MHT CET 2021 23th September Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. What is the formal charge on '$$\mathrm{N}$$' atom in $$\mathrm{NH}_4^{+}$$ ion? 2. Identify most stable free radical from following : 3. Which among the following salt solution in water shows pH less than 7 ? 4. Ethoxy benzene on reaction with hot and concentrated HI forms 5. What is vapour pressure of solution containing $$1.8 \mathrm{~g}$$ glucose in $$16.2 \mathrm{~g}$$ water? ($$\mathrm{P}_ 6. The rate law equation for a reaction between $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ is $$\mathrm{r}=\mathrm{k}[\m 7. Identify product $$\mathrm{C}$$ in following conversion. m - Hydroxy Benzaldehyde $$ \xrightarrow[\text { [Protection of 8. Which of the following is NOT dihydric alcohol? 9. Identify the sugar containing $$\alpha, \beta-1,2$$-glycosidic linkage. 10. What is the freezing point of 1 molal aqueous solution of a non volatile solute? ($$\mathrm{K}_{\mathrm{f}}=1.86 \mathrm 11. How many particles per unit cell are present in $$\mathrm{BCC}$$ structure? 12. Identify ferromagnetic element from following. 13. Identify the reagent used in following conversion. Pent -3 -enenitrile $$\xrightarrow{\mathrm{A}}$$ pent -3 -enal 14. Which of the following complexes is diamagnetic and square planar? 15. What is the mass of $$33.6 \mathrm{~dm}^3$$ of methane gas at S.T.P.? 16. An element with BCC structure has edge length of $$500 \mathrm{~pm}$$. If it's density is $$4 \mathrm{~g} \mathrm{~cm}^{ 17. Identify the reagent (A) used in the following reaction. 18. What is the product formed when side chain chlorination of toluene is carried out followed by acid hydrolysis at $$373 \ 19. A system gives out $$\mathrm{x} \mathrm{~J}$$ of heat and does $$\mathrm{y} \mathrm{~J}$$ of work on it's surrounding. W 20. Which of following reactions yields biphenyl from chlorobenzene? 21. A system does 394 J of work on surrounding by absorbing 701 J heat. What is the change in internal energy of the system? 22. How many electrons flow through the wire if a current of 1.5 ampere flow through it for 3 hours? 23. The conductivity of $$0.3 \mathrm{M}$$ solution of $$\mathrm{KCl}$$ at $$298 \mathrm{~K}$$ is $$0.0627 \mathrm{~S} \math 24. The solubility of $$\mathrm{Ag}_2 \mathrm{C}_2 \mathrm{O}_4$$ is $$2 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1}$$ at 25. Two electrons occupying the same orbital are distinguished by 26. Which statement from following is correct for homolytic fission? 27. Identify catalyst used in manufacturing of HDP. 28. Air is an example of a solution of 29. A gas has a volume of $$3.4 \mathrm{~L}$$ at $$298 \mathrm{~K}$$. What is the final temperature if the volume of gas inc 30. What is the atomic radius of polonium if it crystallises in a simple cubic structure with edge length of unit cell $$336 31. Which among the following halides has triagonal bipyramidal structure? 32. Which among following compounds is used as monomer in preparation of Teflon? 33. Which of the following is NOT obtained when a mixture of bomomethane and bromoethane is treated with sodium in dry ether 34. Time required for $$90 \%$$ completion of a first order reaction is $$t$$. What is the time required for completion of $ 35. A weak monobasic acid is $$3.0 \%$$ dissociated in it's $$0.04 \mathrm{~M}$$ solution. What is the dissociation constant 36. Which of the following alkanes is optically active? 37. Identify the number of unpaired electrons present and geometry respectively of [Co(NH$$_3$$)$$_6$$]$$^{3+}$$ complex. 38. Which among the following compounds is a weakest base? 39. In the cell represented as $$\mathrm{Ni}_{(\mathrm{s})}\left|\mathrm{Ni}_{(\mathrm{IM})}^{2 \oplus}\right|\left|\mathrm{ 40. What is the value of intercept on $$y$$-axis when $$\log \frac{x}{m}$$ is plotted against $$\log P$$ in Freundlich isoth 41. Which from following statements is true for group 16 elements? 42. Which among the following formulae is correctly represented according to stock notation? 43. Identify the major product when anisole is treated with $$\mathrm{Br}_2$$ in presence of acetic acid. 44. All the elements of group 2 react with water to form metal hydroxide and hydrogen, except the element 45. Which of the following compound is obtained when glucose is treated with dilute nitric acid? 46. What is the IUPAC name of glyoxal? 47. The order of reaction for which the units of rate constant are $$\mathrm{mol} \mathrm{~dm}^{-3} \mathrm{~s}^{-1}$$ is 48. Which among the following is a nonferrous alloy? 49. Identify product '$$\mathrm{B}$$' in following reaction. $$\mathrm{CH}_3 \mathrm{Br}+\mathrm{AgNO}_2 \longrightarrow \ma 50. A balloon contains $$2.27 \mathrm{~L}$$ air and has a pressure of $$1.013 \times 10^5 \mathrm{~Nm}^{-2}$$. The balloon r

