MHT CET 2021 24th September Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. Which among the following cations will form lowest stability complex if the ligand remains the same? 2. Identify the change in colour when $$\mathrm{NaCl}$$ solution is titrated against $$\mathrm{AgNO}_3$$ solution using flu 3. The resistance of $$0.2 \mathrm{M}$$ solution of an electrolyte is 30 ohm and conductivity is $$1.2 \mathrm{~S} \mathrm{ 4. Which from the following alloys is used in gas turbine engines? 5. What is percent dissociation of acetic acid in it's $$0.01 \mathrm{~M}$$ solution if dissociation of acid is $$1.34 \tim 6. How many molecules are present in $$22400 \mathrm{~cm}^3$$ of a gas at STP? 7. Calculate osmotic pressure exerted by a solution containing $$0.822 \mathrm{~g}$$ of solute in $$300 \mathrm{~mL}$$ of w 8. The pH of monoacidic weak base is 10.9. Calculate the percent dissociation in 0.02 M solution. 9. Crotonyl alcohol is an example of 10. Which among the following is haloalkyne? 11. Which among the following is a formula of mustard gas? 12. Identify basic $$\alpha$$-amino acid from following. 13. A gas is allowed to expand against a constant external pressure of 2.5 bar from an initial volume 'x' L to final volume 14. identify the species from following that exhibits no bond resonance. 15. When a mixture of vapours of phenol and hydrogen is passed over nickel catalyst at 433 K, the product obtained is 16. A metal has $$\mathrm{BCC}$$ structure with edge length of unit cell $$400 \mathrm{~pm}$$. Density or metal is $$4 \math 17. Which from the following is the correct relationship between standard Gibbs energy change and standard cell potential? 18. What type of following solution is obtained from amalgam of mercury with sodium? 19. Lithium shows diagonal relationship with 20. Which group from following is responsible for $$(-) \mathrm{R}$$ effect? 21. Which of the following reaction is an example of Rosenmund reduction? 22. Which element from following combines with hydrogen to form compound having lowest acidic strength? 23. If decomposition of hydrogen peroxide is a first order reaction, it's rate law equation can be represented as 24. The FCC unit cell of a compound contains ions of $$\mathrm{A}$$ at the corner and ions of $$\mathrm{B}$$ at the centre o 25. To obtain 3-methylbutan-2-ol from acetaldehyde, the Grignard's reagent used is 26. Which of the following is an example of symmetrical tertiary amine? 27. Which among the following is benzylic halide? 28. What is the geometry of $$\mathrm{SbF}_5$$ molecule? 29. Identify the product $$(\mathrm{A})$$ obtained in the following reaction. $$\text { Phenol + concentrated Nitric acid } 30. What is the volume occupied by particles in $$\mathrm{BCC}$$ structure if '$$\mathrm{a}$$' is edge length of unit cell? 31. A reaction is first order with respective to $$\mathrm{A}$$ and second order with respective to $$\mathrm{B}$$. What is 32. Which of the following is an example of primary amine? 33. Which among following statements is true about $$\mathrm{Na}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]$$ ? 34. What is the change in oxidation number of nitrogen in following conversion? $$\mathrm{NO}_3^{-} \longrightarrow \mathrm{ 35. How many values of magnetic quantum number are possible for each value of azimuthal quantum number? 36. What is vapour pressure of solution containing 0.1 mole solute dissolved in $$1.8 \times 10^{-2} \mathrm{~kg} \mathrm{~H 37. Which from following reagents is used to identify straight chain of glucose? 38. Which of the following aldehyde has buttery odour? 39. At $$300 \mathrm{~K}, 22 \mathrm{~g}$$ of $$\mathrm{CO}_2$$ gas exerts a pressure of 5 atmosphere. What is the volume of 40. Which among the following is NOT benzylic halide? 41. Which of the following polymers is used to obtain shopping bags? 42. In a process, a system performs $$238 \mathrm{~J}$$ of work on it's surrounding by absorbing $$54 \mathrm{~J}$$ of heat. 43. When $$\mathrm{x} \mathrm{kJ}$$ heat is provided to a system, work equivalent to $$\mathrm{y} \mathrm{J}$$ is done on it 44. When 2-Chlorobutane is boiled with concentrated alcoholic solution of KOH, the major product formed is 45. Which element from following is a soft element? 46. For the reaction $$\mathrm{A}+\mathrm{B} \rightarrow$$ product, rate of reaction is $$3.6 \times 10^{-2} \mathrm{mol~dm} 47. Identify conjugate acid-base pair in the following reaction. $$ \mathrm{HCl}_{(\mathrm{aq})}+\mathrm{H}_2 \mathrm{O}_{(l 48. The conductivity of $$0.04 \mathrm{~M} \mathrm{~BaCl}_2$$ solution is $$0.0112 \Omega^{-1} \mathrm{~cm}^{-1}$$ at $$25^{ 49. Which from following polymers is used to manufacture tyres? 50. Which among following is an example of cyclic amide?

