MHT CET 2021 21th September Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Find the value of $$-197^\circ$$C temperature in Kelvin. 2. Identify the hydrolysis product of starch. 3. Which carbon atom of ribose sugar is joined to nitrogen base to form nucleoside? 4. Identify secondary allylic alcohol from following. 5. What is the rate of appearance of $$\mathrm{Z}$$ in following reaction? $$3 \mathrm{x} \rightarrow 2 \mathrm{y}+\mathrm{ 6. Slope of the graph between rate ( $$\mathrm{Y}$$-axis) and $$[\mathrm{A}](\mathrm{X}$$-axis) for the first order reactio 7. Identify the product 'P' of following reaction. Ethanoyl chloride $$\buildrel {{H_2}O} \over \longrightarrow $$ P 8. Identify the reagent used in following conversion. 9. Which of following statements is correct for physisorption? 10. Which among the following is NOT an extensive property? 11. Which among the following statements is true for conductivity? 12. Which among the following salts turns blue litmus red in it's aqueous solution? 13. Which from following statements is true for tetrahydrofuran? 14. Identify metal halide from following having highest ionic character? (M = metal atom) 15. What is spin only magnetic moment of an element having one unpaired electron? 16. What is the formal charge on carbon atom in CO$$_3^{2-}$$ ion ? 17. What is the pH of 0.02 M NaOH solution? 18. Which of the following compounds has lower boiling point? 19. A gas is allowed to expand in an insulated container against a constant external pressure of 2.5 atm from $$2.5 \mathrm{ 20. Which of the following solutions shows positive deviation from Raoult's law? 21. Which of the following conjugate bases is stabilized to greater extent due to solvation of ammonia and amines? 22. What is vapour pressure of a solution containing 0.1 mol of non-volatile solute dissolved in 16.2 g of water ? (P$$_1^0= 23. What is the percentage efficiency of packing in BCC structure? 24. Identify amphoteric oxide from following. 25. Identify homopolymer from following. 26. The molar conductivity of $$0.4 \mathrm{~M} \mathrm{~KCl}$$ solution is $$2.5 \times 10^5 \Omega^{-1} \mathrm{~cm}^2 \ma 27. Sunscreen lotions contains nanoparticles of 28. Which from following reactions converts carbonyl group of aldehydes and ketones to methylene group on treatment with zin 29. Which of the following reactions is used for the conversion of alkyl chloride to alkyl iodide? 30. Which of the following amines acts as strongest base? 31. Which among the following is NOT a neutral ligand? 32. What is the volume (in dm$$^3$$) occupied by 75 g ethane at S.T.P. ? 33. Identify the reactant, reagent and condition of Kolbe's reaction from following. 34. The wavelength of a spectral line of caesium is $$460 \mathrm{~nm}$$. What is the frequency of spectral line? 35. Select the catalyst used in hydrogenation of ethene. 36. What is the number of $$-$$CH$$_2$$ - groups present in dodecane? 37. Which among the following statements is NOT true? 38. An element with simple cubic close structure has edge length of unit cell $$3.86 ~\mathop A\limits^o$$. What is the radi 39. In a first order reaction, concentration of reactant is reduced to (1/8)th of concentration in 23.03 minutes. What is ha 40. What is boiling point of a decimolal aqueous solution of glucose if molal elevation constant for water is 0.52$$^\circ$$ 41. What is the work done when a gas is compressed from 2.5 $$\times$$ 10$$^{-2}$$ m$$^3$$ to 1.3 $$\times$$ 10$$^{-2}$$ m$$ 42. Identify homoleptic complex from following : 43. Dissociation constant of propionic acid is $$1.32 \times 10^{-5}$$. Calculate the degree of dissociation of acid in $$0. 44. Identify the product obtained when phenol reacts with concentrated sulphuric acid at $$293 \mathrm{~K}$$ ? 45. The reaction of propane with bromine in presence of UV light predominantly forms 46. Oxidation state of Cr in potassium dichromate is 47. What is the volume of unit cell of a metal (at. mass $$25 \mathrm{~g} \mathrm{~mol}^{-1}$$ ) having $$\mathrm{BCC}$$ str 48. Which among following monomers is used to prepare PVC? 49. What is the number of electrons passed through an electrolyte solution when 1 ampere current is passed for 16.1 minutes? 50. Identify reactant (A) used in the following conversion. Chlorobenzene $$+\mathrm{A} \underset{\mathrm{AlCl}_3}{\stackrel

