MHT CET 2019 3rd May Morning Shift | MHT CET Year Wise Previous Years Questions

Chemistry

1. .What is the shape and magnetic nature of permanganate ion? 2. Which of the following oxides can act both as an oxidising agent as well as reducing agent? 3. "The mass and energy both are conserved in an isolated system", is the statement of 4. Which among the following is correct for electrolysis of brine solution? 5. The number of pi-bonds present in benzoic acid molecule are 6. The elevation in boiling point of 0.25 molal aqueous solution of a substance is $\left(K_o=0.52 \mathrm{~K} \mathrm{~kg} 7. The combining ratios of hydrogen and oxygen in water and hydrogen peroxide are $1: 8$ and $1: 16$. Which law is illustra 8. If a metal crystallises in bcc structure with edge length of unit cell $4.29 \times 10^{-8} \mathrm{~cm}$ the radius of 9. The temperature of $32^{\circ} \mathrm{C}$ is equivalent to 10. The element which does not belong to group 15 is 11. The precipitation power of an electrolyte increases with 12. In leaching of alumina from bauxite by Bayer's process, then ore is treated with 13. The diagonal relationship in Be and Al is due to 14. Carbolic acid is oxidised by acidified sodium dichromate to give 15. The highest oxidation state in plutonium (At. no. $=94$) is 16. In the electrolysis of aqueous sodium chloride with inert electrodes the products obtained at anode and cathode respecti 17. What type of hybridisation is present in carbocation formed during the alkaline hydrolysis of 1 - bromo-1-phenyl ethane? 18. The integrated rate equation for first order reaction, $A \rightarrow$ product, is 19. Calculate E.M.F. of following cell at 298 K $\mathrm{Zn}(s)\left|\mathrm{ZnSO}_4(0.01 \mathrm{M})\right|\left|\mathrm{Cu 20. Which mixture is used for respiration by deep sea divers? 21. Which element among the following is not present in saccharine? 22. Which among the following statements is true about Schottky defect? 23. Which among the following salts, solubility decreases with increase in temperature? 24. Soaps are the sodium or potassium salts of higher fatty acids, containing number of carbon atoms more than, 25. Oxidation state of nitrogen in nitric oxide is 26. Which of the following does not give yellow solid on treatment with sodium hypoiodite? 27. The shape of BrF$_5$ molecule is 28. The alkane formed on heating sodium butanoate with sodalime is 29. A gas performs 0.320 kJ work on surrounding and absorbs 120 J of heat from the surrounding. Hence, change in internal en 30. For the elementary reaction, $3 \mathrm{H}_2(g)+\mathrm{N}_2(g) \longrightarrow 2 \mathrm{NH}_3(g)$ identify the correct 31. Natalite is a mixture of 32. In which among the following compounds, oxidation number of nitrogen is +5 ? 33. 18 gram glucose (Molar mass $=180$ ) is dissolved in 100 ml of water at 300 K . If $R=3$ $0.0821 \mathrm{~L}{-\mathrm{a 34. A flavouring agent found in oil of wintergreen is 35. Which of the following is not the mineral of iron? 36. Which of the following metal halide is more covalent? 37. How many primary amines are possible for molecular formula $\mathrm{C}_3 \mathrm{H}_9 \mathrm{~N}$ ? 38. The conversion of 2-methylpropan-1-ol to 2-methylpropan-2-ol is 39. A polymer which becomes soft on heating and hard on cooling, belongs to class of 40. The effective atomic number of $\operatorname{Iron}(z=26)$ in $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{-3}$ is 41. Which bond in a molecule of ethyl magnesium bromide is ionic in nature? 42. Based on first law of thermodynamics which of the following is correct 43. IUPAC name of the complex Ba[ $\left.\mathrm{CuCl}_4\right]$ is 44. Hinsberg's reagent is 45. Which among the following polymer does not show cross linking in it ? 46. The vitamin that belongs to aromatic series is 47. Which of the following is not present in DNA? 48. The SI unit of electrochemical equivalent is 49. The correct order of boiling points of alkyl halides is 50. The molar conductivities at infinite dilution for sodium acetate, HCl and NaCl are $91 \mathrm{~S} \mathrm{~cm}{ }^2$ $\

