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

Chemistry

1. What is the number of octahedral and tetrahedral voids presents respectively in 0.25 mole of a substance having hcp stru 2. For a reaction $$\mathrm{A} \rightarrow$$ product, rate constant is $$2 \times 10^{-2} \mathrm{~s}^{-1}$$. The initial c 3. When tert-butyl bromide is heated with silver fluoride, the major product obtained is 4. What are the final products obtained by ozonolysis of propene? 5. The vapour pressure of a solvent decreases by 2.5 mm Hg by adding a solute. What is the mole fraction of solute? (Vapour 6. Which element from following belongs to oxygen family? 7. Which among following statements is NOT true for neoprene? 8. The common name of Benzene-1,2-diol is 9. Identify the correct pair of mineral and its formula from following. 10. Which element from following exhibits various different oxidation states from +2 to +7? 11. Which among following compounds has highest boiling point? 12. The dissociation constant of weak monobasic acid is 2.7 $$\times$$ 10$$^{-5}$$. If degree of dissociation of acid is 3 $ 13. Identify order of reaction if it's rate constant is x sec$$^{-1}$$. 14. What is IUPAC name of following compound? 15. Enthalpy of formation of methane is $$-$$75 kJ/mol. What is the enthalpy change for formation of 24 g of methane? 16. The solubility product of a sparingly soluble salt AX$$_2$$ is 3.2 $$\times$$ 10$$^{-8}$$. What is it's solubility in mo 17. Which among the following is true for chemisorption? 18. Identify 'A' in following reaction. A $$\mathrm{\buildrel {Dimethyl\,cadmium} \over \longrightarrow}$$ propanone + cadm 19. What is the resistance of $$0.01 ~\mathrm{M} ~\mathrm{KCl}$$ solution if its conductivity is $$200 ~\mathrm{ohm}^{-1} \m 20. Which of the following concepts is NOT of valence bond theory? 21. Which among the following is a pair of dicarboxylic acids? 22. What is the number of N atoms present in EDTA? 23. Which is C-terminal residue in glycyl alanine? 24. The expansion of gas having no opposing force is called as 25. Molar conductivity of 0.04 M BaCl$$_2$$ solution is 230 $$\Omega^{-1}$$ cm$$^2$$ mol$$^{-1}$$ at 27$$^\circ$$C. What is 26. 1 mole of an ideal gas expands isothermally and reversibly by decreasing pressure form $$210 \mathrm{~kPa}$$ to $$105 \m 27. What is the mass of potassium chloride produced when $$12.25 \mathrm{~g}$$ potassium chlorate undergo decomposition? (At 28. What type of hybridization is present in $$\mathrm{Ni}$$ of $$\left[\mathrm{Ni}(\mathrm{Cl})_4\right]^{2-}$$ and $$\left 29. What is the molar mass of a metal having density 8.57 g cm$$^{-3}$$ and edge length 3.3 $$\mathop A\limits^o $$ ? (packi 30. The wavelength of blue light is $$480 \mathrm{~nm}$$. What is frequency of this light? 31. Identify the reagent used in following conversion. Chloroethane $$\stackrel{\mathrm{A}}{\longrightarrow}$$ Nitro ethane 32. Which of the following polymers is obtained from $$\varepsilon$$-caprolactum? 33. Identify correct composition of water gas from following. 34. Identify the major product formed when 2-Methylhexan-3-ol is heated with concentrated sulphuric acid. 35. For the reaction $$2 \mathrm{~A}+2 \mathrm{~B} \rightarrow 2 \mathrm{C}+\mathrm{D}$$ if $$\mathrm{r}=\mathrm{k}[\mathrm{ 36. What is the difference in molar mass of a member of homologous series from it's neighboring members in gram per mole? 37. Identify $$\mathrm{N}$$ and $$\mathrm{C}$$ terminal of $$\alpha $$-amino acid respectively in following polypeptide frag 38. Which from following formulae is a correct formula to determine percent atom economy? 39. What is IUPAC name of following compound? 40. Identify reductant in following reaction. $$\mathrm{H}_2 \mathrm{~S}+\mathrm{NO}_2 \rightarrow \mathrm{H}_2 \mathrm{O}+\ 41. What is the value of critical temperature of water? 42. Identify the compound from following having lowest boiling point. 43. Which among the following isomers of $$\mathrm{C}_4 \mathrm{H}_9 \mathrm{OH}$$ has lowest boiling point? 44. Which of the following salt solutions is highly acidic? 45. Molal depression constant for a liquid is $$2.77^{\circ} \mathrm{C} ~\mathrm{kg} ~\mathrm{mol}^{-1}$$, in Kelvin scale i 46. Which among the following statement is NOT true about homologous series of organic compounds? 47. If 6 g of solute dissolved in 100 g of water lowers the freezing point by 0.93 K. What is molar mass of solute? (K$$_\ma 48. Which from following electrolytes, molar conductivity is determined using Kohlrausch theory? 49. How many lattice points are present in a face centred cubic unit cell? 50. Which block elements from following are known as transition elements?