Mathematics

1. $$2 \sin \left(\theta+\frac{\pi}{3}\right)=\cos \left(\theta-\frac{\pi}{6}\right)$$, then $$\tan \theta=$$ 2. $$\int[1+2 \tan x(\tan x+\sec x)]^{\frac{1}{2}} d x= $$ 3. The general solution of the differential equation $$\left(3 x y+y^2\right) d x+\left(x^2+x y\right) d y=0$$ is 4. In a meeting $$60 \%$$ of the members favour and $$40 \%$$ oppose a certain proposal. A member is selected at random and 5. The distance between parallel lines $$\begin{aligned} & \bar{r}=(2 \hat{i}-\hat{j}+\hat{k})+\lambda(2 \hat{i}+\hat{j}-2 6. If $$e^{-y} \cdot y=x$$, then $$\frac{d y}{d x}$$ is 7. If the two lines given by $$a x^2+2 h x y+b y^2=0$$ make inclinations $$\propto$$ and $$\beta$$, then $$\tan (\alpha+\be 8. The vertices of triangle $$\mathrm{ABC}$$ are $$\mathrm{A} \equiv(3,0,0) ; \mathrm{B} \equiv(0,0,4) ; \mathrm{C} \equiv( 9. If the lines $\frac{1-x}{3}=\frac{7 y-14}{2 \lambda}=\frac{z-3}{2}$ and $\frac{7-7 x}{3 \lambda}=\frac{y-5}{1}=\frac{6-z 10. A lot of 100 bulbs contains 10 defective bulbs. Five bulbs selected at random from the lot and sent to retain store, the 11. The differential equation of family of circles whose centres lie on $$\mathrm{X}$$-axis is 12. If $$\frac{\cos (A+B)}{\cos (A-B)}=\frac{\sin (C+D)}{\sin (C-D)}$$, then $$\tan A \tan B \tan C=$$ 13. The area of the region bounded by the curve y$$^2$$ = 4x and the line y = x is 14. The general solution of the differential equation $$y(1+\log x)\left(\frac{d x}{d y}\right)-x \log x=0$$ is 15. Negation of the statement $$\forall x \in R, x^2+1=0$$ is 16. The Cartesian equation of the plane passing through the point A(7, 8, 6) and parallel to the XY plane is 17. If $$F(\propto)=\left[\begin{array}{ccc}\cos \propto & -\sin \propto & 0 \\ \sin \propto & \cos \propto & 0 \\ 0 & 0 & 1 18. In a quadrilateral PQRS, M and N are mid-points of the sides PQ and RS respectively. If $$\overline {PS} + \overline {Q 19. A coin is tossed and a die is thrown. The probability that the outcome will be head or a number greater than 4 or both, 20. If vectors $$\bar{a}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \bar{b}=-\hat{i}+2 \hat{j}+\hat{k}$$ and $$\bar{c}=3 \hat{i}+\hat{j} 21. The equation of the plane passing through $$(-2,2,2)$$ and $$(2,-2,-2)$$ and perpendicular to the plane $$9 x-13 y-3 z=0 22. The complex number with argument $$\frac{5 \pi^{\mathrm{c}}}{6}$$ at a distance of 2 units from the origin is 23. If $$\bar{a}=3 \hat{i}-5 \hat{j}, \bar{b}=6 \hat{i}+3 \hat{j}$$ are two vectors and $$\bar{c}$$ is a vector such that $$ 24. If the polar co-ordinates of a point are $$\left(\sqrt{2}, \frac{\pi}{4}\right)$$, then its Cartesian co-ordinates are 25. The equation of the circle whose centre lies on the line $$x-4 y=1$$ and which passes through the points $$(3,7)$$ and $ 26. $$\int_\limits0^{\frac{\pi}{2}} \frac{\sin x-\cos x}{1-\sin x \cos x} d x=$$ 27. If $$A=\left[\begin{array}{ccc}1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1\end{array}\right], \operatorname{adj} A=\left[\begi 28. The shaded figure given below is the solution set for the linear inequations. Choose the correct option. 