Mathematics

1. If A(3, 2, $$-$$1), B($$-$$2, 2, $$-$$3) and D($$-$$2, 5, $$-$$4) are the vertices of a parallelogram, then the area of 2. If $$\hat{a}$$ is a unit vector such that $$(\bar{x}-\hat{a}) \cdot(\bar{x}+\hat{a})=8$$, then $$|\bar{x}|=$$ 3. The equation of line, where length of the perpendicular segment from origin to the line is 4 and the inclination of this 4. If $$\int \frac{\sin x}{\sin (x-\alpha)} d x=A x+B \log \sin (x-\alpha)+c$$, then the value of A and B are respectively 5. The probability distribution of the number of doublets in four throws of a pair of dice is given by 6. Let $$\vec{v}=2 \hat{i}+2 \hat{j}-\hat{k}$$ and $$\bar{w}=\hat{i}+3 \hat{k}$$. If $$\bar{u}$$ is a unit vector, then the 7. S1 : If $$-$$7 is an integer, then $$\sqrt{-7}$$ is a complex number $$\mathrm{S} 2$$ : $$-$$7 is not an integer or $$\s 8. For the probability distribution given by following .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-col 9. $$\int_\limits0^1|5 x-3| d x=$$ 10. Function $$f(x)=e^{-1 / x}$$ is strictly increasing for all $$x$$ where 11. The distance between the parallel lines $$\frac{x-2}{3}=\frac{y-4}{5}=\frac{z-1}{2}$$ and $$\frac{x-1}{3}=\frac{y+2}{5}= 12. The general solution of the differential equation $$\frac{d y}{d x}+\frac{y^2+y+1}{x^2+x+1}=0$$ is 13. $$\tan \left(\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right)=$$ 14. The general solution of the differential equation $$\frac{d x}{d t}=\frac{x \log x}{t}$$ is 15. If $$3 \sin \theta=2 \sin 3 \theta$$ and $$0 16. The maximum value of the objective function $$z=2 x+3 y$$ subject to the constraints $$x+y \leq 5,2 x+y \geq 4$$ and $$x 17. The particular solution of differential equation $$(x+y) d y+(x-y) d x=0$$ at $$x=y=1$$ is 18. $$\int \frac{10^{\frac{x}{2}}}{\sqrt{10^{-x}-10^x}} d x=$$ 19. $$\int_0^{\pi / 2} \frac{\cos x}{3 \cos x+\sin x} d x=$$ 20. If $$A=\left[\begin{array}{rr}2 & 3 \\ 5 & -2\end{array}\right]$$ and $$A^{-1}=K A$$, then $$K$$ is 21. If $$\mathrm{A}=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$$, then $$\mathrm{A}(\ope 22. A random variable X has the following probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td 23. If $$x=-2$$ and $$x=4$$ are the extreme points of $$y=x^3-\alpha x^2-\beta x+5$$, then 24. The coordinates of the foot of the perpendicular drawn from the origin to the plane $$2 x+y-2 z=18$$ are 25. If a circle passes through the points $$(0,0),(x, 0)$$ and $$(0, y)$$, then the coordinates of its centre are 26. If $$A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & -1 & 0 \\ 3 & 3 & -4\end{array}\right], B=\left[\begin{array}{l}1 \\ 1 27. If $$\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}, \overline{\mathrm{b}}=-\hat{\ma 28. If two lines represented by $$a x^2+2 h x y+b y^2=0$$ makes angles $$\alpha$$ and $$\beta$$ with positive direction of $ 29. If $$\tan ^{-1}\left[\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right]=\alpha$$, then the value of $$\s 30. The general solution of the differential equation $$\frac{d y}{d x}=2^{y-x}$$ is 31. The vector equation of the line passing through $$\mathrm{P}(1,2,3)$$ and $$\mathrm{Q}(2,3,4)$$ is 32. Range of the function $$f(x)=3+2^x+4^x$$ is 33. The combined equation of a pair of lines passing through the origin and inclined at $$60^{\circ}$$ and $$30=$$ respectiv 34. $$\int e^{\left(e^x+x\right)} d x=$$ 35. If $$z=x+iy$$ satisfies the condition $$|z+1|=1$$, then $$z$$ lies on the 36. If $$3 \hat{j}, 4 \hat{k}$$ and $$3 \hat{j}+4 \hat{k}$$ are the position vectors of the vertices $$A, B, C$$ respectivel 37. 10 is divided into two parts such that the sum of double of the first and square of the other is minimum, then the numbe 38. In a triangle $$\mathrm{ABC}$$, with usual notations $$\mathrm{a}=2, \mathrm{~b}=3, \mathrm{c}=5$$, then $$\frac{\cos \m 39. If $$f(x)=\frac{1-\sin x+\cos x}{1+\sin x+\cos x}$$, for $$x \neq \pi$$ is continuous at $$x=\pi$$, then the value of $$ 40. 140. Given that total of 16 values is 528 and sum of the squares of deviation from 33 is 9158. The variance is 41. $$\lim _\limits{x \rightarrow 1}\left[\frac{\sqrt{x}-1}{\log x}\right]=$$ 42. If the surrounding air is kept at $$25^{\circ} \mathrm{C}$$ and a body cools from $$80^{\circ} \mathrm{C}$$ to $$50^{\ci 43. Rooms in a hotel are numbered from 1 to 19. Rooms are allocated at random as guests arrive. The first guest to arrive is 44. Negation of the statement : $$3+6>8$$ and $$2+3 45. If $$f(x)=\operatorname{cosec}^{-1}\left[\frac{10}{6 \sin \left(2^x\right)-8 \cos \left(2^x\right)}\right]$$, then $$f^{ 46. The area bounded by the parabola $$y^2=4 a x$$ and its latus-rectum $$x=a$$ is 47. If $$y=\log \sqrt{\tan x}$$, then the value of $$\frac{d y}{d x}$$ at $$x=\frac{\pi}{4}$$ is 48. If $$\mathrm{x}=\mathrm{a}\left(\mathrm{t}-\frac{1}{\mathrm{t}}\right)$$ and $$\mathrm{y}=\mathrm{b}\left(\mathrm{t}+\fr 49. Out of 7 consonants and 4 vowels, the number of words consisting of 3 consonants and 2 vowels are 50. Equation of planes parallel to the plane $$x-2y+2z+4=0$$ which are at a distance of one unit from the point (1, 2, 3) ar