Mathematics

1. A polygon has 44 diagonals. Then the number of sides of the polygon are 2. If $$x=1+2 i$$, then the value of $$x^3+7 x^2-x+16$$ is 3. If $$y^2=a x^2+b x+c$$, where $$a, b, c$$ are constants, then $$y^3 \frac{d^2 y}{d x^2}$$ is equal to 4. The equation of a circle that passes through the origin and cut off intercepts $$-2$$ and 3 on the $$\mathrm{X}$$-axis a 5. Let $$f(x)\matrix{ { = |x| + 3,} & {if\,x \le - 3} \cr { = - 2x,} & {if\, - 3 6. The particular solution of the diffrential equation $$y(1+\log x)=\left(\log x^x\right) \frac{d y}{d x}$$, when $$y(e)=e 7. If statements $$\mathrm{p}$$ and $$\mathrm{q}$$ are true and $$\mathrm{r}$$ and $$\mathrm{s}$$ are false, then truth val 8. Bismath has half life period of 5 days. A sample originally has a mass of 1000 mg, then the mass of Bismath after 30 day 9. In $$\triangle A B C$$, with usual notations, $$2 a b \sin \frac{1}{2}(A+B-C)=$$ 10. $$\tan 3 \mathrm{~A} \cdot \tan 2 \mathrm{~A} \cdot \tan \mathrm{A}=$$ 11. If slope of one of the lines ax$$^2$$ + 2hxy + by$$^2$$ = 0 is twice that of the other, then h$$^2$$ : ab is 12. The general solution of $$\sin ^{-1}\left(\frac{d y}{d x}\right)=x+y$$ is 13. If $$A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1\end{array}\right]$$, then the value of determinant of 14. Solution of the differential equation $$\mathrm{y'=\frac{(x^2+y^2)}{xy}}$$, where y(1) = $$-$$2 is given by 15. The Cartesian equation of a line is $$3 x+1=6 y-2=1-z$$, then its vector equation is 16. The position vector of the point of inersection of the medians of a triangle, whose vertices are $$A(1,2,3), B(1,0,3)$$ 17. $$\int\limits_{ - \pi }^\pi {{{x\sin x} \over {1 + {{\cos }^2}x}}dx = } $$ 18. $$\int {{e^x}\left( {{{x - 1} \over {{x^2}}}} \right)dx = } $$ 19. Area of the triangle formed by the lines $$y^2-9 x y+18 x^2=0$$ and $$y=9$$ is 20. The point on the curve $$y^2=2(x-3)$$ at which the normal is parallel to the line $$y-2 x+1=0$$ is 21. For two events $$\mathrm{A}$$ and $$\mathrm{B}, \mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{5}{6}, \mathrm{P}(\mathrm{A 22. A rectangle of maximum area is inscribed in an ellipse $$\frac{x^2}{25}+\frac{y^2}{16}=1$$, then its dimensions are 23. The area bounded between the curve $$x^2=y$$ and the line $$y=4 x$$ is 24. $$\lim _\limits{x \rightarrow 0} \frac{\cos (m x)-\cos (n x)}{x^2}=$$ 25. The area of the parallelogram whose diagonals are represented by the vectors $$\bar{a}=3 \hat{i}-\hat{j}-2 \hat{k}$$ and 26. If $$\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}=\overline{0}$$ with $$|\overline{\mathrm{a}}|=3,| 27. The plane $$\frac{x}{2}+\frac{y}{3}+\frac{z}{4}=1$$ cuts the $$X$$-axis at A, Y-axis at B and Z-axis at C, then the area 28. A random variable X has following distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:bl 29. A sperical snow ball is forming so that its volume is increasing at the rate of $$8 \mathrm{~cm}^3 / \mathrm{sec}$$. Fin 30. If $$|\bar{u}|=2$$ and $$\bar{u}$$ makes angles of $$60^{\circ}$$ and $$120^{\circ}$$ with axes $$\mathrm{OX}$$ and $$\m 31. If $$A = \left[ {\matrix{ k & 2 \cr { - 2} & { - k} \cr } } \right]$$, then A$$^{-1}$$ does not exists if k 32. If in $$\Delta$$ABC, with usual notations, the angles are in A.P., then $$\mathrm{\frac{a}{c}}$$ sin 2 C + $$\mathrm{\fr 33. A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails, 34. The maximum value of $$z=10 x+25 y$$ subject to $$0 \leq x \leq 3,0 \leq y \leq 3, x+y \leq 5$$ occurs at the point. 35. The expression $$[(p \wedge \sim q) \vee q] \vee(\sim p \wedge q)$$ is equivalent to 36. If a plane meets the axes $$\mathrm{X}, \mathrm{Y}, \mathrm{Z}$$ in $$\mathrm{A}, \mathrm{B}, \mathrm{C}$$ respectively 37. The sum of three numbers is 6. Thrice the third number when added to the first number gives 7. On adding three times fir 38. $$\tan ^{-1}\left(\tan \frac{5 \pi}{6}\right)+\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)=$$ 39. The value of $$\int\limits_0^1 {{{\tan }^{ - 1}}\left( {{{2x - 1} \over {1 + x - {x^2}}}} \right)dx} $$ is 40. $$x=\frac{1-t^2}{1+t^2}$$ and $$y=\frac{2 a t}{1+t^2}$$, then $$\frac{d y}{d x}=$$ 41. $$\int \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x=\quad(\text { where }|x| 42. The domain of the function $$f(x)=\sqrt{x-1}+\sqrt{6-x}$$ is 43. The differential equation of all family of lines $$y=m x+\frac{4}{m}$$ obtained by eliminating the arbitrary constant $$ 44. If the variance of the data 2, 4, 5, 6, 8, 17 is 23.33, then the variance of 4, 8, 10, 12, 16, 34 will be 45. $$y=\tan ^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right), 0 \leq x 46. A random variable X $$\sim$$ B (n, p), if values of mean and variance of X are 18 and 12 respectively, then n = 47. The shortest distance between lines $$\bar{r}=(2 \hat{i}-\hat{j})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})$$ and $$\bar{r}=( 48. The equation of perpendicular bisector of the line segment joining $$A(-2,3)$$ and $$B(6,-5)$$ is 49. If $$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are mutually perpendicular vectors having mag 50. $$\int \frac{\sec ^8 x}{\operatorname{cosec} x} d x= $$