29. $$\begin{aligned} & \text { If the function } \mathrm{f}(\mathrm{x})=1+\sin \frac{\pi}{2}, \quad-\infty is continuous in 30. If $$\int \frac{x^3}{\sqrt{1+x^2}} d x=a\left(1+x^2\right)^{\frac{3}{2}}+b \sqrt{1+x^2}+c$$, then $$a+b=$$, (where $$c$$ 31. $$\mathrm{A}^{-1}=\frac{-1}{2}\left[\begin{array}{cc}1 & -4 \\ -1 & 2\end{array}\right]$$, then $$2 A+I_2=\quad$$ where 32. If $$y=\operatorname{cosec}^{-1}\left[\frac{\sqrt{x}+1}{\sqrt{x}-1}\right]+\cos ^{-1}\left[\frac{\sqrt{x}-1}{\sqrt{x}+1} 33. If $$f(x)=|x-1|+|x-2|+|x-3|, \forall x \in[1,4]$$, then $$\int_\limits1^4 f(x) d x=$$ 34. The general solution of the differential equation $$\frac{d y}{d x}=\frac{x+2 y-1}{x+2 y+1}$$ is 35. If $$\mathrm{X}$$ is a random variable with p.m.f. as follows. $$\begin{aligned} \mathrm{P}(\mathrm{X}=\mathrm{x}) & =\f 36. A body at an unknown temperature is placed in a room which is held at a constant temperature of $$30^{\circ} \mathrm{F}$ 37. The equation of a line passing through $$(\mathrm{p} \cos \propto, \mathrm{p} \sin \propto)$$ ) and making an angle $$(9 38. If $$|\bar{a}|=3,|\bar{b}|=4,|\bar{a}-\bar{b}|=5$$, then $$|\bar{a}+\bar{b}|=$$ 39. $$\tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)=\frac{\pi}{4}$$, then the values of $$x$ 40. If f(x) = 3[x] + 5{x + 1}, where [x] is greatest integer function of x and {x} is fractional part function of x, then f( 41. A stone is thrown into a quite lake and the waves formed move in circles. If the radius of a circular wave increases at 42. The function $$f(x)=\cot ^{-1} x+x$$ is increasing in the interval. 43. $$\lim _\limits{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}=$$ 44. The derivative of $$(\log x)^x$$ with respect to $$\log x$$ is 45. $$\int e^{\tan x}\left(\sec ^2 x+\sec ^3 x \sin x\right) d x=$$ 46. The product of the perpendicular distances from $$(2,-1)$$ to the pair of lines $$2 x^2-5 x y+2 y^2=0$$ is 47. For two data sets each of size 5 , the variance are given to be 4 and 5 and the corresponding means are given to be 2 an 48. The number of ways in which 8 different pearls can be arranged to form a necklace is 49. If $$p, q$$ are true statements and $$r$$ is false statement, then which of the following is correct. 50. The curves $$\frac{x^2}{a^2}+\frac{y^2}{4}=1$$ and $$y^3=16 x$$ intersect each other orthogonally, then $$a^2=$$