Physics

1. If $$\mathrm{m}$$' represents the mass of each molecules of a gas and $$\mathrm{T}$$' its absolute temperature then the 2. The mass of a spherical planet is 4 times the mass of the earth, but its radius (R) is same as that of the earth. How mu 3. For series LCR circuit, which one of the following is a CORRECT statement? 4. Two waves $$\mathrm{Y}_1=0.25 \sin 316 \mathrm{t}$$ and $$\mathrm{Y}_2=0.25 \sin 310 \mathrm{t}$$ are propagation same d 5. In an LCR series a.c. circuit, the voltage across each of the components L, C and R is 60 V. The voltage across the LC c 6. The speed of a ball of radius $$2 \mathrm{~cm}$$ in a viscous liquid is $$20 \mathrm{~cm} / \mathrm{s}$$. What will be t 7. In hydrogen atom an electron revolves around a proton (in nucleus) at a distance 'r' m. the intensity of electric field 8. A particle performing S.H.M. when displacement is '$$x$$', the potential energy and restoring force acting on it are den 9. A molecule consists of two atoms each of mass '$$m$$' and separated by a distance '$$\mathrm{d}$$'. At room temperature, 10. The magnifying power of a refracting type of astronomical telescope is '$$\mathrm{m}$$'. If focal length of eyepiece is 11. A wooden black of mass '$$\mathrm{m}$$' moves with velocity '$$\mathrm{V}$$' and collides with another block of mass '$$ 12. Two charged metallic spheres are joined by a very thin metal wire. If the radius of the larger sphere is four times that 13. Water rises to a height of $$2 \mathrm{~cm}$$ in a capillary tube. If cross-sectional area of the tube is reduced to $$\ 14. The radius of a planet is twice the radius of the earth. Both have almost equal average mass densities. If '$$V_P$$' and 15. The shortest wavelength for Lyman series is 912 $$\mathop A\limits^o $$. The longest wavelength in Paschen series is 16. A balanced bridge is shown in the circuit diagram. The metre bridge wire has resistance $$1 \Omega \mathrm{m}^{-1}$$. Th 17. In Young's experiment with a monochromatic source and two slits, one of the slits is covered with black opaque paper, th 18. A ray of light travels from air to water to glass and again from glass to air. Refractive index of water w.r.t. air is ' 19. In the Bohr model, an electron moves in a circular orbit around the nucleus. Considering an orbiting electron to be a ci 20. In potentiometer experiment, cells of e.m.f. '$$E_1$$' and '$$E_2$$' are connected in series $$\left(E_1>E_2\right)$$ th 21. Three solid spheres each of mass '$$M$$' and radius '$$R$$' are arranged as shown in the figure. The moment of inertia o 22. A body is performing S.H.M. of amplitude 'A'. The displacement of the body from a point where kinetic energy is maximum 23. Eddy currents are produced when 24. The resultant gate and its Boolean expression in the given circuit is 25. When wavelength of incident radiation on the metal surface is reduced from '$$\lambda_1$$' to '$$\lambda_2$$', the kinet 26. A student is throwing balls vertically upwards such that he throws the $$2^{\text {nd }}$$ ball when the $$1^{\text {st 27. Work done in increasing the size of a soap bubble from radius of $$3 \mathrm{~cm}$$ to $$5 \mathrm{~cm}$$ in millijoule 28. What are the values of the currents flowing in each of the following diode circuits $$\mathrm{X}$$ and $$\mathrm{Y}$$ re 29. In the interference experiment using a biprism, the distance of the slits from the screen is increased by $$25 \%$$ and 30. Two waves are represented by the equation, $$\mathrm{y}_1=\mathrm{A} \sin (\omega \mathrm{t}+\mathrm{kx}+0.57) \mathrm{m 31. An ideal gas at pressure '$$p$$' is adiabatically compressed so that its density becomes twice that of the initial. If $ 32. In common emitter amplifier, a change of 0.2 mA in the base current causes a change of 5 mA in the collector current. If 33. Figure shows triangular lamina which can rotate about different axes moment of inertia is maximum, about the axis 34. Which one of the following statements is wrong for an isobaric process? 35. The energy of an electron in the excited hydrogen atom is $$-3.4 \mathrm{~eV}$$. Then according to Bohr's theory, the an 36. For a perfectly black body, coefficient of emission is 37. Two rods of different metals have coefficients of linear expansion '$$\alpha_1$$' and '$$\alpha_2$$' respectvely. Their 38. The temperature of a black body is increased by $$50 \%$$, then the percentage increase in the rate of radiation by the 39. A particle excuting S.H.M starts from the mean position. Its amplitude is 'A' and time period '$$\mathrm{T}$$' At what d 40. The fundamental frequency of an air column in pipe 'A' closed at one end coincides with second overtone of pipe 'B' open 41. An electron is projected along the axis of circular conductor carrying current '$$\mathrm{I}$$' The electron will experi 42. A thin ring of radius '$$R$$' meter has charge '$$q$$' coulomb uniformly spread on it. The ring rotates about its axis w 43. A charged spherical conductor has radius '$$r$$'. The potential difference between its surface and 3 point at a distance 44. In biprims experiment, the $$4^{\text {th }}$$ dark band is formed opposite to one of the slits. The wavelength of light 45. The magnitude of flux linked with coil varies with time as $$\phi=3 t^2+4 t+7$$. The magnitude of induced e.m.f. at $$t= 46. At what rate a single conductor should cut the magnetic flux so that current of $$1.5 \mathrm{~mA}$$ flows through it wh 47. If we increase the frequency of an a.c. supply, then inductive reactance 48. An electron of mass '$$m$$' and a photon have same energy '$$E$$'. The ratio of de-Broglie wavelength of electron to the 49. Two parallel plates with dielectric placed between the plates are as shown in figure. The resultant capacity of capacito 50. A bar magnet has length $$3 \mathrm{~cm}$$, cross-sectional area $$2 \mathrm{~cm}^2$$ and magnetic moment $$3 \mathrm{~A