Mathematics

1. The vector equation of the plane $\mathbf{r}=(2 \hat{\mathbf{i}}+\hat{\mathbf{k}})+\lambda(\hat{\mathbf{i}})+\mu(\hat{\m 2. . Area of the region bounded by $y=\cos x, x=0$, $x=\pi$ and $X$-axis is ... sq. units. 3. The length of the latusrectum of an ellipse is $\frac{18}{5}$ and eccentricity is $\frac{4}{5}$, then equation of the el 4. Let $a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$ and $b:(p \vee s) \leftrightarrow(q \wedge r)$. If the truth values o 5. 5. "If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, the i 6. $$\int \log x \cdot[\log (e x)]^{-2} d x=\ldots$$ 7. If $y=\log \left[\frac{x+\sqrt{x^2+25}}{\sqrt{x^2+25}-x}\right]$ then $\frac{d y}{d x}=\ldots \ldots$ 8. If the scalar triple product of the vectors $-3 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, 3 \hat{\mathbf{i 9. - The edge of a cube is decreasing at the rate of $0.04 \mathrm{~cm} / \mathrm{sec}$. If the edge of the cube is 10 cms 10. The joint equation of lines passing through origin and having slopes $(1+\sqrt{2})$ and $\frac{-1}{1+\sqrt{2}}$ is ..... 11. If $r$ is the radius of spherical balloon at time $t$ and the surface area of balloon changes at a constant rate $K$, th 12. $$\int_0^{\frac{\pi}{2}} \sqrt{\cos \theta} \cdot \sin ^3 \theta d \theta=$$ ............ 13. If $\omega$ is a complex cube root of unity and $A=\left[\begin{array}{ccc}\omega & 0 & 0 \\ 0 & \omega^2 & 0 \\ 0 & 0 & 14. If $A$ and $B$ are square matrices of order 3 such that $|A|=2,|B|=4$, then $|A(\operatorname{adj} B)|=\ldots$ 15. If $\int \frac{1}{1-\cot x} d x=A x+B \log |\sin x-\cos x|+c$ then $A+B=\ldots \ldots$ 16. The polar co-ordinates of $P$ are $\left(2, \frac{\pi}{6}\right)$. If $Q$ is the image of $P$ about the $X$-axis then th 17. $\mathbf{a}$ and $\mathbf{b}$ are non-collinear vectors. If $\mathbf{c}=(x-2) \mathbf{a}+\mathbf{b}$ and $\mathbf{d}=(2 18. Let $X$ be the number of successes in ' $n$ ' independent Bernoulli trials with probability of success $p=\frac{3}{4}$. 19. The slope of normal to the curve $x=\sqrt{t}$ and $y=t-\frac{1}{\sqrt{t}}$ at $t=4$ is .......... 20. Which of the following statement pattern is a tautology? 21. The acute angle between lines $x-3=0$ and $x+y=19$ is....... 22. In $\triangle A B C$, with the usual notations, if $\left(\tan \frac{A}{2}\right)\left(\tan \frac{B}{2}\right)=\frac{3}{ 23. If sum of the slopes of the lines given by $x^2-4 p x y+8 y^2=0$ is three times their product then $p=$ ........... 