Chemistry
1. Copper is extracted from copper pyrites by2. Function of potassium ethyl xanthate in froth floatation process is to make the ore3. Sulphide ore on roasting gives a gas $$X$$. $$X$$ reacts with $$\mathrm{Cl}_2$$ in the presence of activated charcoal to4. Aqueous solution of a salt $$(A)$$ forms a dense white precipitate with $$\mathrm{BaCl}_2$$ solution. The precipitate di5. Bond angle is $$\mathrm{PH}_4^{+}$$ is more than that of $$\mathrm{PH}_3$$. This is because6. Incorrectly matched pair is7. Phosphorus pentachloride8. Identify the set of paramagnetic ions among the following.9. How many moles of acidified $$\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$$ is required to liberate 6 moles of $$\mathrm{I}_10. For $$\mathrm{Cu}_2 \mathrm{Cl}_2$$ and $$\mathrm{CuCl}_2$$ in aqueous medium, which of the following statement is corre11. The coordination number of $$\mathrm{Fe}$$ and $$\mathrm{Co}$$ in the complex ions, $$\left.\mathrm{Fe}\left(\mathrm{C}_12. Number of stereoisomers exhibited by $$\left[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2\right]^{+}$$ is13. Give the IUPAC name of $$\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_4\right]\left[\mathrm{Pt} \mathrm{Cl}_4\right]$$ is14. Prolonged exposure of chloroform in humans may cause damage to liver. It is due to the formation of the following compou15. Which of the following halide shows highest reactivity towards $$\mathrm{S}_{\mathrm{N}} 1$$ reaction?16. In the reaction,
The number of possible isomers for the organic compound X is17. Which of the following on heating gives an ether as major products?
(P) $$\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathr18. The steps involved in the conversion of propan -2-ol to propan -1-ol are in the order
19. Which of the following is the strongest base?20. The product 'P' is
21. Which of the following has the lowest boiling point?22. The carbonyl compound that does not undergo aldol condensation is23. The final product for the reaction is
24. Hinsberg's reagent is25. Which one of the following vitamins is not stored in adipose tissue?26. Hypothyroidism is caused by the deficiency of27. $$\mathrm{C}_1-\mathrm{C}_4$$ glycosidic bond is not found in28. Which of the following polymer has strongest intermolecular forces of attraction?29. Which of the following monomers can undergo condensation polymerisation?30. A food additive that acts as an antioxidant is31. Which of the following is not related to drug-enzyme interaction?32. $$0.4 \mathrm{~g}$$ of dihydrogen is made to react with $$7.4 \mathrm{~g}$$ of dichlorine to form hydrogen chloride. The33. With regard to photoelectric effect, identify the correct statement among the following.34. The last element of the $$p$$-block in 6 th period is represented by the outer most electronic configuration.35. The conjugate base of $$\mathrm{NH}_3$$ is36. A gas mixture contains $$25 \% \mathrm{~He}$$ and $$75 \% \mathrm{~CH}_4$$ by volume at a given temperature and pressure37. The percentage of $$s$$-character in the hybrid orbitals of nitrogen in $$\mathrm{NO}_2^{+}, \mathrm{NO}_3^{-}$$ respect38. The formal charge on central oxygen atom in ozone is39. When the same quantity of heat is absorbed by a system at two different temperatures $$T_1$$ and $$T_2$$, such that $$T_40. The oxidation number of nitrogen atoms in $$\mathrm{NH}_4 \mathrm{NO}_3$$ are41. A Lewis acid '$$X$$' reacts with $$\mathrm{LiAlH}_4$$ in ether medium to give a highly toxic gas. This gas when heated w42. The oxide of potassium that does not exist is43. The metal that produce $$\mathrm{H}_2$$ with both dil. $$\mathrm{HCl}$$ and $$\mathrm{NaOH}(a q)$$ is44. Which of the following is not a pair of functional isomers?45. Identify 'X' in the following reaction.