Mathematics

1. $$\int_\limits0^4 x[x] d x=$$ (where $$[\mathrm{x}]$$ denotes greatest integer function not greater than $$\mathrm{x}]$$ 2. $$\lim _\limits{x \rightarrow 1} \frac{a b^x-a^x b}{x^2-1}=$$ 3. The maximum area of the rectangle that can be inscribed in a circle of radius $$r$$ is 4. The difference between the maximum values of $${ }^6 C_r$$ and $${ }^n C_r$$ is 16, then $$n=$$ 5. If $$f(x)=\frac{x}{2 x+1}$$ and $$g(x)=\frac{x}{x+1}$$, then $$(f \circ g)(x)=$$ 6. If the population grows at the rate of $$8 \%$$ per year, then the time taken for the population to be doubled is (Given 7. If the lines respresented by $$a x^2-b x y-y^2=0$$ make angle $$\alpha$$ and $$\beta$$ with the positive direction of $$ 8. If the probability distribution function of a random variable X is given as .tg {border-collapse:collapse;border-spaci 9. The particular solution of the differential equation $$ \frac{d y}{d x}=\frac{x+y+1}{x+y-1} $$ when $$ \mathrm{x}=\frac{ 10. If $$a \sin \theta=b \cos \theta$$, where $$a, b \neq 0$$, then $$a\cos 2 \theta+b \sin 2 \theta=$$ 11. $$\vec{a}=4 \hat{i}+13 \hat{j}-18 \hat{k}, \vec{b}=\hat{i}-2 \hat{j}+3 \hat{k}$$ and $$\vec{c}=2 \hat{i}+3 \hat{j}-4 \ha 12. If the lines $$\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$$ and $$\frac{x-2}{1}=\frac{y+m}{2}=\frac{z-2}{1}$$ intersect e 13. The length of perpendicular drawn from the point $$2 \hat{i}-\hat{j}+5 \hat{k}$$ to the line $$\overline{\mathrm{r}}=(11 14. $$ \text { If } u=\cos ^3 x, v=\sin ^3 x \text {, then }\left(\frac{d v}{d u}\right)_{x=\frac{\pi}{4}} \text { is equal 15. The arithmetic mean of marks in Mathematics for four divisions A, B, C and D were $$80,75,70$$ and 72 respectively. Thei 16. If the angle between the lines is $$\frac{\pi^{\mathrm{C}}}{4}$$ and slope of one of the lines is $$\frac{1}{2}$$, then 17. $$f(x)=\log |\sin x|$$, where $$x \in(0, \pi)$$ is strictly increasing on 18. The velocity of a particle at time $$t$$ is given by the relation $$v=6 t-\frac{t^2}{6}$$. Its displacement S is zero at 19. The order of the differential equation whose solution is $$y=a \cos x+b \sin x+c e^{-x}$$ is 20. The sqaure roots of the complex number $$(-5-12 \mathrm{i})$$ are 21. If $$\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{c}=\hat{j}-\hat{k}, \vec{a} \times \bar{b}=\bar{c}$$ and $$\vec{a} \cdot \vec 22. Equation of the plane passing through the point $$(1,2,3)$$ and parallel to the plane $$2 x+3 y-4 z=0 $$ 23. The negation of $$p \wedge(q \rightarrow r)$$ is 24. The general solution of the differential equation $$(2 y-1) d x-(2 x+3) d y=0$$ is 25. If $$y=\log _{10} x+\log _x 10+\log _x x+\log _{10} 10$$, then $$\frac{d y}{d x}=$$ 26. If the vectors $$\vec{a}=2 \hat{i}+p \hat{j}+4 \hat{k}$$ and $$\vec{b}=6 \hat{i}-9 \hat{j}+q \hat{k}$$ are collinear, th 27. If $$y=\tan ^{-1}\left[\frac{\log \left(\frac{e}{x^2}\right)}{\log \left(e x^2\right)}\right]+\tan ^{-1}\left[\frac{3+2 28. If the function $$\begin{array}{rlrl} f(x) & =3 a x+b, & & \text { for } x1 \end{array}$$ is continuous at $$x=1$$. Then 29. If $$\mathrm{P}(\mathrm{A})=\frac{3}{10}, \mathrm{P}(\mathrm{B})=\frac{2}{5}, \mathrm{P}(\mathrm{A} \cup \mathrm{B})=\fr 30. $$\int_\limits0^{\pi / 2} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x=$$ 31. Area bounded by the lines $$y=x, x=-1, x=2$$ and the $$X$$-axis is 32. $$\int \frac{\mathrm{dx}}{32-2 \mathrm{x}^2}=\mathrm{A} \log (4-\mathrm{x})+\mathrm{B} \log (4+\mathrm{x})+\mathrm{c}$$, 33. If $$\mathrm{A}$$ and $$\mathrm{B}$$ are the foot of the perpendicular drawn from the point $$\mathrm{Q}(\mathrm{a}, \ma 34. If $$|\vec{a}|=4,|\vec{b}|=5$$, then the values of $$k$$ for which $$\vec{a}+k \vec{b}$$ is perpendicular to $$\vec{a}-k 35. If $$\mathrm{p}$$ : It is raining and $$\mathrm{q}$$ : It is pleasant, then the symbolic form of "It is neither raining 36. Equationof the chord of the circle $$x^2+y^2-4 x-10 y+25=0$$ having mid-point $$(1,2)$$ is 37. $$\int \cos ^3 x \cdot e^{\log (\sin x)} d x=$$ 38. The probability distribution of a discrete random variable X is .tg {border-collapse:collapse;border-spacing:0;} .tg t 39. If $$\mathrm{A}=(-2,2,3), \mathrm{B}=(3,2,2), \mathrm{C}=(4,-3,5)$$ and $$\mathrm{D}=(7,-5,-1)$$ Then the projection of 40. $$\text { If } A=\left[\begin{array}{ll} 2 & -2 \\ 2 & -3 \end{array}\right], B=\left[\begin{array}{cc} 0 & -1 \\ 1 & 0 41. The value of $$\sin ^{-1}\left(\frac{-1}{2}\right)+\sin ^{-1}\left(\frac{-\sqrt{3}}{2}\right)$$ is, 42. If one of the lines given by $$k x^2+x y-y^2=0$$ bisect the angle between the co-ordinate axes then the values of $$k$$ 43. If $$A=\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 1 & a \\ 2 & 4 & 7\end{array}\right]$$ and $$B=\left[\begin{array}{ccc}1 44. The differential equation of the family of parabolas with focus at the origin and the $$X$$-axis a axis, is 45. A die is thrown four times. The probability of getting perfect square in at least one throw is 46. For a $$3 \times 3$$ matrix $$\mathrm{A}$$, if $$\mathrm{A}(\operatorname{adj} \mathrm{A})=\left[\begin{array}{ccc}-10 & 47. In any $$\triangle A B C$$, with usual notations, $$c(a \cos B-b \cos A)=$$ 48. If in a $$\triangle A B C$$, with usual notations, $$\mathrm{a}^2, \mathrm{~b}^2, \mathrm{c}^2$$ are in A.P. then $$\fra 49. The common region of the solutions of the inequations $$x+2 y \geq 4,2 x-y \leq 6$$ and $$x, y>0$$ is 50. If $$\int \frac{(\cos x-\sin x)}{8-\sin 2 x} d x=\frac{1}{p} \log \left[\frac{3+\sin x+\cos x}{3-\sin x-\cos x}\right]+c

