Physics and Chemistry Past Paper PDF

## Physics ### Q1. Two blocks of masses 10 kg and 30 kg are placed along a vertical line. If 10 kg block is raised through a height of 7 cm, then the distance through which other mass should be moved to raise the center of mass of the system by 1 cm is - 1 cm up - 1 cm down - 2 cm down - 2 cm up...

## Physics ### Q1. Two blocks of masses 10 kg and 30 kg are placed along a vertical line. If 10 kg block is raised through a height of 7 cm, then the distance through which other mass should be moved to raise the center of mass of the system by 1 cm is - 1 cm up - 1 cm down - 2 cm down - 2 cm up ### Q2. Statement 1: The plot of atomic number (y-axis) versus the number of neutrons (x-axis) for stable nuclei shows a curvature towards (x-axis) from the line of 45° slope as the atomic number is increased. Statement 2: Proton-proton electrostatic repulsion begin to overcome attractive forces involving protons and neutrons in heavier nuclides. - Statement 1 is true, statement 2 is true, statement 2 is correct explanation for the statement 1. - Statement 1 is true, statement 2 is true, statement 2 is not a correct explanation for statement 1. - Statement 1 is true and statement 2 is false. - Statement 1 is false and statement 2 is true. ### Q3. The stress versus strain graphs for wires of two materials A and B are as shown in figure. Which material is more ductile? A graph with stress on the y axis and strain on the x axis shows two curves, the first labeled WIRE A, lies above the second labeled WIRE B. - Material A - Material B - Both material A and material B - None of these ### Q4. A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and of same material as P are now added as shown in the figure. The ray will now suffer A diagram depicts an equilateral triangle labeled P. A second identical equilateral triangle is attached to the right side of the first labeled R, and a third identical equilateral triangle is attached to the right side of the second labeled Q. - greater deviation. - no deviation. - same deviation. - total internal reflection. ### Q5. The output Y of the logic circuit shown in figure is best represented as: A logic circuit diagram shows three inputs: A, B, and C. Input A is connected to a NOT gate; Input B is connected to a NOT gate; The output of Input A’s NOT gate is connected to the top input of an AND gate; The output of Input B’s NOT gate is connected to the bottom input of an AND gate. The output of the AND gate is connected to the input of a NOT gate. The output of Input C is connected to the top input of an OR gate. The output of the AND gate's NOT gate is connected to the bottom input of an OR gate. The output of the OR gate, labeled Y. - A + B - C - A + B . C - A + B - C - A + B - C ## Chemistry ### Q31 2-Butyne can be obtained by: I. Dehydrogenation of 2-butene. II. Reaction of 1, 1, 1-trichloroethane with Ag powder. III. 1 equivalent of ethyne treated with excess of sodium followed by CH3Cl. - Both I and II - Both II & III - I, II & III - Both I and III ### Q32 For the cell Zn (s) | ZnSO4 (aq) || CuSO4 (aq) | Cu (s), when the concentration of Zn2+ is 10 times the concentration of Cu2+, the expression for AG (in J mol-1) is [F = Faraday's constant, R = universal gas constant, T=temperature, Eºcell = 1.1V] - 2.303 ×RT+1.1 F - 1.1 F - 2.303 ×RT-2.2 F - -2.2 F ### Q33 An organic compound contains 49.3% carbon, 6.84% hydrogen and its vapour density is 73. Molecular formula of the compound is: - C3H5O2 - C6H10O4 - C4H10O2 - C3H10O2 ### Q34 Calculate the percentage of all the monochlorinated products obtained from the chlorination of 2 methyl butane. The relative reactivity of 1º, 2º, and 3º hydrogen to chlorination is (1:3.8: 5). - 15%, 45%, 20%, 25% - 14%, 35%, 23%, 28% - 12%, 30%, 22%, 29% - 17%, 36%, 20%, 23% ### Q35 Assertion: A mixture of plant pigments can be separated by chromatography. Reason: Chromatography is used for the separation of colored substances into individual components. - If both assertion and reason are true and the reason is the correct explanation of the assertion. - If both assertion and reason are true but reason is not the correct explanation of the assertion. - If assertion is true but reason is false. - If the assertion and reason both are false. ### Q36 OH X (CHO₂) Y + CH3CH2COO 1. KMnO2/OH 2. 