Biology, Chemistry, Maths Past Papers PDF

Biology 1. Question 1 Match the entries in Column I with their functions described in Column II. Which one of the following combinations is correct? P - (iv); Q - (iii); R - (ii); S - (i) (a) P - (iii); Q - (i); R - (iv); S - (ii) (b) P - (ii); Q - (iv); R - (i); S - (iii) (c) P - (i); Q - (ii); R - (iii); S - (iv) (d) 1 2. Question 2 Which one of the following best describes peptones? Partially digested proteins (a) Zymogen form of pepsin (b) Activated form of pepsin (c) An intestinal mixture of proteins, mucous and HCO− 3 (d) 2 3. Question 3 Match the biomolecules given in Column I with their corresponding chemical nature given in Column II. Which one of the following combinations is correct? P - (iv); Q - (ii); R - (i); S - (iii) (a) P - (ii); Q - (iv); R - (iii); S - (i) (b) P - (iii); Q - (i); R - (iv); S - (ii) (c) P - (i); Q - (iii); R - (ii); S - (iv) (d) 3 4. Question 4 A mitotic drug inhibits microtubule formation. Which one of the following stages of karyokinesis will be the first to get affected by the drug? Metaphase (a) Anaphase (b) Prophase (c) Telophase (d) 4 5. Question 5 Which one of the following statements regarding seed structure is INCORRECT? In monocot seeds, the membraneous seed coat that is fused with the fruit wall is called the aleurone layer. (a) The endosperm is not present in some of the mature dicot seeds. (b) In dicots, the outer layer of the seed coat is called testa. (c) Coleoptile and coleorhiza are found in monocotyledonous seeds. (d) 5 6. Question 6 Which one of the following anatomical features of wood can be used to estimate the age of a tree growing in a temperate climate? Spring wood and late wood. (a) Heart wood and sap wood. (b) Spring wood and heart wood. (c) Autumn wood and sap wood. (d) 6 7. Question 7 Which one of the following statements is CORRECT about biological nitrogen fixation in plants? The catalytic redox center of Nitrogenase contains Mo and Fe as cofactors. (a) Atmospheric nitrogen is fixed by Nitrogenase by converting N2 to NO− 3. (b) Nitrogenase can function optimally only in the presence of molecular oxygen. (c) The transport of important amides, like asparagine and glutamine, produced by transamination, to different parts of the plant body is mediated by phloem. (d) 7 8. Question 8 Which one of the following is an example of genetic diversity? Variation in the potency and concentration of reserpine produced by Rauwolfia vomitoria. (a) Higher diversity of amphibians in the Western Ghats than in the Eastern Ghats. (b) Greater variation of ecosystems found in India than in Scandinavia. (c) The greater diversity of plant species found in India compared to Central Asia. (d) 8 9. Question 9 When the ribosome encounters a stop codon in the mRNA, during translation, which one of the followng binds to the stop codon? Release factor. (a) Rho factor. (b) Termination factor. (c) Sigma factor. (d) 9 10. Question 10 Match the terms in column I with their corresponding physiological roles given in Column II. Which one of the following combinations is correct? P - (iv); Q - (v); R - (i); S - (ii) (a) P - (v); Q - (i); R - (iv); S - (iii) (b) P - (iii); Q - (ii); R - (v); S - (iv) (c) P - (i); Q - (iv); R - (iii); S - (v) (d) 10 11. Question 11 For which one of the following diseases does the causative agent require the splicing of their hnRNA to generate mature mRNA? Malaria (a) Pertussis (b) Typhoid (c) Tuberculosis (d) 11 12. Question 12 The diagram represents an enzyme, its substrate and potential inhibitors (P, Q, R, S, T). Which one of the following combinations is the best pair of competitive inhibitors for the enzyme? P, S (a) Q, R (b) S, T (c) R, T (d) 12 13. Question 13 In an island with 10,000 individuals, four have sickle cell anemia, a recessive autosomal disease. Assuming that the locus is in Hardy-Weinberg equilibrium, how many individuals in that island are expected to be heterozygous for the disease allele? 392 (a) 4 (b) 9996 (c) 9608 (d) 13 14. Question 14 A 1000 base-pair DNA fragment was cloned between Hind III and EcoR I sites of the plasmid vector (pIAT) of size 3500 base-pair. The cloned fragment had a Not I site as shown in the figure. In order to confirm the presence of the insert, the recombinant plasmid was digested completely with (a) Not I and EcoR I, and (b)Not I and Hind III. In lane 1 the products of the digestion by Not I and EcoR I was loaded. In lane 2 the products of the digestion by Not I and Hind III was loaded. Which one of the following correctly represents the agarose gel electrophoresis profile of the digested recombinant plasmid for (a) and (b), respectively? (a) 14 (b) (c) 15 (d) 16 15. Question 15 The following pedigree chart shows the inheritance of a genetic disorder. I-2 and III-2 are the only affected individuals. Which one of the following is the correct pattern of inheritance of the disorder, and the genotype of the II-3 individual? Autosomal recessive, heterozygous (a) Autosomal dominant, homozygous for the normal allele (b) X-linked recessive, heterozygous (c) Autosomal recessive, homozygous for the normal allele (d) 17 Chemistry 1. Question 1 How many radial nodes does Ca+ have in its 4s orbital? 3 (a) 0 (b) 1 (c) 2 (d) 1 2. Question 2 Amongst O2 , N2 , F2 , and B2 , which molecules will be attracted to an external magnetic field? O2 and B2 (a) F2 , N2 , and B2 (b) O2 , B2 , and N2 (c) O2 and F2 (d) 2 3. Question 3 What is the smallest P−P−P bond angle in the highly reactive allotrope of phosphorus? 