Physics

1. Two rotating bodies $$P$$ and $$Q$$ of masses '$$\mathrm{m}$$' and '$$2 \mathrm{~m}$$' with moment of inertia $$I_P$$ an 2. A sound wave is travelling with a frequency of $$50 \mathrm{~Hz}$$. The phase difference between the two points in the p 3. A logic gate which gives output 'HIGH' only when its two input terminals are at different logic levels with respect to e 4. A circular coil of radius '$$R$$' has '$$N$$' turns of a wire. The coefficient of self induction of the coil will be ( $ 5. An a.c. source of angular frequency '$$\omega$$' is fed across a resistor '$$R$$' and a capacitor '$$C$$' in series. The 6. A transverse wave given by $$y=2 \sin (0.01 x+30 t)$$ moves on a stretched string from one end to another end in 0.5 sec 7. The translational kinetic energy of the molecules of a gas at absolute temperature (T) can be doubled 8. When a light of wavelength '$$\lambda$$' falls on the emitter of a photocells, maximum speed of emitted photoelectrons i 9. A polyatomic gas $$(\gamma=4 / 3)$$ is compressed to $$\left(\frac{1}{8}\right)^{\text {th }}$$ of its volume adiabatica 10. If $$\omega_1$$ is angular velocity of hour hand of clock and $$\omega_2$$ is angular velocity of the earth, then the ra 11. A wire of length 1 m is moving at a speed of 2 m/s perpendicular homogenous magnetic field of 0.5 T. The ends of the wir 12. In Young's double slit experiment, the $$10^{\text {th }}$$ maximum of wavelength '$$\lambda_1$$' is at a distance of '$ 13. A mass $$0.4 \mathrm{~kg}$$ performs S.H.M. with a frequency $$\frac{16}{\pi} \mathrm{Hz}$$. At a certain displacement i 14. The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape 15. A biconvex lens $$\left(R_1=R_2=30 \mathrm{~cm}\right)$$ has focal length equal to the focal length of concave mirror. T 16. In an a.c. circuit, a resistance R = 40 $$\Omega$$ and an inductance 'L' are connected in series. If the phase angle bet 17. A pipe open at both ends of length 1.5 m is dipped in water such that the second overtone of vibrating air column is res 18. Choose the FALSE statement from the following. 19. A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges w 20. If the temperature of the sun is doubled, the rate of energy received by the earth will be increased by a factor 21. Water rises in a capillary tube of radius '$$r$$' up to a height '$$\mathrm{h}$$'. The mass of water in a capillary is ' 22. In a wheatstone's bridge, three resistances $$\mathrm{P}, \mathrm{Q}$$ and $$\mathrm{R}$$ are connected in the three arm 23. If a current flowing in a coil is reduced to half of its initial value, the relation between the new energy $$\left(E_2\ 24. The critical angle for light going from medium A into medium B is $$\theta$$. The speed of light in the medium A is $$\m 25. Which of the following statements is true? ($$\Delta \mathrm{U}=$$ increase in internal energy, $$\mathrm{dW}=$$ work do 26. The frequency of the output signal of an LC oscillator circuit is '$$\mathrm{F}$$' Hz with a capacitance of 0.1 $$\mu \m 27. A solid sphere of mass '$$M$$' and radius '$$R$$' is rotating about its diameter. A solid cylinder of same mass and same 28. When a battery is connected to the two ends of a diagonal of a square conductor frame of side '$$a$$', the magnitude of 29. A car of mass '$$m$$' moving with velocity '$$u$$' on a straight road in a straight line, doubles its velocity in time t 30. A bob of a simple pendulum of mass 'm' is displaced through 90$$^\circ$$ from mean position and released. When the bob i 31. Let '$$\mathrm{W}_1$$' be the work done in blowing a soap bubble of radius '$$r$$' from soap solution at room temperatur 32. A cylindrical rod is having temperatures $$\theta_1$$ and $$\theta_2$$ at its ends. The rate of heat flow is '$$Q$$' $$\ 33. Two concentric coplanar circular loops of radii '$$r{ }_1$$' and '$$r_2$$' respectively carry currents '$$i_1$$' and '$$ 34. The Kirchhoff's current law and voltage law are respectively based upon the conservation of 35. The permeability of a metal is $$0.1256 ~\mathrm{TmA}^{-1}$$. Its relative permeability will be $$\mathrm{\left( {{{{\mu 36. The angular displacement of body performing circular motion is given by $$\theta=5 \sin \frac{\pi t}{6}$$. The angular v 37. A single slit diffraction pattern is formed with white light. For what wavelength of light the $$3^{\text {rd }}$$ secon 38. A point charge $$\mathrm{Q}$$ is placed at the centre of the line joining two equal point charges $$+\mathrm{q}$$ and $$ 39. If the charge on the capacitor is increased by 2 C the energy stored in it increased by 21%. Total original charge on th 40. A nucleus breaks into two nuclear parts, which have their velocity ratio $$2: 1$$. The ratio of their nuclear radii will 41. A body performing uniform circular motion of radius 'R' has frequency 'n'. It centripetal acceleration is 42. For a gas molecule with 6 degrees of freedom, which one of the following relation between gas constant '$$\mathrm{R}$$' 43. When the battery across the plates of a charged condenser is disconnected and a dielectric slab is introduced between it 44. The width of central maximum of a diffraction pattern on a single slit does not depend upon 45. If the amplitude of linear S.H.M. is decreased then 46. In an n-p-n transistor 200 electrons enter the emitter in 10$$^{-8}$$ second. If 1% electrons are lost in the base, then 47. In the given figure potential at point 'A' is 900 volt and point 'B' is earthed. What will be the potential at point 'P' 48. Kinetic energy of a proton is equal to energy '$$E$$' of a photon. Let '$$\lambda_1$$' be the de-Broglie wavelength of p 49. A drop of liquid of density '$$\rho$$' is floating half immersed in a liquid of density '$$d$$'. If '$$T$$' is the surfa 50. Assuming the atom is in the ground state, the expression for the magnetic field at a point nucleus in hydrogen atom due

MHT CET 2021 22th September Morning Shift

MCQ (Single Correct Answer)

-0

$$\tan ^{-1}\left(\tan \frac{5 \pi}{6}\right)+\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)=$$

$$3 \pi$$

$$\frac{-\pi}{6}$$

$$\frac{\pi}{6}$$

MHT CET 2021 22th September Morning Shift

MCQ (Single Correct Answer)

-0

The value of $$\int\limits_0^1 {{{\tan }^{ - 1}}\left( {{{2x - 1} \over {1 + x - {x^2}}}} \right)dx} $$ is

$$-$$1

MHT CET 2021 22th September Morning Shift

MCQ (Single Correct Answer)

-0

$$x=\frac{1-t^2}{1+t^2}$$ and $$y=\frac{2 a t}{1+t^2}$$, then $$\frac{d y}{d x}=$$

$$\frac{a\left(t^2+1\right)}{2 t}$$

$$\frac{a\left(t^2-1\right)}{t}$$

$$\frac{a\left(1-t^2\right)}{2 t}$$

$$\frac{a\left(t^2-1\right)}{2 t}$$

MHT CET 2021 22th September Morning Shift

MCQ (Single Correct Answer)

-0

$$\int \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x=\quad(\text { where }|x| < 1)$$

$$2 \tan ^{-1} x-\log \left|1+x^2\right|+c$$

$$x \tan ^{-1} \mathrm{x}+\log \left|1+\mathrm{x}^2\right|+\mathrm{c}$$

$$\tan ^{-1} \mathrm{x}+\log \left|1+\mathrm{x}^2\right|+\mathrm{c}$$

$$2 x \tan ^{-1} x-\log \left|1+x^2\right|+c$$

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