46. Which of the following is not a green house gas?47. A metal exists as an oxide with formula $$M_{0.96}$$ O. Metal, $$M$$ can exist as $$M^{2+}$$ and $$M^{3+}$$ in its oxide48. A metal crystallises in face centred cubic structure with metallic radius $$\sqrt{2} \mathop A\limits^o$$. The volume of49. Silicon doped with gallium forms50. The pair of electrolytes that posses same value for the constant $$(A)$$ in the Debye-Huckel-Onsager equation, $$\Lambda51. Which of the following pair of solutions is isotonic?52. Solute '$$X$$' dimerises in water to the extent of $$80\%$$. 2.5g of '$$X$$' in $$100 \mathrm{~g}$$ of water increases t53. Given $$E_{F{e^{3 + }}/F{e^{2 + }}}^o = + 0.76\,V$$ and $$E_{\mathrm{I}_2 / \mathrm{I}^{-}}^0=+0.55 \mathrm{~V}$$. The 54. If an aqueous solution of $$\mathrm{NaF}$$ is electrolysed between inert electrodes, the product obtained at anode is55. In which of the following cases a chemical reaction is possible?56. The time required for $$60 \%$$ completion of a first order reaction is $$50 \mathrm{~min}$$. The time required for $$9357. For an elementary reaction $$2 A+3 B \rightarrow 4 C+D$$ the rate of appearance of $C$ at time '$$T$$' is $$2.8 \times 158. The rate constant of a reaction is given by $$k=P Z e^{-E_a / R T}$$ under standard notation. In order to speed up the r59. A sol of $$\mathrm{AgI}$$ is prepared by mixing equal volumes of $$0.1 \mathrm{~M} \mathrm{~AgNO}_3$$ and $$0.2 \mathrm{60. During adsorption of a gas on a solid at low temperature
Mathematics
1. If $$2^x+2^y=2^{x+y}$$, then $$\frac{d y}{d x}$$ is2. If $$f(x)=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$$, then $$f^{\prime}(\sqrt{3})$$ is3. The right hand and left hand limit of the function are respectively.
$$f(x)=\left\{\begin{array}{cc}
\frac{e^{1 / x}-1}{4. If $$y=2 x^{n+1}+\frac{3}{x^n}$$, then $$x^2 \frac{d^{2 y}}{d x^2}$$ is5. If the curves $$2 x=y^2$$ and $$2 x y=K$$ intersect perpendicularly, then the value of $$K^2$$ is6. If $$(x e)^y=e^y$$, then $$\frac{d y}{d x}$$ is7. If the side of a cube is increased by $$5 \%$$, then the surface area of a cube is increased by8. The value of $$\int \frac{1+x^4}{1+x^6} d x$$ is9. The maximum value of $$\frac{\log _e x}{x}$$, if $$x>0$$ is10. The value of $$\int e^{\sin x} \sin 2 x d x$$ is11. The value of $$\int_{-1 / 2}^{1 / 2} \cos ^{-1} x d x$$ is12. If $$\int \frac{3 x+1}{(x-1)(x-2)(x-3)} d x A \log |x-1| B \log |x-2|+C \log |x-3|+C$$, then the values of $$A, B$$ and 13. Find the value of $$\int_0^1 \frac{\log (1+x)}{1+x^2} d x$$ is14. The area of the region bounded by the curve $$y^2=8 x$$ and the line $$y=2 x$$ is15. The value of $$\int_{-\pi / 2}^{\pi / 2} \frac{\cos x}{1+e^x} d x$$ is16. The order of the differential equation obtained by eliminating arbitrary constants in the family of curves $$c_1 y=\left17. The general solution of the differential equation $$x^2 d y-2 x y d x=x^4 \cos x d x$$ is18. The area of the region bounded by the line $$y=2 x+1, X$$-axis and the ordinates $$x=-1$$ and $$x=1$$ is19. The two vector $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\20. If $$\mathbf{a}$$ and $$\mathbf{b}$$ are unit vectors and $$\theta$$ is the angle between $$\mathbf{a}$$ and $$\mathbf{b21. The curve passing through the point $$(1,2)$$ given that the slope of the tangent at any point $$(x, y)$$ is $$\frac{3 x22. If $$|\mathbf{a}+\mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=144|\mathbf{a}|=6$$, then $$|\mathbf{b}|$$ is equal to23. The point $$(1,-3,4)$$ lies in the octant24. If the vectors $$2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mat25. The distance of the point $$(1,2,-4)$$ from the line $$\frac{x-3}{2}=\frac{y-3}{3}=\frac{z+5}{6}$$ is26. The sine of the angle between the straight line $$\frac{x-2}{3}=\frac{3-y}{-4}=\frac{z-4}{5}$$ and the plane $$2 x-2 y+z27. If a line makes an angle of with each of $$X$$ and $$Y$$-axis, then the acute angle made by Z-axis is28. Corner points of the feasible region determined by the system of linear constraints are $$(0,3),(1,1)$$ and $$(3,0)$$. L29. The feasible region of an LPP is shown in the figure. If $$z=11 x+7 y$$, then the maximum value of $$Z$$ occurs at
30. A die is thrown 10 times, the probability that an odd number will come up at least one time is31. If $$A$$ and $$B$$ are two events such that $$P(A)=\frac{1}{3}, P(B)=\frac{1}{2}$$ and $$P(A \cap B)=\frac{1}{6}$$, then32. Events $$E_1$$ and $$E_2$$ from a partition of the sample space $$S$$. $$A$$ is any event such that $$P\left(E_1\right)=33. The probability of solving a problem by three persons $$A, B$$ and $$C$$ independently is $$\frac{1}{2}, \frac{1}{4}$$ a34. If $$n(A)=2$$ and total number of possible relations from Set A to set B is 1024, then $$n(B)$$ is35. The value of $$\sin ^2 51^{\circ}+\sin ^2 39^{\circ}$$ is36. If $$\tan A+\cot A=2$$, then the value of $$\tan ^4 A+\cot ^4 A=$$37. If $$A=\{1,2,3,4,5,6\}$$, then the number of subsets of A which contain at least two elements is38. If $$z=x+i y$$, then the equation $$|z+1|=|z-1|$$ represents39. The value of $${ }^{16} C_9+{ }^{16} C_{10}-{ }^{16} C_6-{ }^{16} C_7$$ is40. The number of terms in the expansion of $$(x+y+z)^{10}$$ is41. If $$P(n): 2^n42. The two lines $$l x+m y=n$$ and $$l^{\prime} x+m^{\prime} y=n^{\prime}$$ are perpendicular if43. If the parabola $$x^2=4$$ ay passes through the point $$(2,1)$$, then the length of the latus rectum is44. If the sum of $$n$$ terms of an AP is given by $$S_n=n^2+n$$, then the common difference of the $$\mathrm{AP}$$ is45. The negation of the statement "For all real numbers $$x$$ and $$y, x+y=y+x^{\prime \prime}$$ is46. The standard deviation of the data 6, 7, 8, 9, 10 is47. $$\lim _\limits{x \rightarrow 0}\left(\frac{\tan x}{\sqrt{2 x+4}-2}\right) \text { is equal to }$$48. If a relation $$R$$ on the set $$\{1,2,3\}$$ be defined by $$R=\{(1,1)\}$$, then $$R$$ is49. Let $$f:[2, \infty) \rightarrow R$$ be the function defined $$f(x)=x^2-4 x+5$$, then the ranges of $$f$$ is50. If $$A, B, C$$ are three mutually exclusive and exhaustive events of an experiment such that $$P(A)=2 P(B)=3 P(C)$$, the51. The domain of the function defined by $$f(x)=\cos ^{-1} \sqrt{x-1}$$ is52. The value of $$\cos \left(\sin ^{-1} \frac{\pi}{3}+\cos ^{-1} \frac{\pi}{3}\right)$$ is