60◦ (a) 109◦ (b) 45◦ (c) 120◦ (d) 3 4. Question 4 Which of the following is an ore of iron? Siderite (a) Bauxite (b) Malachite (c) Quartz (d) 4 5. Question 5 Which parameters are plotted in the Ellingham diagram? ∆r G◦ vs T (a) ∆r H◦ vs T (b) ∆r S◦ vs T (c) ∆r S◦ vs P (d) 5 6. Question 6 Which of the following compounds will NOT undergo the Finkelstein reaction with NaI via SN 2 pathway? II and III (a) I and III (b) II and IV (c) I and IV (d) 6 7. Question 7 Which one amongst the following is the most efficient way of synthesizing n-propyl benzene? I (a) II (b) III (c) IV (d) 7 8. Question 8 Which amongst the following are chiral compounds? II and IV (a) I and IV (b) II and III (c) I and II (d) 8 9. Question 9 Which one amongst the following bases is NOT present in RNA? III (a) I (b) II (c) IV (d) 9 10. Question 10 Which amongst the following are aromatic? I and II (a) III and IV (b) II and IV (c) I and III (d) 10 11. Question 11 Why is it harder to compress liquids and solids relative to gases? Molecules are closer to each other in solids and liquids. (a) Due to the presence of electron-nuclear attraction in solids and liquids. (b) Due to the absence of electron-nuclear attraction in solids and liquids. (c) Solids and liquids have definite volume. (d) 11 12. Question 12 Related to the Freundlich adsorption isotherm, which one of the following statements is NOT correct? It holds good over a wide range of pressures. (a) 1 The value of is between 0 and 1. n (b) The Freundlich adsorption isotherm equation is an empirical equation. (c) It is used for the adsorption of both gases and solutions. (d) 12 13. Question 13 Consider the following reaction: − C(g) + 4H(g); ∆a H 0 = 1665 kJ mol−1 CH4 (g) → Which of the statements is FALSE? ∆a H 0 is the mean bond enthalpy of a C-H bond. (a) All four C-H bonds in CH4 are identical in bond length and energy. (b) The energy required to break individual C-H bonds in successive steps is different. (c) Mean C-H bond enthalpies differ slightly from compound to compound. (d) 13 14. Question 14 In two solutions X (hexane and benzene) and Y (water and HCl), what types of deviations from Raoult’s law are observed? No deviation (ideal behaviour) and negative deviation, respectively. (a) Negative deviation and positive deviation, respectively. (b) Positive deviation and negative deviation, respectively. (c) Positive deviation and no deviation (ideal behaviour), respectively. (d) 14 15. Question 15 In aqueous solution, the hydronium ion gets further hydrated to give which of the following species? H9 O 4 + (a) H7 O 4 + (b) H3 O 2 + (c) H5 O 3 + (d) 15 Mathematics 1. Question 1 Let f : R → (0, ∞) be a continuous decreasing function. Suppose f (0), f (1),... , f (10) are in a geometric progression with common ratio 15. R 10 In which of the following intervals does the value of 0 f (x)dx lie? (0, 2f (0)) (a) (4f (0), 6f (0)) (b) (8f (0), 10f (0)) (c) (12f (0), 14f (0)) (d) 1 2. Question 2 Let M be a 3 × 3 matrix with real entries such that           x1 x1 0   x1  x2  : M x2  = 0 = x2  : x1 + x2 = 0 = x2 + x3.     x3 x3 0 x3 What is the value of the determinant of M ? 0 (a) 1 (b) 2 (c) 3 (d) 2 3. Question 3 What is the locus of the center of circles passing through the origin (0, 0) with fixed radius? Circle (a) Hyperbola (b) Parabola (c) Line (d) 3 4. Question 4 Let α be a real number. What is the total number of distinct point(s) of intersection between the parabola y = x2 + 4x sin α + 6 and the pair of lines y 2 = 1? Zero (a) One (b) Two (c) Four (d) 4 5. Question 5 Let L be a straight line passing through the origin, and it makes angles α, β and γ with the positive X, Y and Z-axes, respectively. What is the value of cos 2α + cos 2β + cos 2γ ? −1 (a) 3 (b) 1 (c) −3 (d) 5 6. Question 6 What is the total number of distinct divisors of 29 × 319 ? 200 (a) 30 (b) 435 (c) 100 (d) 6 7. Question 7 Suppose the mean and the standard deviation of the data {x1 , x2 , · · · , x9 } are µ and σ(6= 0), respectively. After including one more data value x10 , the mean of the data {x1 , x2 , · · · , x9 , x10 } remains µ. What is the standard deviation of the data {x1 , x2 , · · · , x9 , x10 }? 3 √ σ 10 (a) √ 10 σ 3 (b) 10 σ 9 (c) 9 σ 10 (d) 7 8. Question 8 1 Consider three biased coins. Let the probability of getting head be and the 3 2 probability of getting tail be in each of the coins. Consider the experiment 3 of tossing the three coins one by one, and the following events: E : “at least two heads show up” F : “first coin shows tail”. What is the conditional probability of E given that F has already occured? 1 9 (a) 2 9 (b) 1 4 (c) 4 9 (d) 8 9. Question 9 Which of the following differential equations has y = ex as one of its particular solutions? d2 y dy y − ex + y 2 = e2x dx2 dx (a) d2 y dy y + ex + y 2 = e2x dx2 dx (b) d2 y dy y − ex + y 2 = ex dx2 dx (c) d2 y dy y + ex + y 2 = ex dx2 dx (d) 9 10. Question 10 What is the area of the region n 2 o (x, y) : 0 ≤ y ≤ xex , 0 ≤ x ≤ 1 ? 1 (e − 1) 2 (a) 1 e 2 (b) e−1 (c) e−2 (d) 10 11. Question 11 Consider the objective function Z =x−y subject to the constraints: x + 2y ≤ 10 x+y ≥2 x ≥ 0, y ≥ 0. What is the minimum value of Z subject to the above constraints? −5 (a) −2 (b) 2 (c) −10 (d) 11 12. Question 12 Let p(x) = x2 + bx + c be a quadratic polynomial with real coefficients b and c. Suppose p(1) = 5 and p(−1) = 3. What is the product of the roots of p(x) = 0? 3 (a) −1 (b) 2 (c) 1 (d) 12 13. Question 13 Let f : (−1, 2) → R be a differentiable function such that 2 f 0 (x) = and f (0) = 0. x2 − 5 Then in which of the following intervals does f (1) lie? (−∞, 0) (a) (0, 2) (b) (2, 4) (c) (4, ∞) (d) 13 14. Question 14 h πi Let f (x) = sin(3x), x ∈ 0,. Which of the following statements is true? 2 π π f is decreasing on ,. 4 2 (a) π π f is increasing on ,. 4 2 (b) π π π π f is increasing on , and decreasing on ,. 4 3 3 2 (c) π π π π f is decreasing on , and increasing on ,. 4 3 3 2 (d) 14 15. Question 15 Which one of the following functions is differentiable at x = 0? cos |x| (a) sin |x| (b) 1 |x| 2 (c) |x| (d) 15 Physics 1. Question 1 A ball is thrown vertically upwards with an initial speed u from a height h above the ground. The ball eventually hits the ground with a speed v. The acceleration due to gravity is g and the air resistance is negligible. What is the average speed of the ball over its entire trajectory? u2 + v 2 2(u + v) (a) v+u 2 (b) gh 2(u + v) (c) u2 + gh 2(u + v) (d) 1 2. Question 2 Two cubes A and B of same dimensions are made of different materials with densities ρA and ρB , respectively. Cube A floats in water with a fraction η of its volume immersed. When cube B is placed on top of cube A, it is found that cube A is just entirely immersed, while cube B is entirely above the surface of the water. What is the ratio ρB /ρA ? (1 − η)/η (a) η/(1 − η) (b) η (c) 1/η (d) 2 3. Question 3 An object is placed in front of a convex lens. A real inverted image of double its size is formed. When the object is moved closer to the lens by a distance d, the image shifts away from the lens by a distance 8d from its previous position. What is the magnitude of the magnification in the final setup? 