MHT CET 2021 23th September Morning Shift

MCQ (Single Correct Answer)

-0

The particular solution of differential equation $$(x+y) d y+(x-y) d x=0$$ at $$x=y=1$$ is

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

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

$$\log \left|\frac{x^2+y^2}{2}\right|=\frac{\pi}{4}-2 \tan ^{-1}\left(\frac{y}{x}\right)$$

MHT CET 2021 23th September Morning Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{10^{\frac{x}{2}}}{\sqrt{10^{-x}-10^x}} d x=$$

$$2 \sqrt{10^{-x}+10^x}+c$$

$$\frac{2}{2 \sqrt{10^{-x}+10^x}}+c$$

$$\frac{1}{\log 10} \sin ^{-1}\left(10^{\mathrm{x}}\right)+\mathrm{c}$$

$$\frac{1}{\log 10} \cos ^{-1}\left(10^x\right)+c$$

MHT CET 2021 23th September Morning Shift

MCQ (Single Correct Answer)

-0

$$\int_0^{\pi / 2} \frac{\cos x}{3 \cos x+\sin x} d x=$$

$$\frac{3 \pi}{20}-\frac{\log 3}{100}$$

$$\frac{3 \pi}{10}-\frac{\log 3}{10}$$

$$\frac{3 \pi}{20}+\frac{\log 3}{10}$$

$$\frac{3 \pi}{20}-\frac{\log 3}{10}$$

MHT CET 2021 23th September Morning Shift

MCQ (Single Correct Answer)

-0

If $$A=\left[\begin{array}{rr}2 & 3 \\ 5 & -2\end{array}\right]$$ and $$A^{-1}=K A$$, then $$K$$ is

$$\frac{-1}{19}$$

$$-19$$

$$\frac{1}{19}$$

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