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

Chemistry

1. What are the formulae of the compounds formed when lanthanoids (Ln) react with nitrogen and halogen respectively? 2. Identify '$$\mathrm{A}$$' in the following reaction. $$A \stackrel{\text { Na/dry ether }}{\longrightarrow}$$ 3,4-diethy 3. For the reaction $$2 \mathrm{NO}+\mathrm{Cl}_2 \rightarrow 2 \mathrm{NOCl}$$ What is the relation between $$\frac{\mathr 4. What type of hybridization is exhibited by [CoF$$_6$$]$$^{3-}$$ ? 5. Which among the following is NOT the use of SO$$_2$$ gas? 6. Glucose and gluconic acid on oxidation with dilute nitric acid forms saccharic acid. This reaction confirms that glucose 7. Identify $$-$$I effect causing group from following. 8. Which from following instruments is used to determine the crystal structure? 9. Solubility of $$\mathrm{AgCl}$$ is $$7.2 \times 10^{-7} \mathrm{~mol} ~\mathrm{dm}^{-3}$$. What is it's solubility produ 10. Identify compound $$\mathrm{A}$$ used in following reaction. Benzoic acid $$\underset{\Delta}{\stackrel{A}{\longrightarr 11. In a first order reaction concentration of reactant decreases from 20 m mol to 10 m mol in 1.151 min. What is rate const 12. Which among following compounds is a primary amine? 13. Which among following properties of lanthanoids is NOT true? 14. How many total voids are present in 1 mole of compound that forms hcp structure? 15. Identify neutral complex from following. 16. How many molecules of methyl iodide are required to obtain tetramethyl ammonium iodide from dimethyl amine? 17. Which of the following processes does NOT involve use of dihydrogen? 18. Which of the following compounds does NOT exhibit optical isomerism? 19. What is the value of '$$\mathrm{x}$$' in order to balance the following redox reaction by ion electron method? $$\quad \ 20. Which among the following carbohydrates is a trisaccharide? 21. "Mass can neither be created nor destroyed" is the statement of 22. What is bond angle O-S-O in SO$$_2$$ molecule? 23. Which of the following bonds has highest bond enthalpy? 24. Which of the following compounds is optically inactive? 25. Which type of reaction order is followed by radioactive processes? 26. What is the total number of Bravais lattices present in seven types of crystal system? 27. Which among the following aqueous salt solution is used in conductivity cell to determine cell constant? 28. Calculate heat of formation of $$\mathrm{HCl}$$ gas from following reaction. $$\mathrm{H}_{2(\mathrm{~g})}+\mathrm{Cl}_{ 29. What is the value of frequency of radiation when transition occurs between two stationary states that differ in energy b 30. What is molar concentration of weak monobasic acid if dissociation constant is 5 $$\times$$ 10$$^{-8}$$ and undergoes 0. 31. A substance containing hydrogen and releasing H$$^+$$ in aqueous medium is acid. Identify theory suggesting this concept 32. What is the molar conductivity of $$0.05 \mathrm{M}$$ solution of sodium hydroxide, if it's conductivity is $$0.0118 \ma 33. Which among the following compounds has highest boiling point? 34. What is IUPAC name of the following compound? 35. What is molar mass of metal with BCC structure having density 10 g cm$$^{-3}$$ and edge length 200 pm? 36. Calculate difference between $$\Delta \mathrm{H}$$ and $$\Delta \mathrm{U}$$ for following reaction at $$25^{\circ} \mat 37. What is cryoscopic constant of water if $$5 \mathrm{~g}$$ of glucose in $$100 \mathrm{~g}$$ of water has depression in f 38. Which of the following pairs of alkenes is an example of position isomers? 39. Which of the following polymers is used in the preparation of cinema films? 40. In carbinol system isobutyl alcohol is named as 41. Which among the following is strongest acid? 42. Identify the isomerism exhibited by methoxyethane and propan-1-ol. 43. Which of the following statements is correct for boiling point of a liquid? 44. Henry's law constant for $$\mathrm{CH}_3 \mathrm{Br}$$ is $$0.16 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{bar}^{-1}$$ at $ 45. Identify negatively charged sol from following. 46. Which of the following monomer is used for preparation of Nylon-6? 47. Keeping temperature constant the pressure of 11.2 dm$$^3$$ of a gas was increased from 105 kPa to 420 kPa. What is the n 48. The change in internal energy of a system depends upon 49. How many faraday of electricity is required to produce 10 g of calcium metal (molar mass = 40 g mol$$^{-1}$$) from calci 50. Identify the product formed in the following reaction, $$\mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_2-\mathrm{CHO

