image 'n' times the size of the object. The image distance is 37. A solid sphere of mass $$\mathrm{M}$$, radius $$\mathrm{R}$$ has moment of inertia '$$\mathrm{I}$$' about its diameter. 38. The depth 'd' below the surface of the earth where the value of acceleration due to gravity becomes $$\left(\frac{1}{n}\ 39. Silicon and copper are cooled from 300 K to 100 K, the specific resistance (resistivity) 40. Two bodies rotate with kinetic energies 'E$$_1$$' and 'E$$_2$$'. Moments of inertia about their axis of rotation are 'I$ 41. When a photosensitive surface is irradiated by light of wavelengths '$$\lambda_1$$' and '$$\lambda_2$$', kinetic energie 42. An electron (e) moves in circular orbit of radius 'r' with uniform speed 'V'. It produces magnetic field 'B' at the cent 43. The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is 'V'. For the satel 44. An inductor coil takes current 8A when connected to an 100 V and 50 Hz a.c. source. A pure resistor under the same condi 45. A disc of radius 0.4 m and mass one kg rotates about an axis passing through its centre and perpendicular to its plane. 46. For a monoatomic gas, work done at constant pressure is W. The heat supplied at constant volume for the same rise in tem 47. In Fraunhofer diffraction pattern, slit width is 0.2 mm and screen is at 2m away from the lens. If wavelength of light u 48. A spherical conducting shell of inner radius 'r$$_1$$' and outer radius 'r$$_2$$' has a charge 'Q'. A charge $$-$$q is p 49. The frequency of a tuning fork is 'n' Hz and velocity of sound in air is 'V' m/s. When the tuning fork completes 'x' vib 50. A charge of magnitude '2e' and mass '4m' is moving in an electric field $$\overrightarrow E $$. The acceleration imparte

MHT CET 2021 20th September Morning Shift

MCQ (Single Correct Answer)

-0

If $$\int \frac{1+x^2}{1+x^4} d x=\frac{1}{\sqrt{2}} \tan ^{-1}\left[\frac{f(x)}{\sqrt{2}}\right]+c$$, then $$f(x)=$$

$$x+\frac{1}{x^2}$$

$$x-\frac{1}{x^2}$$

$$x+\frac{2}{x}$$

$$x-\frac{1}{x}$$

MHT CET 2021 20th September Morning Shift

MCQ (Single Correct Answer)

-0

The value of $$\sin 18^{\circ}$$ is

$$\frac{4}{\sqrt{5}-1}$$

$$\frac{\sqrt{5}-1}{4}$$

$$\frac{\sqrt{5}+1}{4}$$

$$\frac{4}{\sqrt{5}+1}$$

MHT CET 2021 20th September Morning Shift

MCQ (Single Correct Answer)

-0

If $$4 \sin ^{-1} x+6 \cos ^{-1} x=3 \pi$$, where $$-1 \leq x \leq 1$$, then $$x=$$

$$\frac{1}{2}$$

$$\frac{1}{\sqrt{2}}$$

$$\frac{-1}{2}$$

MHT CET 2021 20th September Morning Shift

MCQ (Single Correct Answer)

-0

If $$h(x)=\sqrt{4 f(x)+3 g(x)}, f(1)=4, g(1)=3, f^{\prime}(1)=3, g^{\prime}(1)=4$$, then $$h^{\prime}(1)=$$

$$\frac{5}{12}$$

$$\frac{12}{5}$$

$$\frac{-5}{12}$$

$$\frac{-12}{7}$$

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