Physics

1. Two identical particles each of mass '$$m$$' are separated by a distance '$$d$$'. The axis of rotation passes through th 2. An electron makes a transition from an excited state to the ground state of a hydrogen like atom. Out of the following s 3. If the horizontal velocity given to a satellite is greater than critical velocity but less than the escape velocity at t 4. Two identical springs of constant '$$\mathrm{K}$$' are connected in series and parallel in shown in figure. A mass '$$\m 5. The radii of curvature of both the surfaces of a convex lens of focal length '$$\mathrm{f}$$' and focal power '$$\mathrm 6. A photon has wavelength $$3 \mathrm{~nm}$$, then its momentum and energy respectively will be $$[\mathrm{h}=6.63 \times 7. A stone is projected vertically upwards with velocity 'V. Another stone of same mass is projected at an angle fo $$60^{\ 8. A glass slab has refractive index '$$\mu$$' with respect to air and the critical angle for a ray of light in going from 9. A glass tube of uniform cross-section is connected to a tap with a rubber tube. The tap is opened slowly. Initially the 10. A sonometer wire of length 25 cm vibrates in unison with a tuning fork. When its length is decreased by 1 cm, 6 beats ar 11. The plates of a parallel plate capacitor of capacity '$$\mathrm{C}_1$$' are moved closer together until they ant half th 12. A p-n junction photodiode is fabricated from a semiconductor with a band gap of $$2.5 \mathrm{~eV}$$. It can detect a si 13. Two tuning forks of frequencies $$320 \mathrm{~Hz}$$ and $$480 \mathrm{~Hz}$$ are sounded together to produce sound wave 14. A monoatomic ideal gas initially at temperature $$\mathrm{T}_1$$ is enclosed in a cylinder fitted with 8 frictionless pi 15. For a monoatomic gas, the work done at constant pressure is '$$\mathrm{W}$$' The heat supplied at constant volume for th 16. A thin metal disc of radius 'r' floats on water surface and bends the surface downwards along the perimeter making an a 17. A particle performing linear S.H.M. of amplitude $$0.1 \mathrm{~m}$$ has displacement $$0.02 \mathrm{~m}$$ and accelerat 18. The electric field intensity on the surface of a charged solid sphere of radius '$$r$$' and volume charge dentiy '$$\rho 19. A step up transformer operates on $$220 \mathrm{~V}$$ and supplies current of $$2 \mathrm{~A}$$. The ratio of primary an 20. The ratio of maximum to minimum wavelength in Balmer series of hydrogen atom is 21. The work done in blowing a soap bubble of volume '$$\mathrm{V}$$' is '$$\mathrm{W}$$'. The work required to blow a soap 22. A current carrying loop is placed in a uniform magnetic field. The torque acting on the loop does not depend upon 23. Let A, B and C be the three points in a uniform electric field $$\text { ( } \overrightarrow{\mathrm{E}})$$ as shown. Th 24. For the output of the following logic circuit to be 'I', the values of inputs A and B should be respectively 25. In photoelectric experiment keeping the frequency of incident radiation and accelerating potential fixed, if the intensi 26. In Young's double slit experiment, in an interference pattern, a minimum is observed exactly in front of one slit. The d 27. A beam of light having wavelength $$5400 \mathrm{~A}$$ from a distant source falls on a single slit $$0.96 \mathrm{~mm}$ 28. In the part of an a.c. circuit as shown, the resistance $$R=0.2 \Omega$$. At a certain instant $$(\mathrm{V_A-V_B})= 0.5 29. In the circuit shown in the figure, a.c. source gives voltage $$\mathrm{V}=20 \cos (2000 \mathrm{t})$$. Impedance and r. 30. When an air column in a pipe open at both ends vibrates such that four antinodes and three nodes are formed, then the co 31. Two identical ideal diodes are connected to an ammeter and a d.c source (1 volt) as shown. In which one of the following 32. The period of revolution of planet $$\mathrm{A}$$ around the sun is 8 times that of planet $$\mathrm{B}$$. How many time 33. Two identical capacitors have the same capacitance '$$\mathrm{C}$$'. One of them is charged to potential '$$\mathrm{V_1} 34. A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring balance reads $$ 35. In a potentiometer experiement, when three cells $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ are connected in series, 36. A current '$$I$$' is flowing in a conductor of length '$$L$$' when it is bent in the form of a circular loop, its magnet 37. Two long conductors, separated by a distance '$$\mathrm{d}$$' carry currents '$$\mathrm{I}_1$$' and '$$\mathrm{I}_2$$' i 38. A body attached to one end of a string performs motion along a vertical circle. Its centripetal acceleration, when the s 39. A coil has an area $$0.06 \mathrm{~m}^2$$ and it has 600 turns. After placing the coil in a magnetic field of strength $ 40. . If the current of '$$I$$' A gives rise to a magnetic flux '$$\phi$$' through a coil having '$$N$$' turns then mangetic 41. An ideal gas with pressure $$\mathrm{P}$$, volume $$\mathrm{V}$$ and temperature $$\mathrm{T}$$ is expanded isothermally 42. Which graph shows the correct variation of r.m.s. current 'I' with frequency 'f' of a.c. in case of (LCR) parallel reson 43. At what temperature does the average translational kinetic energy of a molecule in a gas becomes equal to kinetic energy 44. The temperature difference between two sides of an iron plate, $$1.8 \mathrm{~cm}$$ thick is $$9^{\circ} \mathrm{C}$$. H 45. Internal energy of $$n_1$$ moles of hydrogen at temperature '$$T$$' is equal to internal energy of '$$n_2$$' moles of he 46. A body of mass '$$\mathrm{m}$$' and radius of gyration '$$\mathrm{K}$$' has an angular momentum $$\mathrm{L}$$. Its angu 47. Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference b 48. A body is executing S.H.M. under the action of force having maximum magntude $$50 \mathrm{~N}$$. When its energy is half 49. The peak value of an alternating emf '$$\mathrm{e}$$' given by $$\mathrm{e}=\mathrm{e}_0 \cos \omega \mathrm{t}$$ is 10 50. The wavelength of sound in any gas depends upon