Mathematics

1. $$\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]+\cot ^{-1}(-\sqrt{3})=$$ 2. If $$\mathrm{m}$$ is order and $$\mathrm{n}$$ is degree of the differential equation $$y=\frac{d p}{d x}+\sqrt{a^2 p^2-b 3. The surface area of a spherical balloon is increasing at the rate $$2 \mathrm{~cm}^2 / \mathrm{sec}$$. Then rate of incr 4. The p.m.f. of a random variable X is $$\mathrm{P(X = x) = {1 \over {{2^5}}}\left( {_x^5} \right),x = 0,1,2,3,4,5}=0$$ th 5. $$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are vectors such that $$|\overline{\mathrm{a}}|= 6. If $$\frac{n !}{2 !(n-2) !}$$ and $$\frac{n !}{4 !(n-4) !}$$ are in the ratio $$2: 1$$, then $$n=$$ 7. p : It rains today q : I am going to school r : I will meet my friend s : I will go to watch a movie. Then symbolic form 8. If $$a=\lim _\limits{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^2}$$ and $$b=\lim _\limits{n \rightarrow \infty} \fra 9. If $$\omega$$ is complex cube root of unity and $$(1+\omega)^7=A+B\omega$$, then values of A and B are, respectively 10. If $$[\bar{a} \bar{b} \bar{c}]=4$$, then the volume (in cubic units) of the parallelopiped with $$\bar{a}+2 \bar{b}, \ba 11. The variance of the following probability distribution is, 12. The general solution of the differential equation $$\cos x \cdot \sin y d x+\sin x \cdot \cos y d y=0$$ is 13. $$\overline{\mathrm{a}}, \overline{\mathrm{b}}$$ and $$\overline{\mathrm{c}}$$ are three vectors such that $$\overline{\ 14. $$\int \sec ^4 x \cdot \tan ^4 x d x=\frac{\tan ^m x}{m}+\frac{\tan ^n x}{n}+c$$ (where c is constant of integration), t 15. The x-intercept of a line passing through the points $$\left(\frac{-1}{2}, 1\right)$$ and (1, 2) is : 16. The Cartesian equation of the line passing through the points A(2, 2, 1) and B(1, 3, 0) is 17. If the variance of the numbers $$2,3,11$$ and $$x$$ is $$\frac{49}{4}$$, then the values of $$x$$ are 18. The differential equation of an ellipse whose major axis is twice its minor axis, is 19. The solution set for the system of linear inequations $$x+y \geq 1 ; 7 x+9 y \leq 63 ; y \leq 5 ; x \leq 6, x \geq 0$$ a 20. $$\cos ^{-1}\left(\frac{4}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)=$$ 21. The co-factors of the elements of second column of $$\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 2 & 1 \\ -1 & 3 & 4\end{a 22. The Cartesian equation of the plane $$\overline{\mathrm{r}}=(\hat{\mathrm{i}}-\hat{\mathrm{j}})+\lambda(\hat{\mathrm{i}} 23. The principal solutions of $$\sqrt{3} \sec x+2=0$$ are 24. $$\int \operatorname{cosec}(x-a) \operatorname{cosec} x d x=$$ 25. If $$f(x)=2x^3-15x^2-144x-7$$, then $$f(x)$$ is strictly decreasing in 26. The equation of the plane that contains the line of intersection of the planes. $$x+2 y+3 z-4=0$$ and $$2 x+y-z+5=0$$ an 27. If the sum of mean and variance of a binomial distribution for 5 trials is 1.8, then probability of a success is 28. $$y=\sqrt{e^{\sqrt{x}}}$$, then $$\frac{d y}{d x}=$$ 29. If area of the parallelogram with $$\bar{a}$$ and $$\bar{b}$$ as two adjacent sides is 20 square units, then the area of 30. If $$f(x) = {{{4^{x - \pi }} + {4^{x - \pi }} - 2} \over {{{(x - \pi )}^2}}}$$, for $$x \ne \pi $$, is continuous at $$x 31. The equation of tangent to the circle $$x^2+y^2=64$$ at the point $$\mathrm{P\left(\frac{2\pi}{3}\right)}$$ is 32. If $$2 f(x)-3 f\left(\frac{1}{x}\right)=x$$, then $$\int_\limits1^e f(x) d x=$$ 33. Water is being poured at the rate of 36 m$$^3$$/min. into a cylindrical vessel, whose circular base is of radius 3 m. T 34. If the equation $$3x^2-kxy-3y^2=0$$ represents the bisectors of angles between the lines $$x^2-3xy-4y^2=0$$, then value 35. The general solution of $$\left(x \frac{d y}{d x}-y\right) \sin \frac{y}{x}=x^3 e^x$$ is 36. The area bounded by the parabola $$y=x^2$$ and the line $$y=x$$ is 37. If $$y=\sin ^{-1}\left[\cos \sqrt{\frac{1+x}{2}}\right]+x^x$$, then $$\frac{d y}{d x}$$ at $$x=1$$ is 38. Negation of $$(p \wedge q) \rightarrow(\sim p \vee r)$$ is 39. If $$A^{-1}=\left[\begin{array}{lll}3 & 2 & 6 \\ 1 & 1 & 2 \\ 2 & 5 & 5\end{array}\right]$$, then $$A=$$ 40. The joint equation of pair of lines through the origin and making an equilateral triangle with the line $$y=3$$ is 41. If $$\bar{r}=-4 \hat{i}-6 \hat{j}-2 \hat{k}$$ is a linear combination of the vectors $$\bar{a}=-\hat{i}+4 \hat{j}+3 \hat 42. If $$A^{-1}=\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$$ and $$B^{-1}=\left[\begin{array}{cc}1 & 0 \\ -3 43. Two unbiased dice are thrown. Then the probability that neither a doublet nor a total of 10 will appear is 44. The population of a city increases at a rate proportional to the population at that time. If the population of the city 45. Let $$A=[a, b, c, d], B=[1,2,3]$$. Relation $$R_1, R_2, R_3, R_4$$ are as follows : $$\begin{aligned} & R_1=[(\mathrm{a} 46. If $$\cos x=\frac{24}{25}$$ and $$x$$ lięs in first quadrant, then $$\sin \frac{x}{2}+\cos \frac{x}{2}=$$ 47. If $$\int_\limits2^e\left[\frac{1}{\log x}-\frac{1}{(\log x)^2}\right] d x=a+\frac{b}{\log 2}$$, then 48. The vector equation of the line whose Cartesian equations are y = 2 and 4x $$-$$ 3z + 5 = 0 is 49. $$\int \frac{2 x^2-1}{x^4-x^2-20} d x=$$ 50. If $$x=a(t+\sin t), y=a(1-\cos t)$$, then $$\frac{d y}{d x}=$$