Does not exist53. If $$A=\left(\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right)$$ then $$A^4$$ is equal to54. If $$A=\{a, b, c\}$$, then the number of binary operations on $$A$$ is55. If $$\left(\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right) A=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$$56. If $$f(x)=\left|\begin{array}{ccc}x^3-x & a+x & b+x \\ x-a & x^2-x & c+x \\ x-b & x-c & 0\end{array}\right|$$, then57. If $$A$$ and $$B$$ are square matrices of same order and $$B$$ is a skew symmetric matrix, then $$A^{\prime} B A$$ is58. If $$A$$ is a square matrix of order 3 and $$|A|=5$$, then $$\mid A$$ adj. $$A \mid$$ is59. If $$f(x)=\left\{\begin{array}{cc}\frac{1-\cos K x}{x \sin x}, & \text { if } x \neq 0 \\ \frac{1}{2}, & \text { if } x=60. If $$a_1 a_2 a_3 \ldots a_9$$ are in AP, then the value of $$\left|\begin{array}{lll}a_1 & a_2 & a_3 \\ a_4 & a_5 & a_6
Physics
1. The value of acceleration due to gravity at a height of $$10 \mathrm{~km}$$ from the surface of earth is $$x$$. At what 2. Young's modulus of a perfect rigid body is3. A wheel starting from rest gains an angular velocity of $$10 \mathrm{~rad} / \mathrm{s}$$ after uniformly accelerated fo4. Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged, if the densi5. A sphere, a cube and a thin circular plate all of same material and same mass initially heated to same high temperature6. In an adiabatic expansion of an ideal gas the product of pressure and volume7. A certain amount of heat energy is supplied to a monoatomic ideal gas which expands at constant pressure. What fraction 8. A tray of mass $$12 \mathrm{~kg}$$ is supported by two identical springs as shown in figure. When the tray is pressed do9. A train whistling at constant frequency $$n$$ is moving towards a station at a constant speed $$v$$. The train goes past10. A point charge $$q$$ is placed at the corner of a cube of side $$a$$ as shown in the figure. What is the electric flux t11. The electric field lines on the left have twice the separation on those on the right as shown in figure. If the magnitud12. An infinitely long thin straight wire has uniform charge density of $$\frac{1}{4} \times 10^{-2} \mathrm{~cm}^{-1}$$. Wh13. A dipole moment $$p$$ and moment of inertia $$I$$ is placed in a uniform electric field $$\mathbf{E}$$. If it is displac14. The difference between equivalent capacitances of two identical capacitors connected in parallel to that in series is $$15. Figure shows three points $$A, B$$ and $$C$$ in a region of uniform electric field $$\mathbf{E}$$. The line $$A B$$ is p16. When a soap bubble is charged?17. A hot filament liberates an electron with zero initial velocity. The anode potential is $$1200 \mathrm{~V}$$. The speed 18. A metal rod of length $$10 \mathrm{~cm}$$ and a rectangular cross-section of $$1 \mathrm{~cm} \times \frac{1}{2} \mathrm19. A car has a fresh storage battery of emf $$12 \mathrm{~V}$$ and internal resistance $$2 \times 10^{-2} \Omega$$. If the 20. A potentiometer has a uniform wire of length $$5 \mathrm{~m}$$. A battery of emf $$10 \mathrm{~V}$$ and negligible inter21. The colour code for a carbon resistor of resistance $$0.2 \mathrm{k} \Omega \pm 10 \%$$ is22. Each resistance in the given cubical network has resistance of $$1 \Omega$$ and equivalent resistance between $$A$$ and 23. $$I-V$$ characteristic of a copper wire of length $$L$$ and area of cross-section $$A$$ is shown in figure. The slope of24. In the given figure, the magnetic field at $$O$$.