4 (a) 1/2 (b) 8 (c) 16 (d) 3 4. Question 4 The frequency of the whistle of a train moving with a constant speed is observed by a stationary detector on the platform to be ν1. The frequency of the same whistle is detected to be ν2 inside another train moving on a parallel track, at a speed v towards the first train. If the speed of sound in air is taken to be vsound , what is the ratio v/vsound ? ν2 − ν1 ν1 (a) ν2 − ν1 ν2 (b) ν2 ν1 (c) ν1 ν2 (d) 4 5. Question 5 A current I flows through a cylindrical cable of length L and uniform cross-sectional area A. The power dissipated due to the current is P1. The cable is cut into two equal halves. If the cross-sectional area and the current flowing through the two halves remain unchanged and the power dissipated in each half is P2 , which of the following options is correct? P2 = P1 /2 (a) P2 = 2P1 (b) P2 = P1 (c) P2 = P1 /4 (d) 5 6. Question 6 Particle A with charge Q and particle B with charge 2Q are fixed at positions ~rA and ~rB , respectively. The force on A due to B is F~BA , and that on B due to A is F~AB. Which of the following options is correct? F~AB = −F~BA (a) F~AB = F~BA (b) F~AB = 2F~BA (c) F~AB = −2F~BA (d) 6 7. Question 7 The magnetic flux φB (t) through a coil at a time t is given by φB (t) = φ0 cos ωt, where 0 ≤ ωt ≤ π and φ0 is a non-zero constant. At what time is the magnitude of the induced emf a maximum? π 2ω (a) π ω (b) π 4ω (c) 0 (d) 7 8. Question 8 The intrinsic electron and hole concentrations of a Si-based intrinsic (0) (0) semiconductor are ne and nh , respectively. Upon doping with trivalent impurities the respective carrier concentrations become ne and nh. Which of the following options is true? (0) nh > nh (a) (0) ne > ne (b) ne = nh (c) (0) (0) ne and nh are independent of temperature. (d) 8 9. Question 9 The velocity v(t) of a particle moving in one dimension is given by:    αt, 0 ≤ t ≤ T /3 v(t) = αT /3, T /3 ≤ t ≤ 2T /3   α (T − t) , 2T /3 ≤ t ≤ T, where α (6= 0) is a constant. What is the total displacement of the particle from time t = 0 to t = T ? 2αT 2 9 (a) 4αT 2 9 (b) 8αT 2 9 (c) 7αT 2 9 (d) 9 10. Question 10 Two fixed point particles, each of charge +q, are separated by a distance 2L. Another point charge +q of mass m is oscillating about its equilibrium position as indicated√in the figure below. The time period of oscillation is given by T = 2π 3/2 α m/q. Given that 0 is the permittivity of free space, which of the following options is the dimensionally correct expression for α in SI units? 2L +q +q, m +q 1/2 0 L3/2 (a) 1/2 0 L (b) 3/2 0 L1/2 (c) 3/2 0 L (d) 10 11. Question 11 What is the effective resistance between A and B in the circuit shown below? 2R 3R R R 3R A B 2R 3R R 4R 3 (a) R 3 (b) 2R 3 (c) R 6 (d) 11 12. Question 12 Two spherical bodies A and B each of mass M and radius R are located such that their centers are apart by a distance of 4R as shown in the figure. An object C of mass m is thrown from the surface of A directly towards the center of B with a speed v0 = 2vmin , where vmin is the minimum speed needed for C to reach the surface of B. Given that G is the universal gravitational constant, how does the speed v(x) of C change as a function of its distance x from the center of A? R v0 R A B C 4R √ 2 2GM R v(x) = 1/2 x (4R − x)1/2 (a) √ 2R 2GM R v(x) = x(4R − x) (b) √ GM R v(x) = x1/2 (4R − x)1/2 (c) √ 6R2 2GM R v(x) = x3/2 (4R − x)3/2 (d) 12 13. Question 13 Consider the Bohr model of an atom where an electron of charge −e revolves around a nucleus of charge +e in an orbit of radius r. The electron has an orbital angular momentum 2~. If the nucleus had charge +2e, what would have been the radius of the orbit of the electron with the same principal quantum number? r/2 (a) 2r (b) r (c) √ 2r (d) 13 14. Question 14 A quantity has been measured to have a value of 0.00230 in some units. How many significant figures does the measured value have? 3 (a) 5 (b) 4 (c) 2 (d) 14 15. Question 15 Consider a Carnot heat engine operating between a heat reservoir at temperature 600 K, and an external atmosphere at temperature 300 K. In one cycle, 1000 kJ of heat is extracted from the heat reservoir, and the associated work is input to a reversible refrigerator that operates between 200 K and the same external atmosphere at 300 K. The refrigerator completes one cycle and releases heat into the atmosphere. How much heat is released into the atmosphere at the end of one cycle of the combined system? 2000 kJ (a) 2500 kJ (b) 1000 kJ (c) 500 kJ (d) 15 1. Match the features of a plant cell listed in Column I with their corresponding examples in Column II. Choose the CORRECT combination from the options below. A. i and t; ii and r; iii and s; iv and q B. i and u; ii and r; iii and s; iv and p C. i and u; ii and r; iii and q; iv and p D. i and r; ii and t; iii and s; iv and q 2. Shown below are some of the reactions that occur in the metabolic pathway leading to complete oxidation of glucose during aerobic respiration. Choose the CORRECT sequence of reactions during the complete oxidation of glucose. A. ii; i; iii; iv B. i; iii; iv; ii C. i; ii; iii; iv D. ii; iii; i; iv 3. In a given species of flowering plant, the colour of the seeds is exclusively determined by the colour of its seed coat. Seed coat colour in this species is governed by a nuclear gene with two alleles. TheWHITE (W) allele is dominant over brown (w) allele. If a plant with brown seeds (ww) is crossed as a female with pollen from a white seed (WW) plant, what will be the seed colour and the genotype of the embryo in the resultant seeds obtained from this cross? A. Brown seeds with Ww embryo B. White seeds with Ww embryo C. Brown seeds with ww embryo D. White seeds with ww embryo 4. During the CoVID-19 pandemic, SARS-CoV2 virus mutated multiple times giving rise to many variants. What is the genetic material of the SARS-CoV2 virus? A. Single stranded RNA B. Double stranded RNA C. Single stranded DNA D. Double stranded DNA 5. Lymph is an important body fluid. Choose the INCORRECT statement about the lymph. A. It remains as an interstitial fluid and is never put back into circulation. B. It is the interstitial fluid generated by the passage of liquid between the cells of the capillary. C. It is colourless and has similar mineral composition as of plasma. D. Fat digested in the intestine is absorbed through the lymph. 