MHT CET 2021 24th September Morning Shift

MCQ (Single Correct Answer)

-0

If $$y=\tan ^{-1}\left[\frac{\log \left(\frac{e}{x^2}\right)}{\log \left(e x^2\right)}\right]+\tan ^{-1}\left[\frac{3+2 \log x}{1-6 \log x}\right]$$, then $$\frac{d^2 y}{d x^2}=$$

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

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

$$\frac{3}{1+x^2}$$

MHT CET 2021 24th September Morning Shift

MCQ (Single Correct Answer)

-0

If the function

$$\begin{array}{rlrl} f(x) & =3 a x+b, & & \text { for } x<1 \\ & =11, & & \text { for } x=1 \\ & =5 a x-2 b, & \text { for } x>1 \end{array}$$

is continuous at $$x=1$$. Then, the values of $$a$$ and $$b$$ are

$$\mathrm{a}=2, \mathrm{~b}=3$$

$$\mathrm{a=3, b=3}$$

$$\mathrm{a=2, b=2}$$

$$\mathrm{a}=3, \mathrm{~b}=2$$

MHT CET 2021 24th September Morning Shift

MCQ (Single Correct Answer)

-0

If $$\mathrm{P}(\mathrm{A})=\frac{3}{10}, \mathrm{P}(\mathrm{B})=\frac{2}{5}, \mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{3}{5}$$, then $$\mathrm{P}(\mathrm{A} / \mathrm{B}) \times \mathrm{P}(\mathrm{B} / \mathrm{A})=$$

$$\frac{1}{3}$$

$$\frac{1}{12}$$

$$\frac{1}{10}$$

$$\frac{1}{4}$$

MHT CET 2021 24th September Morning Shift

MCQ (Single Correct Answer)

-0

$$\int_\limits0^{\pi / 2} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x=$$

4log3

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

2log4

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