25. The magnetic field at the origin due to a current element $$i d \mathbf{l}$$ placed at a point with vector position $$\m26. A long cylindrical wire of radius $$R$$ carries a uniform current $$I$$ flowing through it. The variation of magnetic fi27. A cyclotron is used to accelerate protons $$\left({ }_1^l \mathrm{H}\right)$$ deuterons $$\left({ }_1^2 \mathrm{H}\right28. A paramagnetic sample shows a net magnetisation of $$8 \mathrm{Am}^{-1}$$ when placed in an external magnetic field of $29. The ratio of magnetic field at the centre of a current carrying circular coil to its magnetic moment is $$x$$, if the cu30. In a permanent magnet at room temperature31. A rod of length $$2 \mathrm{~m}$$ slides with a speed of $$5 \mathrm{~ms}^{-1}$$ on a rectangular conducting frame as sh32. The current in a coil of inductance $$0.2 \mathrm{H}$$ changes from $$5 \mathrm{~A}$$ to $$2 \mathrm{~A}$$ in $$0.5 \mat33. In the given circuit the peak voltage across $$C, L$$ and $$R$$ are $$30 \mathrm{~V}, 110 \mathrm{~V}$$ and $$60 \mathrm34. The power factor of $$R-L$$ circuit is $$\frac{1}{\sqrt{3}}$$. If the inductive reactance is $$2 \Omega$$. The value of 35. In the given circuit, the resonant frequency is
36. A light beam of intensity $$20 \mathrm{~W} / \mathrm{cm}^2$$ is incident normally on a perfectly reflecting surface of s37. An object approaches a convergent lens from the left of the lens with a uniform speed $$5 \mathrm{~m} / \mathrm{s}$$ and38. The refracting angle of prism is $$A$$ and refractive index of material of prism is $$\cot \frac{A}{2}$$. The angle of m39. The following figure shows a beam of light converging at point $$P$$. When a concave lens of focal length $$16 \mathrm{~40. Three polaroid sheets $$P_1, P_2$$ and $$P_3$$ are kept parallel to each other such that the angle between pass axes of 41. Two poles are separated by a distance of $$3.14 \mathrm{~m}$$. The resolving power of human eye is $$1 \mathrm{~min}$$ o42. In Young's double slit experiment, the distance between the slits and the screen is $$1.2 \mathrm{~m}$$ and the distance43. The de-Broglie wavelength associated with electron of hydrogen atom in this ground state is44. The following graph represents the variation of photocurrent with anode potential for a metal surface. Here $$I_1, I_2$$45. The period of revolution of an electron revolving in nth orbit of $$\mathrm{H}$$-atom is proportional to46. Angular momentum of an electron in hydrogen atom is $$\frac{3 h}{2 \pi}$$ ($$h$$ is the Planck's constant). The KE of th47. A beam of fast moving alpha particles were directed towards a thin film of gold. The parts $$A, B$$ and $$C$$ of the tra48. Two protons are kept at a separation of $$10 \mathrm{~nm}$$. Let $$F_n$$ and $$F_e$$ the nuclear force and the electroma49. During a $$\beta^{-}$$-decay50. A radio-active elements has half-life of 15 years. What is the fraction that will decay in 30 years?51. A $$220 \mathrm{~V}$$ AC supply is connected between points $$A$$ and $$B$$ as shown in figure, what will be the potenti52. In the following circuit what are P and Q
53. A positive hole in a semiconductor is54. Two long straight parallel wires are a distance $$d$$ part. They carry steady equal currents flowing out of the plane of55. A cylindrical wire has a mass $$(0.3 \pm 0.003) \mathrm{g}$$, radius $$(0.5 \pm 0.005) \mathrm{mm}$$ and length $$(6 \pm56. At a metro station, a girl walks up a stationary escalator in $$20 \mathrm{~s}$$. If she remains stationary on the escal57. Rain is falling vertically with a speed of $$12 \mathrm{~ms}^{-1}$$. A woman rides a bicycles with a speed of $$12 \math58. One end of a string of length $$l$$ is connected to a particle of mass $$m$$ and the other to a small peg on a smooth ho59. A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it a60. A thin uniform rectangular plate of mass $$2 \mathrm{~kg}$$ is placed in $$x y$$-plane as shown in figure. The moment of
1
KCET 2020
MCQ (Single Correct Answer)
+1
-0
A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time $$t$$ is proportional to
A
$$t^{1 / 2}$$
B
$$t$$
C
$$t^{3 / 2}$$
D
$$t^2$$
2
KCET 2020
MCQ (Single Correct Answer)
+1
-0
A thin uniform rectangular plate of mass $$2 \mathrm{~kg}$$ is placed in $$x y$$-plane as shown in figure. The moment of inertial about $$x$$-axis is $$I_x=0.2 \mathrm{~kgm}^2$$ and the moment of inertia about $$Y$$-axis is $$I_y=0.3 \mathrm{~kgm}^2$$. The radius of gyration of the plate about the axis passing through $$O$$ and perpendicular to the plane of the plate is
A
50 cm
B
5 cm
C
38.7 cm
D
31.6 cm