6. Interneurons play an important role in the execution of spinal cord-mediated reflex action. Where are these interneurons located? A. Gray matter B. White matter C. Dorsal root ganglion D. Muscle spindle 7. Osmoreceptors are sensitive to changes in ionic concentrations and volumes of body fluids. Which among the following best describes the function of these osmoreceptors? A. They stimulate hypothalamus to facilitate the release of the anti-diuretic hormone and increase water reabsorption. B. They stimulate pituitary gland to facilitate the secretion of mineralocorticoids to adjust the changes in mineral composition of the body fluid. C. They stimulate atrial wall to release atrial natriuretic factor to induce vasodilation and reduce blood pressure. D. They stimulate renin production to induce vasoconstriction and increase blood pressure. 8. A single point mutation in gene ‘X’ results in breathing difficulty, hypertension as well as partial sterility. Which among the following phenomenon best explains the observed phenotypes? A. Pleiotropy B. Incomplete dominance C. Linkage D. Partial dominance Page 2 9. In a cross between individuals of the genotypes PpQQRrSS and ppqqRrSS, what will be the expected number of progenies with the genotype ppQQRrSS in a population of 400 individuals, assuming independent assortment? A. 0 B. 100 C. 200 D. 25 10. Organisms in which of the following phyla are triploblastic, acoelomate and have bilateral symmetry? A. Platyhelminthes B. Mollusca C. Arthropoda D. Hemichordata 11. Consider the following biomes: Tropical Rainforest (P); Tundra (Q); Desert (R) and Coastal zone (S). Choose the most probable descending order of Net Primary Productivity of these biomes. A. P > S > Q > R B. P > Q > S > R C. Q > P > S > R D. R > Q > S > P 12. Nine percent of a population cannot taste a certain food item because of a recessive allele of the gene IAT. Assuming the population is in Hardy-Weinberg equilibrium, what will be the frequency of dominant and recessive alleles, respectively? A. 0.7 and 0.3 B. 0.9 and 0.1 C. 0.3 and 0.7 D. 0.1 and 0.9 13. As opposed to DNA replication within the cell, discontinuous synthesis of DNA does NOT occur in a polymerase chain reaction (PCR). Why? A. Denaturation step in PCR substitutes for the replication fork and Taq polymerase extends DNA only in the 5′ to 3′ direction. B. The replication fork is formed and Taq polymerase extends DNA in both 3′ to 5′ and 5′ to 3′ direction. C. Denaturation step in PCR substitutes for the replication fork and Taq polymerase extends DNA only in the 3′ to 5′ direction. D. The replication fork is formed and DNA ligase activity of the Taq polymerase joins the discontinuous fragments. 14. Which of the following figures CORRECTLY represents the chemiosmotic hypothesis of ATP syn- thesis occuring in a mitochondrion in a cell? (Keys for the figure; IMS: Intermembrane space, IMM: Inner mitochondrial membrane, MM: Mitochondrial matrix, ETC: Electron transport chain) Page 3 A. B. C. D. 15. Let ‘X’ be the perpendicular distance from the centromere of each chromosome to the equatorial plane of a human cell. Which of the following stages of the cell cycle is most likely to have the HIGHEST average value of ‘X’ ? A. Late anaphase B. Metaphase C. Early anaphase D. Early metaphase Page 4 IISER Aptitude Test 2022 Chemistry 1 1. The products of the reaction between aqueous solutions of K4 [Fe(CN)6 ] and 2 H2 O2 are A. K3 [Fe(CN)6 ] and KOH B. K3 [Fe(CN)6 ] and H2 O C. K3 [Fe(CN)6 ], H2 O and O2 D. K4 [Fe(CN)5 (OH)] and HCN 2. For the colourless complex [M(H2 O)6 ]n+ , where M is a 3d transition metal, the CORRECT ground state d-electron configuration of M is A. (t2g )6 (eg )4 B. (t2g )3 (eg )0 C. (t2g )6 (eg )2 D. (t2g )4 (eg )2 3. Choose the correct statement about the structure of C60 fullerene. A. 5-membered rings are fused with 6-membered rings ONLY. B. 6-membered rings are fused with 5-membered rings ONLY. C. 6-membered rings are fused with 6-membered rings ONLY. D. 5-membered rings are fused with both 5-membered and 6-membered rings. 4. The first to fifth ionization energies (IE) of two p-block elements X and Y are given below. IE1 (eV) IE2 (eV) IE3 (eV) IE4 (eV) IE5 (eV) X 6.0 18.8 28.4 120.0 153.7 Y 8.2 16.3 33.5 45.1 166.7 The number of valence electrons in X and Y respectively are A. 3, 4 B. 4, 5 C. 3, 5 D. 1, 4 5. Which of the following expressions represents the hydrogen atom wave function ψ(r) shown in the figure below? (r is the distance of the electron from the nucleus and a0 is a constant) 3/2 1 1 r A. √ 2− e−r/2a0 4 2π a0 a0 3/2 1 1 B. √ e−r/2a0 π a0 3/2 1 1 r C. √ e−r/2a0 6π a0 a0 3/2 2r 2r2 1 1 D. √ 3− + 2 e−r/3a0 3π a 0 a0 9a0 6. Which of the following molecules are aromatic? A. M, N and O only B. M, N, O, and P C. M and O only D. N and P only Page 2 7. Which of the following are aryl bromides? A. N and P only B. N, O and P only C. M, O and P only D. N and O only 8. Benzamide is treated with Br2 and NaOH(aq) to form the product X, which is then reacted with NaNO2 and HCl(aq) at 0 − 5 ◦ C to form Y. Y is immediately treated with ethanol to give Z. What is Z? A. B. C. D. Page 3 9. In the following reaction sequence, the major products M, N, and O respectively are A. B. C. D. Page 4 10. The major product P of the following reaction is A. B. C. D. 11. An aqueous solution contains 1.0 M of X2+ and 0.001 M of Y2+ ions at 25 ◦ C. X2+ and Y2+ ions do not interact with each other. This solution is put in an electrolytic cell and the voltage is gradually increased till a current begins to flow through the cell. The voltage is maintained at this point and a deposit is observed on the cathode. What is the composition of the material deposited on the cathode? (Given: Atomic weight of X is 63 and Y is 200. X2+ + 2e− → X, E 0 = 0.35 V, Y2+ + 2e− →Y, E 0 = 0.40 V, E 0 is the standard reduction potential.) A. Only X B. 24% X and 76% Y by weight C. 98% X and 2% Y by weight D. Only Y Page 5 12. For the reaction involving ideal gases, A(g) + 2B(g) ⇋ 2C(g) + 3D(g), which of the following plots is qualitatively correct? (Kp and Kc are the equilibrium constants in terms of pressure and concentration respectively. T is the absolute temperature.) A. B. C. D. a 13. The van der Waals equation for a real gas is given by P + 2 (V − b) = RT. What is the dimension a V of ? b A. ML2 T−2 B. ML−1 T−2 C. MLT−2 D. ML2 T−1 14. 