Physics

1. The magnetic potential energy stored in a certain inductor is $$25 \mathrm{~mJ}$$, when the current in the inductor is $ 2. A pendulum is oscillating with frequency '$$n$$' on the surface of the earth. It is taken to a depth $$\frac{R}{2}$$ bel 3. The molar specific heats of an ideal gas at constant pressure and volume are denoted by '$$\mathrm{C}_{\mathrm{p}}$$' an 4. In a pure silicon, number of electrons and holes per unit volume are $$1.6 \times 10^{16} \mathrm{~m}^{-3}$$. If silicon 5. A charge moves with velocity '$$V$$' through electric field $$(E)$$ as well as magnetic field (B). then the force acting 6. Light of frequency two times the threshold frequency is incident on photosensitive material. If the incident frequency i 7. For a transitor, $$\frac{1}{\alpha_{\mathrm{DC}}}-\frac{1}{\beta_{\mathrm{DC}}}$$ is equal to [ $$\alpha_{\mathrm{DC}}$$ 8. In diffraction experiment, from a single slit, the angular width of central maximum does NOT depend upon 9. The resultant capacity between points A and B in the given circuit is 10. When an electron in hydrogen atom jumps from third excited state to the ground state, the de-Broglie wavelength associat 11. A long solenoid carrying a current produces a magnetic field B along its axis. If the number of turns per $$\mathrm{cm}$ 12. A ray of light is incident at an angle 'I' on one face of thin prism. The ray emerges normally from the other face. Refr 13. The temperature difference bewtween two sides of metal plate, $$3 \mathrm{~cm}$$ thick is $$15^{\circ} \mathrm{C}$$. Hea 14. The current in the following circuit is 15. A particle of mass '$$m$$' collides with another stationary particle of mass '$$M$$'. A particle of mass '$$\mathrm{m}$$ 16. An air filled parallel plate capacitor has a capacity $$2 \mathrm{~pF}$$. The sepeartion of the plates is doubled and th 17. A black body has maximum wavelength '$$\lambda_{\mathrm{m}}$$' at temperature $$2000 \mathrm{~K}$$. Its corresponding wa 18. A monoatomic gas at pressure '$$\mathrm{P}$$' having volume '$$\mathrm{V}$$' expands isothermally to a volume $$2 \mathr 19. A particle moves in a circular orbit of radius '$$r$$' under a central attractive force, $$F=-\frac{k}{r}$$, where $$\ma 20. A black reactangular surface of area '$$a$$' emits energy '$$\mathrm{E}$$' per second at $$27^{\circ} \mathrm{C}$$. If l 21. A closed organ pipe of length '$$\mathrm{L}_c$$' and an open organ pipe of length '$$\mathrm{L}_{\mathrm{o}}$$' contain 22. The moment of inertia of a circular disc of radius $$2 \mathrm{~m}$$ and mass $$1 \mathrm{~kg}$$ about an axis XY passin 23. A progressive wave of frequency 50 Hz is travelling with velocity 350 m/s through a medium. The change in phase at a giv 24. Find the value of $$-$$197$$^\circ$$C temperature in Kelvin. 25. The surface tension of most of the liquid decreases with rise in 26. Which one of the following equations specifies an isobaric process? $$[Q=$$ heat supplied $$\Delta P, \Delta V$$ and $$\ 27. A simple harmonic progressive wave is given by $$Y=Y_0 \sin 2 \pi\left(n t-\frac{x}{\lambda}\right)$$. If the wave veloc 28. In a meter bridge experiment, the balance point is obtained at length $$\ell_1 \mathrm{~cm}$$ from left end when resista 29. In the graphical representation of e.m.f. '$$\mathrm{e}$$' and current '$$\mathrm{i}$$' versus '$$\omega \mathrm{t}$$' f 30. The moment of inertia of a body about a given axis is $$1.2 \mathrm{~kg} / \mathrm{m}^3$$. Initially the body is at rest 31. An alternating voltge is represented by $$\mathrm{V}=80 \sin (100 \pi \mathrm{t}) \cos (100 \pi \mathrm{t})$$ volt. The 32. When the value of acceleration due to gravity '$$g$$' becomes $$\frac{g}{3}$$ above surface of height '$$h$$' then relat 33. In biprism experiment, 21 fringes are observed in a given region using light of wavelength 4800 $$\mathop A\limits^o $$. 34. A wire of length '$$L$$'; having resistance '$$R$$' falls from a height '$$\ell$$' in earth's horizontal magnetic field 35. Two wires '$$\mathrm{A}$$' and '$$\mathrm{B}$$' of equal length are connected in left and right gap respectively of mete 36. A glass cube of length $$24 \mathrm{~cm}$$ has a small air bubble trapped inside. When viewed normally from one face it 37. What is susceptibility of a medium, if its relative permeability is 0.85? 38. In fundamental mode, the time required for the sound wave to reach upto the closed end of pipe filled with air is $$t$$ 39. A particle of mass '$$m$$' is kept at rest at a height $$3 R$$ from the surface of earth, where '$$R$$' is radius of ear 40. '$$\mathrm{F}$$' is the force between the two identical charged particles placed at a distance '$$\mathrm{Y}$$' from eac 41. A coil of radius '$$\mathrm{r}$$' is placed on another coil (whose radius is '$$\mathrm{R}$$' and current through it is 42. '$$\lambda_1$$' is the wavelength of series limit of Lyman series, '$$\lambda_2$$' is the wavelength of the first line l 43. The velocity of a small ball of mass '$$M$$' and density '$$\mathrm{d}_1$$' when dropped in a container filled with glyc 44. A sphere of mass 25 gram is placed on a vertical spring. It is compressed by $$0.2 \mathrm{~m}$$ using a force $$5 \math 45. A bomb is dropped by an aeroplane flying horizontally with a velocity $$200 \mathrm{~km} / \mathrm{hr}$$ and at a height 46. A series combination of resistor 'R' and capacitor 'C' is connected to an a.c. source of angular frequency '$$\omega$$'. 47. A double slit experiment is immersed in water of refractive index 1.33. The slit separationis 1 $$\mathrm{mm}$$ and the 48. Two small drops of mercury each of radius '$$R$$' coalesce to form a large single drop. The ratio of the total surface e 49. On a photosensitive surface, if the intensity of incident radiation is increased, the stopping potential 50. A particle executes linear S.H.M. The mean position of oscillation is at the principal axis of a convex lens of focal le