2. HO COOH Find the structure of X. - An image depicting a benzene ring with a side chain that includes a carbonyl group - An image depicting a benzene ring with a side chain that includes a carboxyl group - An image depicting a benzene ring with two side chains, one that includes a carbonyl group and one that includes a carboxyl group - An image depicting a benzene ring with a side chain that includes a hydroxyl group ### Q37 Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R: Assertion A: The HOH bond angle in water molecule is 104.5°. Reason R: The lone pair lone pair repulsion of electrons is higher than the bond pair bond pair repulsion. - A is false but R is true - A is true but R is false - Both A and R are true, but R is not the correct explanation of A - Both A and R are true, and R is the correct explanation of A ### Q38 The compound, whose stereo-chemical formula is written below, exhibits x geometrical isomers and y optical isomers. An image depicting a four-carbon chain with a double bond between the second and third carbons. The first carbon is attached to a methyl group and a hydrogen atom. The third carbon is attached to a hydrogen atom and a methylene group. The fourth carbon is attached to a methylene group and a hydroxyl group. The hydroxyl group is attached to a methyl group. - 4 and 4 - 2 and 2 - 2 and 0 - 4 and 2 ### Q39 Consider the following statements. I. The entropy in isolated system with only p-V work is always maximised at equilibrium. II. It is possible for the entropy of close system to increase substantially in an irreversible process. III. Without the help of an external agency, spontaneous process cannot be reversed. IV. ΔSsystem is zero for reversible process in any system. Which of the above statement(s) is/are correct? - I, II, III - I, IV - II and III - II, III and IV ### Q40 Na2B4O7.10H2O is correctly represented as - Na2B4O5(OH)4]8H2O - Na2 [B4(H2O)407]. 6H2O - 2NaBO2. Na2 B2O3.10H2O - None of the above ### Q41 Match the chemical conversions in list I with appropriate reagents in list II and select the correct answer using the code given below the list. List-I P. Cl List-II (i) Hg(OAc)2; I. (ii) NaBH4 Q. ☑ ONa ☑ OEt II. NaOEt R. S. OH III. Et - Br IV. OH (i) BH3; (ii) H2O2/NaOH - P - II, Q - III, R – I, S – IV - P - III, Q – II, R - I, S - IV - P - II, Q - III, R - IV, S - I - P - III, Q - II, R - IV, S - I ### Q42 Na+, Mg2+, Al3+ and Si4+ ions are isoelectronic. The order of ionic radii of these ions. - Na+ > Mg2+ > Al3+ Si4+ - Na+ > Mg2+ > Al3+ < Si4+ - Na+ < Mg2+ < Al3+ < Si4+ - Na+ < Mg2+ > Al3+ > Si4+ ### Q43 Identify the incorrect statement: - CuSO4 reacts with KCl in aqueous solution to give Cu2Cl2 - CuSO4 reacts with KI in aqueous solution to give Cu2I2 - CuSO4 reacts with NaOH and glucose in aqueous medium to give Cu2O - CuSO4 on strong heating gives CuO ### Q44 The elements X and Y form compound having molecular formula XY2 and XY4 (both are non electrolytes). When dissolved in 20 g benzene, 1gXY2 lowers the freezing point by 2.3°C whereas 1 g of XY4 lowers the freezing point by 1.3°C. Molal depression constant for benzene is 5.1. Thus atomic masses of X and Y respectively are - 42.64, 21.10 - 25.59, 42.64 - 21.10, 42.64 - 42.64, 25.69 ### Q45. In which of the following reaction, cyanide will be obtained as a major product? - An image depicting a four-carbon chain with a