2 g of naphthoic acid (molecular weight = 172 g mol−1 ) dissolved in 20 mL of benzene shows a freezing point depression of 2 K. For benzene, the freezing point depression constant, Kf = 5 K kg mol−1 and the density is 0.88 g mL−1. What is the magnitude of the van’t Hoff factor? A. 0.605 B. 605.0 C. 0.688 Page 6 D. 688.0 15. Identify the correct order of the molecules with respect to the magnitude of their dipole moment: A. B. C. D. Page 7 1. A randomly chosen card from a deck of 52 cards is given to be a black card (i.e. Spade or Club). What is the probability that it is either a face card (i.e. King, Queen or Jack) or a Spade? A. 8/13 B. 9/13 C. 19/26 D. 7/13 2. Let ω be a complex root of the quadratic polynomial x2 + x + 1. The value of 1 2 1 1 ω+ · ω + 2 · · · ω 100 + 100 ω ω ω is A. -233 B. -231 C. 233 D. 231 3. Let f (x) = an xn + an−1 xn−1 + · · · + a1 x + a0 be a polynomial. Suppose that d2 f d3 f d5 f df f (0) = 0, = 1, = 4 and =. dx x=0 dx2 x=0 dx3 dx5 Then f (5) = A. 55 B. 25 C. 35 D. 105 4. Let S be the set of all unit vectors in the XY -plane. Then the set S has A. Infinitely many elements B. 2 elements C. 4 elements D. 8 elements 5. A lab reports that the global average temperature in the year 2020 was 14.9◦ C and predicts that the global average temperature will increase at the rate of 1% per year. What will be the global average temperature in the year 2035? A. 17.298◦ C B. 15.049◦ C C. 17.135◦ C D. 17.471◦ C 6. Let X be the set of all 2 × 2 matrices with real entries and R ⊂ X × X be the relation R = {(A, B) : AB = BA}. Which of the following statements is true? A. R is reflexive and symmetric but not transitive B. R is reflexive and transitive but not symmetric C. R is symmetric and transitive but not reflexive D. R is an equivalance relation 7. For a natural number n, let Cn be the curve in the XY -plane given by y = xn , where 0 ≤ x ≤ 1. Let An denote the area of the region bounded between Cn and Cn+1. Then the largest value of An is 1 A. 6 1 B. 2 1 C. 3 1 D. 12 R1 8. Let f be a continuous function on [0, 1] and F be its antiderivative. If F (0) = 1 and 0 f (x) dx = 1, then F (1) is A. 2 B. 0 C. 1 1 D. 2 9. Let a be a nonzero real number and f : R → R be a continuous function such that f 0 (x) > 0 for all x ∈ R. Consider g(x) = f (2a2 x − ax2 ). Then g has A. Local maxima at x = a if a > 0 B. Local maxima at x = a if a < 0 C. Local minima at x = a if a > 0 D. A point of inflection at x = a 10. Let A be the matrix   cos θ 0 − sin θ  1 1 1 . sin θ 0 cos θ For any natural number k, the determinant of Ak is A. 1 B. -1 C. (−1)k Page 2 D. 0 11. Consider the vectors ~a = î + xĵ + 2k̂, ~b = î + 2ĵ + xk̂, ~c = 2î + ĵ + 3k̂. The values of x for which there is at least one nonzero vector perpendicular to the vectors ~a, ~b and ~c are A. 0, 2 B. -2, 2 C. 7/2, 0 D. 4, -2 12. Consider the tangent lines to the circle x2 + y 2 = 1 at points P = (1, 0) and Q = ( √12 , √12 ). If R is the point of intersection of these two tangent lines, then ∠P RQ is: 3π A. 4 π B. 4 5π C. 6 π D. 6 13. The function given by f (x) = 2x3 − 15x2 + 36x − 5 is A. Increasing on the interval (0, 2) B. Decreasing on the interval (−3, 0) C. Increasing on the interval (2, 3) D. Decreasing on the interval (3, ∞) 14. The value of the integral Z 100 [x] dx, 1 x where [x] is the greatest integer less than or equal to x for any real number x, is 10099 A. log 99! 10099 B. log 98! 10098 C. log 99! 10098 D. log 98! 15. For arbitrary constants α, β , the differential equation representing the family of curves y = (αx+β)ex is Page 3 A. y 00 − 2y 0 + y = 0 B. y 00 − y 0 + y = 0 C. y 00 − 2y 0 − y = 0 D. y 00 − y 0 − y = 0 Page 4 Physics: Set A 1. A particle experiences an acceleration ⃗a = α⃗v , where ⃗v is the velocity of the particle and α is a constant. If the distances traveled by the particle in the time intervals t2 − t1 and t3 − t1 are S12 and S13 , respectively, which of the following relations is true? S13 exp[α(t3 − t1 )] − 1 A. = S12 exp[α(t2 − t1 )] − 1 S13 exp[α(t3 − t1 )] B. = S12 exp[α(t2 − t1 )] S13 log[α(t3 − t1 )] C. = S12 log[α(t2 − t1 )] S13 log[α(t3 − t1 )] − 1 D. = S12 log[α(t2 − t1 )] − 1 2. A point mass m attached to a massless string is undergoing circular motion in a vertical plane. The length of the string is R and the acceleration due to gravity is g. If the minimum value of the tension in the string is 2mg, the maximum speed of this circular motion of the point mass is √ A. 7gR. r 7gR B.. 2 √ C. 6gR. √ D. 4 gR. Page 2 3. An object is released from rest from the inner edge of a hemispherical bowl, and it falls under gravity. The coefficient of kinetic friction between the object and the bowl is µ. If the object covers an angular displacement θ with respect to the center of the hemisphere when it stops for the first time, which of the following expressions is correct? A. µ = cot(θ/2) B. µ = cot(θ) C. µ = tan(θ) D. µ = tan(θ/2) Page 3 4. As shown in the figure a block is resting on a frictionless floor and is attached to the free end of a spring. The right edge of the block in equilibrium is at a distance d from the wall. When the spring is compressed by a distance d/2 and released, the time-period of the motion is T. Similarly, when compressed by a distance 2d and released, the time-period is T0. Considering elastic collision between the block and the wall, what is the value of the quantity T0 /T ? d A. 2/3 B. 1 C. 3/4 D. 1/4 Page 4 5. A liquid of density ρ in a container weighs W. A cubic block of side L and density ρb < ρ is pushed by a stick to completely submerge the block in the liquid without touching the bottom. If g is the acceleration due to the gravity and liquid displaced by the stick is negligible, what is the new weight of the container as registered by the weighing machine below? A. W + ρgL3 B. W + ρb gL3 C. W + (ρ − ρb )gL3 D. W + (ρb − ρ)gL3 Page 5 6. A monoatomic ideal gas at pressure P and volume V is first adiabatically compressed V to volume and then is allowed to expand isothermally back to its original volume. 