Physics

1. A perfect gas of volume 10 litre n compressed isothermally to a volume of 1 litre. The rms speed of the molecules will 2. In the arrangement of the capacitors as shown in figure, each capacitor is of 6 $$\mu$$F, then equivalent capacity betwe 3. The relation obeyed by a perfect gas during an adiabatic process is $$\mathrm{PV}^{3 / 2}$$. The initial temperature of 4. What is the additional energy that should be supplied to a moving electron to reduce its de Broglie wavelength from $$1 5. A convex lens of focal length $$\mathrm{T}$$ is used to form an image whose size is one fourth that of size of the objec 6. A particle at rest starts moving with a constant angular acceleration of $$4 \mathrm{~rad} / \mathrm{s}^2$$ in a circula 7. A metal conductor of length $$1 \mathrm{~m}$$ rotates vertically about one of its ends at an angular velocity of $$5 \ma 8. A black rectangular surface of area '$$\mathrm{A}$$' emits energy '$$\mathrm{E}$$' per second at $$27^{\circ} \mathrm{C} 9. A disc of radius 0.4 metre and mass 1 kg rotates about an axis passing through its centre and perpendicular to its plane 10. The output of an 'OR' gate is 'one' 11. A monoatomic gas is suddenly compressed to (1/8)th of its initial volume adiabatically. The ratio of the final pressure 12. In the case of insulators, a band gap and conduction band is respectively 13. In a single slit diffraction pattern, the distance between the first minimum on the left and the first minimum on the ri 14. A conducting rod of length $$1 \mathrm{~m}$$ has area of cross-section $$10^{-3} \mathrm{~m}^2$$. One end is immersed in 15. Which one of the following statements is true? 16. A particle executes S.H.M. of period $$\frac{2 \pi}{\sqrt{3}}$$ second along a straight line $$4 \mathrm{~cm}$$ long. Th 17. Two consecutive harmonics of an air column in a pipe closed at one end are of frequencies 150 Hz and 250 Hz. The fundame 18. Two masses '$$m_{\mathrm{a}}$$' and '$$\mathrm{m}_{\mathrm{b}}$$' moving with velocities '$$v_{\mathrm{a}}$$' and '$$v_{ 19. A sample of radioactive element contains $$8 \times 10^{16}$$ active nuclei. The halt-life of the element is 15 days. Th 20. In Young's double slit experiment, with a source of light having wavelength $$6300 \mathop A\limits^o$$, the first maxim 21. What should be the radius of water drop so that excess pressure inside it is 72 Nm$$^{-2}$$ ? (The surface tension of w 22. A body of density $$V$$ is dropped from (at rest) height '$$h$$' into a lake of density '$$\delta$$' $$(\delta > \rho)$$ 23. A parallel plate air capacitor is charged upto 100 V. A plate 2 mm thick is inserted between the plates. Then to maintai 24. A uniformly charged semicircular arc of radius '$$r$$' has linear charge density $$(\lambda)$$, is the electric field at 25. The P.E. 'U' of a moving particle of mass 'm' varies with 'x'-axis as shown in figure. The deBroglie wavelength or the p 26. An inductive coil has a resistance of $$100 ~\Omega$$. When an a.c. signal of frequency $$1000 \mathrm{~Hz}$$ is applied 27. The ratio of radii of gyration of a circular ring and circular disc of the same mass and radius, about an axis passing t 28. Two wires carrying currents $$5 \mathrm{~A}$$ and $$2 \mathrm{~A}$$ are enclosed in a circular loop as shown in the figu 29. A particle is suspended from a vertical spring which is executing S.H.M. of frequency $$5 \mathrm{~Hz}$$. The spring is 30. Photoelectrons are emitted when photons of energy $$4.2 ~\mathrm{eV}$$ are incident on a photosensitive metallic sphere 31. A cricket player hit a ball like a projectile but the fielder caught the ball after 2 second. The maximum height reached 32. In an ideal step down transformer, out of the following quantities, which quantity increases in the secondary coil? 33. An air column in a pipe, which is closed at one end will be in resonance with a vibrating tuning fork of frequency 264 H 34. The surface energy of a liquid drop is 'U'. It splits up into 512 equal droplets. The surface energy becomes 35. A rectifier is used to 36. Two stars 'P' and 'Q' emit yellow and blue light respectively. The relation between their temperatures $$\left(\mathrm{T 37. Inside a vessel filled with liquid a converging lens is placed as shown in figure. The lens has focal length $$15 \mathr 38. A metal wire of length $$2500 \mathrm{~m}$$ is kept in east-west direction, at a height of $$10 \mathrm{~m}$$ from the g 39. A body is projected from earth's surface with thrice the escape velocity from the surface of the earth. What will be its 40. The depth at which acceleration due to gravity becomes $$\frac{\mathrm{g}}{\mathrm{n}}$$ is [ $$\mathrm{R}$$ = radius of 41. A series LCR circuit with resistance (R) $$500 ~\mathrm{ohm}$$ is connected to an a.c. source of $$250 \mathrm{~V}$$. Wh 42. The gyromagnetic ratio of an electron in an hydrogen atom, according to Bohr model is 43. A body performs S.H.M. under the action of force '$$\mathrm{F}_1$$' with period '$$\mathrm{T}_1$$' second. If the force 44. Beats are produced by waves $$\mathrm{y_1=a\sin2000\pi t}$$ and $$\mathrm{y_2=a\sin2008\pi t}$$. The number of beats hea 45. In Young's double slit experiment, the intensity at a point where the path difference is $$\frac{\lambda}{4}$$ [ $$\lamb 46. The magnetic field at the centre of a current carrying circular coil of area 'A' is 'B'. The magnetic moment of the coil 47. A galvanometer has resistance '$$\mathrm{G}$$' $$\Omega$$ and '$$\mathrm{I}_{\mathrm{g}}$$' is current flowing through i 48. In potentiometer experiment, null point is obtained at a particular point for a cell on potentiometer wire '$$\mathrm{x} 49. A hollow charged metal sphere has radius 'R'. If the potential difference between its surface and a point at a distance 50. The relation between magnetic moment 'M' of revolving electron and principle quantum number 'n' is