double bond between the second and third carbons. The first carbon is attached to a phenyl group and a carbonyl group. The fourth carbon is attached to a methylene group. The reaction arrow points to the right. Below the arrow is written “(i) LiAlH₄, (ii) H₂O^*” - An image depicting a four-carbon chain with a double bond between the second and third carbons. The first carbon is attached to a phenyl group and a ketone group. The third carbon is attached to an amine group. To the right side of the image is written a reaction arrow pointing to the right. Below the arrow is written “NaOH, Br₂” - An image depicting a four-carbon chain with a double bond between the second and third carbons. The first carbon is attached to a phenyl group and a carbonyl group. The third carbon is attached to an amine group. To the right side of the image is written a reaction arrow pointing to the right. Below the arrow is written “P₄O₁₀” - An image depicting a four-carbon chain with a double bond between the second and third carbons. The first carbon is attached to a phenyl group and a carbonyl group. The third carbon is attached to a hydroxyl group. To the right side of the image is written two reaction arrows pointing to the right. Below the first is written “SOCI₂” and the second is written “NH₃” ### Q46 Various products formed on oxidation of 2,5-dimethylhexan-3-one are - CH3-CH-COOH (i) CH3 - CH3-CH-CH2-COOH (11) CH3 - (iii) CH3COOH - (iv) HCOOH - (i) and (iii) - (i), (ii) and (iii) - (i), (ii), (iii) and (iv) - (iii) and (iv) ## Math ### Q61 The mean and variance of 10 observations are found to be 10 and 5 respectively. On rechecking it is found that an observation 5 is incorrect. If the incorrect observation is replaced by 15, then the correct variance is - 7 - 8 - 9 - 4 ### Q62 Let A = (aij) 3x3 and B = (bij) 3x3 where bij = aijtan Vi, j. Number of such matrices A whose elements are selected from the set {0, 1,2, 3} such that A = B, are - 29 - 212 - 26 - 28 ### Q63 Consider a relation R defined as aRb if 2 + ab > 0 where a, b are real numbers. Then, the relation R is - reflexive and symmetric - symmetric and transitive - transitive and reflexive - None of these ### Q64 If A(3, 2, 0), B(5, 3, 2) and C(-9, 6, 3) are three points forming a triangle and AD is bisector of the angle /BAC, then AD meets BC at the point - (19/8, 57/16, 17/16) - (19/8, 57/16, 17/16) - (19/8, 57/16, 17/16) - None of these. ### Q65 The solution of differential equation (y+zxy(x+y))dx + (yxy(x+y) - x)dy = 0, is - (z2+y2)/2 + 2tan-1(z/√y) = C - (z2+y2)/2 + 2tan-1(√z/y) = C - (z2+y2)/2 + 2tan-1(√y/z) = C - None of these ### Q66 In an increasing geometric progression, the sum of the first and the last term is 99, the product of the second and the second last term is 288 and the sum of all the terms is 189. Then, the number of terms in the progression is equal to - 5 - 6 - 7 - 8 ### Q67 The value of limx→∞ [(e^(x/2)) / (x^(1/2))] is equal to - e - e ^ -1 - e^(1/2) - 1/e ### Q68 If all roots of the equation f(x) = x5 - 12x4 + bx³ + cx² + ex + 64 = 0 are positive, then which has the greatest numerical (absolute) value - b - c - d - e ### Q69. A bag contains 40 tickets numbered from 1 to 40. Two tickets are drawn from the bag without replacement. The probability that the 2nd ticket is a perfect square given that the 1st ticket was a perfect square is - 1/3 - 5/39 - 3/80 - 1/8 ### Q70 The number of point(s) of minima of the polynomial y = 10x6 - 24x5 + 15x4 - 40x² + 108 is(are) equal to - 1 - 2 - 3 - 4 ### Q71 Let I₁ = ∫₀^e x²e^x dæ and I₂ = ∫₀^e 2x²e^x dx, then the value of I₁ + I₂ is equal to - 1 - 2 - e - e^2 ### Q72 If principal argument of zo satisfying |z³| = √2 and arg(z - 5i) = π/4 simultaneously is θ, then identify the incorrect statement(s)? - |z| = √2 - tan 2θ = 8/15 - tan θ = 1/4 - | z - 5i | = 4√2 ### Q73 Consider two lines in space as L₁: r→ =i+j+2k+λ(3i-i-k) and L₂: r→ = 4i + 3j + 6k + μ(i + 2k) where λ, μ∈ R. If the shortest distance between these lines is d. Then the value of d will be: - 5 - 6 - 7 - 8 ### Q74 If a directrix of a hyperbola centered at the origin and passing through the point (4,-2√3) is 5x = 4√5 and its eccentricity is e, then: - 4e^4-24e^2+35=0 - 4e^4+8e^2-35=0 - 4e^4-24e^2+27=0 - 4e^4-12e^2-27=0 ### Q75 Coefficients of z^r [0 <r < (n-1)] in the expansion of (x+3)^-1+(x+3)^-2(x+2)+(x+3)^-3(x+2)² + ... + (x + 2)^-1 - nC_r(3 - 2^r) - nC_r(3^r - 2^r) - nC_r(3^r + 2^(n-r)) - None of these ### Q76 If the graph of the function y = (ab)²x²+2(a+b^2c)x + 1(a ≠ b) is strictly above the x axis, then - a<b<c - a<c<b - b<a<c - c<b<a ### Q77 Let (x, y) = 0 be the equation of a circle if (0, 1) = 0 has equal roots. A = 2, 2 and 4 (1, 0) has roots λ = 5, then, find the centre of the circle. - (29/10, 2) - (29/10, 2) - (29/10, -2) - None of these ### Q78 The number of solutions of the equation sinx = (sinx) ^ (1/2) is/are - one - two - three - zero ### Q79. A function f: Z → Z is defined as f(n) = { n+1, if n ∈ odd integer ; n/2, if n ∈ even integer }. If k ∈ odd integer and f(f(f(k))) = 33, then the sum of the digits of k is - 7 - 5 - 9 - 8 ### Q80 Let u→ = i→ + j→, v→ = i→ - j→ and w→ = 2i→ + 2j→ + 3k→. If n→ is a unit vector such that u→.n→ = 0 and v→.n→ = 0, then w→.n→ may be equal to - 1 - 2 - 3 - 0 ## Numerical ### Q21 The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of 1 at 10°C. Now the end P is maintained at 10°C, while the end S is heated and maintained at 400°C. The system is thermally insulated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is 1.2 x 10-5 K-1, the change in length of the wire PQ is: (Mark answer in mm to nearest whole number) ### Q22 The densities of two solid spheres A and B of the same radii R vary with radial distance r as PA(r) = k(r/R) and PB (r) = k(r / R) ^ 5, respectively, where k is a constant. The moments of inertia of the individual spheres about axes passing through their centres are IA and IB, respectively. If IA / IB = R^7 / 10, the value of n is ### Q23 A drop of liquid of radius R = 10^-2m having surface tension S = Nm^-1 / 4π divides itself into K identical drops. In the process the total change in the surface energy ΔU = 10^-3 J. If K = 10^6 then the value of a is ### Q24. If a coil of 40 turns and area 4.0 cm² is suddenly removed from a magnetic field, it is observed that a charge of 2.0 × 10^-4C flows into the coil. If the resistance of the coil is 800, the magnetic flux density is......T. ### Q25 Standing waves are produced by the superposition of two waves y1 = 0.05 sin(3nt - 2x) Y2 = 0.05 sin(3nt + 2x) where, x and y are in metres and t is in second. If the amplitude of the particle at x = 0.5m is R, find 1000R. [Given, cos 57.3° = 0.54] ### Q26 A block of mass 2 kg is kept at the origin at t = 0 and is having velocity 4√5 m s^-1 in the positive x direction. The only force on it is a conservative and its potential energy is defined as U = x^2+ 6x^2 + 15. Its velocity when the force acting on it is minimum (after the time t = 0) is - ### Q27 A beam of light of wavelength 600 nm from a monochromatic source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between the first minima on either side of the central maxima is d (mm), find 10d ### Q28 When switch S is closed, then the reading of ammeter is A, then value of 10A is A circuit diagram depicting a battery, an ammeter and a circuit that branches off to a parallel resistor and series resistors. ### Q29 Light of intensity = 3 W m^-2 is incident on a perfectly absorbing metal surface of area 1 m² making an angle of 60° with the normal. If the force exerted by the photons on surface is px 10^-9 (in Newton) find the value of p. ### Q30 A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance 2 m when each is carrying