24. $$\frac{1-2\left[\cos 60^{\circ}-\cos 80^{\circ}\right]}{2 \sin 10^{\circ}}=\ldots \ldots$$ 25. The order of the differential equation of all circles which lie in the first quadrant and touch both the axes is...... 26. If $f(x)$ is continuous at $x=3$, where $$\begin{aligned} f(x) & =a x+1, & \text { for } x \leq 3 \\ & =b x+3 & , \text 27. The probability that three cards drawn from a pack of 52 cards, all are red is 28. For any non zero vector, a, b, c $\mathbf{a} \cdot[(\mathbf{b}+\mathbf{c}) \times(\mathbf{a}+\mathbf{b}+\mathbf{c})]=$ . 29. The domain of the real valued function $f(x)=\sqrt{\frac{x-2}{3-x}}$ is...... 30. If $y=\tan ^{-1}\left(\frac{1-\cos 3 x}{\sin 3 x}\right)$, then $\frac{d y}{d x}=$ ....... 31. If $z=a x+b y ; a, b>0$ subject to $x \leq 2, y \leq 2, x+y \geq 3, x \geq 0, y \geq 0$ has minimum value at $(2,1)$ onl 32. The direction ratios of the normal to the plane passing through origin and the line of intersection of the planes $x+2 y 33. $$\begin{aligned} &\text { The pdf of a random variable } X \text { is }\\ &\begin{aligned} f(x) & =3\left(1-2 x^2\right 34. The eccentricity of the hyperbola $25 x^2-9 y^2=225$ is ....... 35. If $f(x)=x+\frac{1}{x}, x \neq 0$, then local maximum and minimum values of function $f$ are respectively....... 36. Derivative of $\sin ^{-1}\left(\frac{t}{\sqrt{1+t^2}}\right)$ with respect to $\cos ^{-1}\left(\frac{1}{\sqrt{1+t^2}}\ri 37. A player tosses 2 fair coins. He wins Rs. 5 if 2 heads appear, Rs. 2 If 1 head appear and Rs. 1 if no head appears, then 38. In $\triangle A B C$, with the usual notations, if $\sin B \sin C=\frac{b c}{a^2}$, then the triangle is. ........... 39. If $A=\left\{x \in R / x^2+5|x|+6=0\right\}$ then $n(A)=\ldots \ldots$ 40. $$\int \frac{d x}{(\sin x+\cos x)(2 \cos x+\sin x)}=$$ 41. The solution of differential equation $\left(x^2+1\right) \frac{d y}{d x}+\left(y^2+1\right)=0$ is $\ldots$ 42. $\sin \left[3 \sin ^{-1}(0.4)\right]=\ldots \ldots$ 43. If line $\frac{2 x-4}{\lambda}=\frac{y-1}{2}=\frac{z-3}{1}$ and $\frac{x-1}{1}=\frac{3 y-1}{\lambda}=\frac{z-2}{1}$ are 44. For a sequence $\left(t_n\right)$, if $S_n=5\left(2^n-1\right)$ then $t_n=$ ......... 45. $$\begin{aligned} & \text { If } f(x)=\left[\tan \left(\frac{\pi}{4}+x\right)\right]^{\frac{1}{x}}, \quad x \neq 0 \\ & 46. Which of the following function has period 2? 47. Which of the following can not be the direction cosines of a line? 48. If $A, B, C$ are $p^{\text {th }}, q^{\text {th }}$ and $r^{\text {th }}$ terms of a GP respectively then $A^{q-r} \cdot 49. $$\int_{\frac{\pi}{18}}^{\frac{4 \pi}{9}} \frac{2 \sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}} d x=\ldots \ldots$$ 50. The maximum value of $Z=5 x+4 y$, Subject to $y \leq 2 x, x \leq 2 y, x+y \leq 3, x \geq 0, y \geq 0$ is ........