8 What is the final pressure of the gas? A. 4P B. 2P C. P P D. 2 Page 6 7. A uniform taut string with two point charges q and −q attached to its ends passes over two massless pullies kept L distance apart as shown in the figure. If f is the fundamental frequency of the part of the string over pullies, which of the following statements is correct? A. f ∝ L−2 B. f ∝ L−1 C. f ∝ L D. f ∝ L2 Page 7 8. Two uniformly charged concentric thin spherical shells of radii r1 and r2 have charges +Q and −Q, respectively. How does the electrostatic potential vary with distance from the center of the shells? A. C. B. D. Page 8 9. Consider a very long cylinder of radius a having a uniform positive charge density ρ. A sphere of radius a has been carved out (see figure), leaving no charge in that region. The distance radially outward to the cylinder, as measured from the center of the sphere is x. At what value of x will the electric field be maximum? 4 A. a 3 2 B. a 3 3 C. a 2 D. a Page 9 10. In the given circuit, the box B either contains a capacitor, or an inductor or a resistor. The current I versus time t plots for three cases (a1 , a2 , a3 ) are shown in figures. The switch S is closed at time t = 0. Which of the following is correct? B R A S I a1 I a2 I a3 0 t 0 t 0 t A. a1 corresponds to a resistor, a2 corresponds to a capacitor, a3 corresponds to an inductor. B. a1 corresponds to a resistor, a2 corresponds to an inductor, a3 corresponds to a capacitor. C. a1 corresponds to an inductor, a2 corresponds to a resistor, a3 corresponds to a capacitor. D. a1 corresponds to an inductor, a2 corresponds to a capacitor, a3 corresponds to a resistor. Page 10 11. In the given circuit each of the resistors is of 1 kΩ resistance and each of the capacitors has 4 µF capacitance. What is the charge in the capacitor between the points B and F? F G B C E H A D 5V A. 10 µC B. 15 µC 40 C. µC 7 60 D. µC 7 Page 11 12. A thin lens made of material of refractive index nl forms the image at the position I of a point object held at O on the central axis of the lens, as is shown in the ray diagram below. Consider that the refractive index of the medium is nm and nl > nm for the figure given. Where does the image form when nl < nm ? A O B C I D A. At point B B. At point A C. At point C D. At point D Page 12 13. A conducting sphere of radius a initially contains a uniform volume charge density ρ. What is the electric flux Φ through a spherical surface of radius 2a centered at a point on the surface of the charged sphere (see figure) at a later time t? (ϵ0 is the permittivity of free space.) 4 A. Φ = πa3 ρ 3ϵ0 32 3 B. Φ = πa ρ 3ϵ0 16 C. Φ = πa2 ρ ϵ0 4 D. Φ = πa2 ρ ϵ0 Page 13 14. The figures in the options show the photocurrent J of a photoelectric material versus the frequency f of an incident light beam. The light beam can have three different intensities I1 , I2 , I3 , with I3 > I2 > I1. Which of the options is correct? A. B. C. D. Page 14 15. Consider that in a fission of a single Plutonium (Pu239 ) atom 207 MeV energy is released. Assuming all atoms of Plutonium undergo fission, which of the following options is the closest estimate of the amount of Plutonium required for a 20,000 units of TNT explosion? (1 unit of TNT= 4.184 × 109 J, 1 eV= 1.6 × 10−19 J) A. 1 kg. B. 10 kg. C. 60.0 g. D. 0.5 kg. Page 15 IISER Aptitude Test 2021 Biology 1. Which one of the following epithelial cell types is commonly found in the inner surface of the fallopian tubes? A. Ciliated B. Columnar C. Squamous D. Cuboidal 2. Which of the following is not an asexual reproductive structure? A. Isogametes of Cladophora B. Conidia of Penicillium C. Zoospores of Chlamydomonas D. Gemmules in a sponge 3. Which one of the following is an example of palindromic DNA sequence? A. 50 GAATTC 30 30 CTTAAG 50 B. 50 GACTTC 30 30 CTGAAG 50 C. 50 GAAGTC 30 30 CTTCAG 50 D. 50 GACCAG 30 30 CTGGTC 50 4. Some individuals start sneezing when the pollen content is high in the air. Primarily which Ig isotype will these individuals produce as an immune response? A. IgE B. IgA C. IgM D. IgG1 5. Which of these factors is least likely to cause deviation from the Hardy-Weinberg equilibrium? A. Reduction in population size B. Mutation C. Gene flow D. Genetic drift 6. Motivated by the classic experiment by Frederick Griffith and the work of Avery, Macleod and McCarty to identify the transforming principle, a scientist redesigned and performed the experiment with S-strain and R-strain of Streptococcus pneumonae as summarized in the table below. Treatment Experimental Condition T1 S-strain (heat-killed) injected into mice T2 S-strain (heat-killed) + R-strain (live) together injected into mice T3 Nucleic acids isolated from S-strain (heat-killed) + R-strain (live), incubated with RNase, and injected into mice T4 Nucleic acids isolated from S-strain (heat-killed) + R-strain (live), incubated with DNase, and injected into mice T5 S-strain (live) injected into mice T6 R-strain (live) injected into mice From the options below, identify the outcomes of the treatments (T1 to T6) on the viability of the mice. A. T1: live, T2: die, T3: die, T4: live, T5: die, T6: live B. T1: live, T2: live, T3: die, T4: live, T5: live, T6: live C. T1: live, T2: die, T3: die, T4: die, T5: live, T6: die D. T1: live, T2: die, T3: live, T4: die, T5: die, T6: live 7. Which of the following is/are produced by a plant during photosynthesis with far-red light? A. Only ATP B. ATP, NADPH and H+ C. NADPH and H+ D. Only NADPH 8. The map of a 4000 base pair (bp) plasmid DNA marking the locations of different restriction enzyme cut sites is shown in the figure below. The numbers in brackets indicate the base pair positions where the enzymes cut. This plasmid is completely digested first with the combination of restriction enzymes PstI and HindIII, and then with EcoRI and SalI. The final digested plasmid is analyzed by agarose gel electrophoresis. Page 2 Which