same charge q. If the free charged particle is displaced from its equilibrium position through distance x (x <<1 m). The particle executes SHM. Its angular frequency of oscillation will be ______ ×10^8 rad s^-1 (if q^2 = 10C^2 ) ### Q51 Resistance of 0.2M solution of an electrolyte is 500. The specific conductance of the solution is 1.3Sm^-1. If resistance of the 0.4M solution of the same electrolyte is 2600, its molar conductivity is N × 10^-4Sm² mol^-1, Find 4 N. ### Q52 Identify the total number of atoms in product Q in the given sequence of reaction C6H5NH2 → X → Y → Z → P → Q NaNO2+HCI Cu2 (CN)2 H2O/H+ NaOH/CaO, Cl2, hv(Excess) ### Q53 Total number of monochlorinated products of CH3-CH2-CH2-CH3 is ### Q54 The molarity of HNO3 in a sample which has density 1.4 g/mL and mass percentage of 63% is (Molecular Weight of HNO3 = 63) ### Q55 The titration curve for Ephedrine (EP) a weak base dissolved in 182 mL of H₂O when carried out with 1 M HCl solution is reproduced below. A graph depicting pH on the y axis and volume on the x axis. The y axis is divided into 1 unit increments from 0 to 11. The x axis is divided into 1 unit increments from 0 to 16. The graph shows the formation of three plateaus with an inflection point at 9mL and 18mL At point of equivalence, calculate pH and report the value of (pH + log 3) as integer answer. ### Q56 Calculate the difference in the heat of formation (in calories) of carbon monoxide at constant pressure and at constant volume at 27°C. ### Q57. For the equation CaCO3 (s) → CaO (s) + CO2 (g), K1000 = 0.059. Exactly 10 g of CaCO3 is placed in a 10 L container at 1000 K. After equilibrium is reached, what mass of CaCO3 remains? (Round off to the nearest integer) ### Q58 Calculate the EAN of central atom in the following complex [Cr(CO)6] ### Q59 What is the number of visible lines when an electron returns from 5th orbit to the ground state in H-spectrum? ### Q60 The following data were obtained during the first order thermal decomposition of SO2Cl2 at a constant volume SO2Cl2(g) →SO2(g) + Cl2(g) Experiment Time/s-1 Total pressure/atm 1 0 0.5 2 100 0.6 Calculate y when the rate of the reaction y x 10^4 when total pressure is 0.65 atm. Given (log5 = 0.699, log2 = 0.301) (round off to nearest integer) ### Q81 1 Let In = ∫(from 0 to 1) ( 1 + x^2 / 2 + x^4/3 + ... + x^(2n) / (2n))dx where n ∈ N. If limn→∞ I_n can be expressed as a rational number in the lowest form, then find the value of p + q. ### Q82 The area (in sq. units) enclosed by the solution set of [x][y] = 3 is equal to (where [.] denotes greatest integer function) ### Q83 Given three points on the xy plane O(0, 0), A(1,0) and B(-1,0). Point P is moving on the plane satisfying the condition (PA→PB→) + 3(OA→OB→) = 0. If the maximum and minimum values of |PA||PB| are M and m respectively then find the values of M^2 + m^2. ### Q84 If the range of f(x) = (2x^2-14x+22)/(x^2-7x+12) is (a, b), then (a + b) is ### Q85 Let tanα, tanβ and tanγ; α, β, γ≠ (2n-1)π / 2, n∈ N be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If circumcentre of ΔABC coincides with origin and its orthocentre lies on y-axis, then the value of ((cos^3α+cos^3β+cos^3γ) / (cosacosβcosy))^2 is equal to: ### Q86 Let A be a 2 x 2 matrix such that A [3 0 ; 0 2] = [8 0 ; 0 8] & 2|A| = 8, then sum of diagonal elements of A^2 is: ### Q87 A term is randomly chosen from the expansion of [4 + (1/√5)]^{20}. If the probability that it is a rational term is P, then 420P is equal to ### Q88 1 a 0 Let A = [ 0 1 b ; 0 c 1] where a, b, c ∈ R. If the sum o of all non-real roots of the equation A-xI = 0 is k-mabc, Vk, m∈ Z, then the value of k + m is equal to ### Q89 If 5^3^5 - 3^3^3 is divided by 10, then the remainder obtained is ### Q90 From the string abacabababcdced, if 5 letters should be selected, then the number of ways in which this selection can be done is