MHT CET 2021 21th September Morning Shift

MCQ (Single Correct Answer)

-0

The derivative of $$(\log x)^x$$ with respect to $$\log x$$ is

$$(\log x)^x\left[\frac{1}{\log x} \log (\log x)\right]$$

$$(\log x)^x\left[\log x+\frac{1}{\log (\log x)}\right]$$

$$x(\log x)^x\left[\frac{1}{\log x}+\log (\log x)\right]$$

$$x(\log x)^x\left[\log x+\frac{1}{\log (\log x)}\right]$$

MHT CET 2021 21th September Morning Shift

MCQ (Single Correct Answer)

-0

$$\int e^{\tan x}\left(\sec ^2 x+\sec ^3 x \sin x\right) d x=$$

$$\tan x \cdot e^{\tan x}+c$$

$$(1+\tan \mathrm{x}) \mathrm{e}^{\tan \mathrm{x}}+\mathrm{c}$$

$$\sec \mathrm{x} \cdot \mathrm{e}^{\tan \mathrm{x}}+\mathrm{c}$$

$$\mathrm{e}^{\tan x}+\tan \mathrm{x}+\mathrm{c}$$

MHT CET 2021 21th September Morning Shift

MCQ (Single Correct Answer)

-0

The product of the perpendicular distances from $$(2,-1)$$ to the pair of lines $$2 x^2-5 x y+2 y^2=0$$ is

$$\frac{9}{\sqrt{5}}$$ units

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

4 units

9 units

MHT CET 2021 21th September Morning Shift

MCQ (Single Correct Answer)

-0

For two data sets each of size 5 , the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance of the combined data set is

$$\frac{13}{2}$$

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

$$\frac{11}{2}$$

$$\frac{15}{2}$$

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