one of the following options correctly represents the bands sizes (in bp) obtained on the gel? A. 220, 540, 900 and 2340 B. 220, 540, 1200 and 2040 C. 540, 760, 1200 and 1500 D. 320, 540, 800 and 2340 9. The following plot represents the change in the rate of photosynthesis with leaf temperature for two plants, P1 and P2. Which one of the following statements correctly describes the characteristics of P1 and P2 plants? A. Plant P1 is a C3 plant having temperate adaptation whereas Plant P2 is a C4 plant with tropical adaptation Page 3 B. Plant P1 is a C4 plant having temperate adaptation whereas Plant P2 is a C3 plant with tropical adaptation C. Plant P1 is a C4 plant having tropical adaptation whereas Plant P2 is a C3 plant with temperate adaptation D. Plant P1 is a C3 plant having tropical adaptation whereas Plant P2 is a C4 plant with temperate adaptation 10. The figure (i) represents two categories of animals (X and Y) with respect to their response to the external environment. The figure (ii) represents two broad categories of animals (Type a and Type b) with respect to their body surface area to volume ratio. Which combination most suitably represents the following animals in the order: humming bird; crocodile; frog; polar bear? A. Xa; Yb; Ya; Xb B. Xb; Ya; Yb; Xa C. Ya; Yb; Xa; Xb D. Yb; Xb; Xa; Ya 11. In plants, ammonium ions are produced by protonation of ammonia. Which enzyme uses these ammonium ions to convert an alpha-keto acid into an amino acid? A. Glutamate dehydrogenase B. Nitrogenase C. Transacetylase D. Lactate dehydrogenase 12. Which one of the following physiological functions is common between the small intestine and the renal tubules? Page 4 A. Absorption of glucose B. Excretion of waste materials C. Excretion of water D. Absorption of proteins 13. Match the following pairs of interating species to the corresponding names of the interactions. Name of interacting species Name of interaction i Herbivores and Plants a Mutualism ii Cuckoo and Crow b Predation iii Sea anemone and Clown fish c Parasitism iv Fungus and Cyanobacteria (Lichens) d Commensalism Pick the correct option from below. A. i and b; ii and c; iii and d; iv and a B. i and c; ii and b; iii and d; iv and a C. i and b; ii and d; iii and c; iv and a D. i and b; ii and a; iii and c; iv and d 14. The following events are associated with meiosis: i) appearance of recombinant nodules ii) formation of meiotic spindle iii) formation of chiasmata iv) formation of synaptonemal complex Which of the following is the correct sequence of these events during meiosis? A. iv → i → iii → ii B. iii → iv → ii → i C. iv → iii → i → ii D. i → iii → iv → ii 15. Which of the following floral formulae represents a zygomorphic flower with diadelphous androecium and superior ovary? A. B. Page 5 C. D. Page 6 Chemistry 16. The F-P-Cl bond angles in the most stable structure of PF3 Cl2 are close to A. 90◦ and 120◦. B. 90◦ , 120◦ , and 180◦. C. 90◦ only. D. 90◦ and 180◦. 17. The correct statement about the bond angles and bond lengths in Al2 Cl6 is (Clt = terminal Cl; Clb = bridging Cl) A. ∠Clt –Al–Clt > ∠Clb –Al–Clb and Al–Clb > Al–Clt. B. ∠Clt –Al–Clt > ∠Clb –Al–Clb and Al–Clt > Al–Clb. C. ∠Clt –Al–Clt = ∠Clb –Al–Clb and Al–Clt > Al–Clb. D. ∠Clb –Al–Clb > ∠Clt –Al–Clt and Al–Clb > Al–Clt. 18. Among CH3 SiCl3 , (CH3 )2 SiCl2 and (CH3 )3 SiCl, which one is used to synthesize straight chain (linear) and which one is used to prepare branched chain (cross-linked) silicone polymer, respectively? A. (CH3 )2 SiCl2 and (CH3 )SiCl3 B. (CH3 )SiCl3 and (CH3 )2 SiCl2 C. (CH3 )2 SiCl2 and (CH3 )3 SiCl D. (CH3 )3 SiCl and (CH3 )2 SiCl2 19. Which one of the following statements is INCORRECT about a complex of a divalent ion with atomic number 25? (BM = Bohr Magneton) A. Complex with weak field ligands in tetrahedral geometry has a magnetic moment of 1.73 BM. B. Complex with weak field ligands in tetrahedral geometry has a magnetic moment of 5.92 BM. C. Complex with strong field ligands in octahedral geometry has a magnetic moment of 1.73 BM. D. Complex with weak field ligands in octahedral geometry has a magnetic moment of 5.92 BM. 20. Ni(CO)4 is diamagnetic because A. Ni has completely filled 3d orbitals. B. it is a square planar complex. C. CO is a strong field ligand. D. it has synergic bonding. Page 7 21. The correct order for the relative energies of the following sawhorse conformations is A. IV > III = II > I. B. IV > III > II > I. C. II ≈ III > IV > I. D. I > II = III > IV. 22. Among the haloarenes (I–IV) shown below, the correct order of reactivity for the substitution reaction with NaOH is A. II > III ≈ I > IV. B. I > IV > III > II. C. II > III > IV > I. D. IV > I ≈ III > II. 23. Consider the following reaction sequence, and identify the correct statements: (i) The products P and R can form addition product with HCN. (ii) The product Q has no chiral center. (iii) The product R can undergo Cannizzaro reaction. (iv) The product S is a saturated hydrocarbon. A. (i) and (iv) B. (iii) and (iv) C. (i) and (ii) Page 8 D. (ii) and (iii) 24. The major product of the reaction of salicylaldehyde with one equivalent of MeMgBr, followed by acid neutralization is A. II. B. I. C. IV. D. III. 25. The total number of stereoisomers possible for the following structure is A. 8. B. 4. C. 2. D. 6. 26. For a homogeneous reaction involving ideal gases, equilibrium constants at 27 ◦ C are Kp = 9.98 × 1027 and Kc = 4.0 × 1024. If the enthalpy change of the reaction is −18.4 kJmol−1 , the internal energy change is [Use R= 8.314 JK−1 mol−1 ] A. −20.89 kJmol−1. B. −15.91 kJmol−1. C. −13.41 kJmol−1. D. −23.39 kJmol−1. 27. The probability density of an electron in 1s orbital for an H atom is maximum A. at the nucleus. B. at the Bohr radius. C. at twice the Bohr radius. D. at infinite distance. 28. Which of the following statements is INCORRECT? A. Half-life of a zero order reaction is proportional to the rate constant. Page 9 B. Half-life of a zero order reaction is proportional to the initial concentration of reactant. C. Half-life of a first order reaction is independent of the initial concentration of reactant. D. Half-life of a first order reaction is inversely proportional to the rate constant. 