MHT CET 2021 20th September Evening Shift

MCQ (Single Correct Answer)

-0

If $$\cos x=\frac{24}{25}$$ and $$x$$ lięs in first quadrant, then $$\sin \frac{x}{2}+\cos \frac{x}{2}=$$

$$\frac{6}{5 \sqrt{2}}$$

$$\frac{8}{5 \sqrt{2}}$$

$$\frac{7}{5 \sqrt{2}}$$

$$\frac{1}{5 \sqrt{2}}$$

MHT CET 2021 20th September Evening Shift

MCQ (Single Correct Answer)

-0

If $$\int_\limits2^e\left[\frac{1}{\log x}-\frac{1}{(\log x)^2}\right] d x=a+\frac{b}{\log 2}$$, then

$$a=-e, b=2$$

$$a=e, b=-2$$

$$a=e, b=2$$

$$a=-e, b=-2$$

MHT CET 2021 20th September Evening Shift

MCQ (Single Correct Answer)

-0

The vector equation of the line whose Cartesian equations are y = 2 and 4x $$-$$ 3z + 5 = 0 is

$$\overline{\mathrm{r}}=(2 \hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda(3 \hat{\mathrm{i}}-4 \hat{\mathrm{k}})$$

$$\overline{\mathrm{r}}=\left(2 \hat{\mathrm{j}}+\frac{5}{3} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}})$$

$$\bar{r}=(2 \hat{i}+\hat{k})+\lambda(3 \hat{i}+4 \hat{j})$$

$$\overline{\mathrm{r}}=\left(2 \hat{\mathrm{j}}+\frac{5}{3} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}-4 \hat{\mathrm{k}})$$

MHT CET 2021 20th September Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{2 x^2-1}{x^4-x^2-20} d x=$$

$$\frac{1}{\sqrt{5}} \log \left|\frac{x+\sqrt{5}}{x-\sqrt{5}}\right|+\tan ^{-1}\left(\frac{x}{2}\right)+c$$

$$\frac{1}{2 \sqrt{5}} \log \left|\frac{x+\sqrt{5}}{x-\sqrt{5}}\right|+\tan ^{-1}\left(\frac{x}{2}\right)+c$$

$$\frac{1}{2 \sqrt{5}} \log \left|\frac{x-\sqrt{5}}{x+\sqrt{5}}\right|+\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)+c$$

$$\frac{1}{2} \log \left|\frac{x-\sqrt{5}}{x+\sqrt{5}}\right|+\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)+c$$

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