Physics

1. In amplitude modulation, the amplitude of carrier wave is $A_c$ and that of the modulating signal is $A_m$. In practice, 2. A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their $P^{\text {th 3. Glass has refractive index $\mu$ with respect to air and the critical angle for a ray of light going from glass to air i 4. Maximum kinetic energy gained by the charged particle in the cyclotron is independent of 5. A molecule of water on the surface experiences a net 6. The magnifying power of a telescope is nine. When it is adjusted for parallel rays, the distance between the objective a 7. The SI unit and dimensions of Stefan's constant $\sigma$ in case of Stefan's law of radiation is 8. In a hydrogen atom, an electron of charge $e$ revolves in a orbit of radius $r$ with speed $v$. Then, magnetic moment as 9. $V-I$ characterstics of LED is shown correctly by graph 10. The stopping potential of the photoelectrons, from a photo cell is 11. The refractive index of the material of crystal is 1.68 and that of castor oil is 1.2. When a ray of light passes from o 12. Consider a particle of mass $m$ suspended by a string at the equator. Let $R$ and $M$ denote radius and mass of the eart 13. Six very long insulated copper wires are bound together to form a cable. The currents carried by the wires are $I_1=+10 14. The fundamental frequency of sonometer wire increases by 9 Hz , if its tension is increased by $69 \%$, keeping the leng 15. In case of dimensions of electric field and electric dipole moment the power of mass is reswpectively, 16. A potentiometer wire has length $L$ For given cell of emf $E$, the balancing length is $\frac{L}{3}$ from the positive e 17. For homogeneous isotropic material, which one of the following cannot be the value of Poisson's ratio? 18. A mass is whirled in a circular path with constant angular velocity and its linear velocity is $v$. If the string is now 19. A circular coil and a square coil is prepared from two identical metal wires and a current is passed through it. Ratio o 20. In Young's double slit experiment fifth dark fringe is formed opposite to one of the slit. IID is the distance between t 21. Figure show the circular coil carrying current $I$ kept very close but not touching at a point $A$ on a straight conduct 22. A 220 V input is supplied to a transformer. The output circuit draws a current of 2.0 A at 440 V . If the ratio of outpu 23. A sonometer wire is in unison with a tuning fork, when it is stretched by weight $w$ and the corresponding resonating le 24. If the speed of an electron of hydrogen atom in the ground state is $2.2 \times 10^6 \mathrm{~m} / \mathrm{s}$, then its 25. A rod $l \mathrm{~m}$ long is acted upon by a couple as shown in the figure. The moment of couple is $\tau \mathrm{~Nm}$ 26. The vectors $(\mathbf{A}+\mathbf{B})$ and $(\mathbf{A}-\mathbf{B})$ are at right. angles to each other. This is possible 27. A coil has inductance 2 H . The ratio of its reactance, when it is connected first to an $A C$ source and then to DC sou 28. A person measures a time period of a simple pendulum inside a stationary lift and finds it to be $T$. If the lift starts 29. A charged conductor produces an electric field of intensity $10^3 \mathrm{~V} / \mathrm{m}$ just outside its surface in 30. In damped SHM, the SI unit of damping constant is 31. A wire of length $L$ and radius $r$ is rigidly fixed at one end. On stretching the other end of the wire with a force $F 32. When certain metal surface is illuminated with a light of wavelength $\lambda$, the stopping potential is $V$, When the 33. Which of the following regions of a transistors are, respectively, heavily dopped and lightly dopped? 34. A hole is drilled half way to the centre of the earth. A body weighs 300 N on the surface of the earth. How much will, i 35. Eight identical drops of water falling through air with uniform velocity of $10 \mathrm{~cm} / \mathrm{s}$ combine to fo 36. A solid sphere rolls down from top of inclined plane, 7 m high, without slipping. Its linear speed at the foot of plane 37. A body of mass $m$ is performing a UCM in a circle of radius $r$ with speed $v$. The work done by the centripetal force 38. Which of the following is the dimensional formula for electric polarisation? 39. The phenomenon of interference is based on 40. A vector $P$ has $X$ and $Y$ components of magnitude 2 units and 4 units respectively. A vector $Q$ along negative $X$-a 41. A magnetizing field of $5000 \mathrm{~A} / \mathrm{m}$ produces a magnetic flux of $4 \times 10^{-5} \mathrm{~Wb}$ in an 42. When a large bubble rises from bottom of a water lake to its surface, then its radius doubles. If the atmospheric pressu 43. A block of mass $M$ is pulled along a smooth horizontal surface with a rope of mass $m$ by force $F$. The acceleration o 44. In the network shown cell E has internal resistance $r$ and the galvanometer shows zero deflection. If the cell is repla 45. In hydrogen emission spectrum, for any series, the principal quantum number is $n$. Corresponding maximum wavelength $\l 46. $\left[\mathrm{L}^2 \mathrm{M}^1 \mathrm{~T}^{-2}\right]$ are the dimensions of 47. For formation of beats, two sound notes must have 48. If the radius of the circular path and frequency of revolution of a particle of mass $m$ are doubled, then the change in 49. The total energy of a simple harmonic oscillaior is proportional to 50. The rms speed of oxygen molecule in a gas is $u$, If the temperature is doubled and the molecules dissociates into two a

MHT CET 2019 3rd May Morning Shift

MCQ (Single Correct Answer)

-0

If $y=\tan ^{-1}\left(\frac{1-\cos 3 x}{\sin 3 x}\right)$, then $\frac{d y}{d x}=$ .......

$-\frac{3}{2}$

$-\frac{1}{2}$

$\frac{3}{2}$

$\frac{1}{2}$

MHT CET 2019 3rd May Morning Shift

MCQ (Single Correct Answer)

-0

If $z=a x+b y ; a, b>0$ subject to $x \leq 2, y \leq 2, x+y \geq 3, x \geq 0, y \geq 0$ has minimum value at $(2,1)$ only, then......

$a>b$

$a=b$

$a< b$

$a=1+b$

MHT CET 2019 3rd May Morning Shift

MCQ (Single Correct Answer)

-0

The direction ratios of the normal to the plane passing through origin and the line of intersection of the planes $x+2 y+3 z=4$ and $4 x+3 y+2 z=1$ are $\ldots \ldots$

$2,3,1$

$1,2,3$

$3,1,2$

$3,2,1$

MHT CET 2019 3rd May Morning Shift

MCQ (Single Correct Answer)

-0

$$\begin{aligned} &\text { The pdf of a random variable } X \text { is }\\ &\begin{aligned} f(x) & =3\left(1-2 x^2\right), & & 0< x<1 \\ & =0 & & \text { otherwise } \end{aligned} \end{aligned}$$

The $P\left(\frac{1}{4}< x<\frac{1}{3}\right)=\ldots$

$\frac{179}{864}$

$\frac{159}{864}$

$\frac{169}{864}$

$\frac{189}{864}$

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