29. The time required for reducing 1 mole of MnO4 − (aq.) to Mn2+ (aq.) when a current of 2.5 A is passed during electrolysis is A. 53.6 hours. B. 12.9 microeconds. C. 10.7 hours. D. 64.8 microseconds. 30. Based on the relative stabilities and barriers, which among the following schematic energy diagrams would best correspond to the reaction scheme shown below? [k and k 0 are similar in magnitude] A. B. Page 10 C. D. Page 11 Mathematics 31. What is the maximum value of cos4 (x) + sin2 (x) + cos(x), when x ≥ 0? A. 2 B. 1 √ C. 2 √ D. 2 2 32. Out of a pack of ten cards numbered 1 to 10, a boy draws a card at random and keeps it back. Then a girl draws a card at random from the same pack. If the boy’s card reads m, and the girl’s card reads n, then what is the probability that m > n, given that m is even? 1 A. 2 1 B. 3 1 C. 4 1 D. 5 33. Suppose a, b ∈ R are such that the points (a, b), (a2 , b2 ), and (a3 , b3 ) in the coordinate plane are distinct, collinear, and the line passing through these points is not parallel to the y-axis. Then, for all such choices of (a, b), the slope of the line passing through these three points can take A. exactly two values. B. infinitely many values. C. exactly three values. D. exactly one value. 34. Define f : [2, 22] → R by f (x) = max{n(1 − |x − (2n + 1)|) : n = 1, 2,... , 10}. The area of the region {(x, y) : 0 ≤ y ≤ f (x), x ∈ [2, 22]} is A. 55. B. 60. C. 5. D. 10. √ 1 x 35. The value of the limit lim (sin x) (ex + x) x is x→0+ A. e2. B. 1. C. e. D. 0. Page 12 36. Let f : R → R be a continuous function satisfying Z x x2 /2 f (x) = e + tf (t)dt for all x. 0 Then which of the following is correct? √ A. 5 < f ( 2) < 6 √ B. 2 < f ( 2) < 3 √ C. 3 < f ( 2) < 4 √ D. 4 < f ( 2) < 5 37. For each a ∈ R, define a a pa (z) = z 2 + 2ea−e z + ea−e. Then, which one of the followings is true? A. pa has only non-real complex roots for all a ∈ R. B. pa has a real root for all a ∈ R. C. pa has a real root if and only if a ≥ 1. D. pa has a real root if and only if a ≤ −1. 38. The number of functions f : {1, 2, 3, 4, 5} −→ {1, 2, 3, 4, 5} such that f (f (n)) = n for all n ∈ {1, 2, 3, 4, 5}, is A. 41. B. 25. C. 31. D. 120. 39. Let P1 : x + y + z = 1, P2 : 2x + y + z = 3 be two planes, and let L denote the line of intersection of P1 and P2. Let P be the plane passing through the point (1, 2, 1), and normal to L. Which of the following equations represents P ? A. y − z = 1 B. x + z = 2 C. x + 2y + z = 6 D. x + y + 2z = 5 40. Let f (x) = ln(1 + x) for x ≥ 0. The value of π √ f ( 3 cos θ) Z 2 √ √ dθ 0 f ( 3 sin θ) + f ( 3 cos θ) is π A.. 4 Page 13 π B.. 6 π C.. 3 π D.. 2 41. The area enclosed by the curves y = 1 + | sin x|, y = −| sin x| and the lines x = 0, x = 2π is A. 8 + 2π. B. 8 + 4π. C. 8 + 6π. D. 8 + 8π. 42. Consider the function f : R → R defined by f (x) = x2 |x|. Then, which of the following statements is correct? A. f 0 is differentiable but f 00 is not differentiable. B. f is continuous but not differentiable. C. f is differentiable but f 0 is not differentiable. D. f 00 is differentiable. 43. Let A be a 2 × 2 matrix such that 2 0 1 0 0 A +A+ =. 1 0 0 0 Let I denote the 2 × 2 identity matrix. Which of the following statements is correct? A. Both A and A + I are invertible. B. A is invertible but A + I may not be invertible. C. A + I is invertible but A may not be invertible. D. Neither A + I nor A may be invertible. 44. If three real numbers a, b, c are in arithmetic progression, the value of the determinant x2 + 3 x2 + 4 x2 + 5 x2 + 4 x2 + 5 x2 + 6 x2 + a x2 + b x2 + c is A. 0. B. 2a. C. a + c − b. D. x2 + 2b. Page 14 45. Consider the two data sets S1 = {1, 2, 4, 8, 9, 11, 15, 20, 27, 29, 33}, S2 = {51, 52, 54, 58, 59, 61, 65, 70, 77, 79, 83}. Let m1 , m2 and v1 , v2 be the means and the variances of S1 and S2 , respectively. Then, which of the following relations is correct? A. m2 = m1 + 50, v2 = v1. B. m2 = m1 + 50, v2 = v1 + 50. C. m2 = m1 , v2 = v1. D. m2 = m1 + 50, v2 < v1. Page 15 Physics 46. A door of mass M and width L is hinged at one end and rotates about a vertical axis without friction. A bullet of mass m (m M ) fired perpendicularly to the door at a speed v gets embedded in it at a distance x from its axis of rotation. Assuming the door was stationary initially, how does the resultant angular speed ω of the door vary as a function of x? ω L x A. ω L x B. ω L x C. ω L L x D. 3 47. A body of mass m executes simple harmonic motion along a line with time period T and energy E. What is the magnitude of the maximum acceleration of the body? √ r 2 2π E A. T m r 2π E B. T m √ r 2 E C. T m r π E D. T m 48. An athlete runs on a straight track. She starts from rest and runs with a constant acceleration for the first 2 seconds, reaching a speed of 9 m s−1. She then continues at this constant speed for some time before slowing down to a halt at a constant deceleration. The total time taken, from start to Page 16 finish, is 12 seconds. If the magnitude of her acceleration is twice the magnitude of deceleration, then what is the total distance covered by her? A. 81 m B. 108 m C. 90 m D. 72 m 49. A capacitor of capacitance C consists of two large parallel metal plates. The coefficient of linear expansion of the metal is α. What is the change in capacitance if the temperature of the plates rises by ∆T , while the gap between the plates is kept fixed? A. 2α∆T C B. α∆T C C. −α∆T C D. −2α∆T C 50. What are the charges stored in the 2 µF and 4 µF capacitors in the given circuit a long time after the key K is closed? 4k 2k 2 µF 4 µF K 2k 4k 12 V A. 8 µC and 8 µC respectively B. 18 µC and 18 µC respectively 16 8 C. µC and µC respectively 3 3 8 16 D. µC and µC respectively 3 3 51. Consider a point charge +q moving with a constant velocity ~v = v k̂ in vacuum in the presence of an ~ = Ex î + Ey ĵ and a magnetic field B electric field E ~ = Bx î + By ĵ. Unit vectors î, ĵ, and k̂ are in the directions of x, y, and z axes, respectively. Which of the following relations is correct? A. Ex = v By , Ey = −v Bx B. Ex = −v Bx , Ey = −v By C. Ex = −v By , Ey = v Bx D. Ex = v Bx , Ey = v By Page 17 52. Four point charges q, −2q, −3q and 4q are placed at the four vertices of a regular tetrahedron of side L, while a charge 5q is placed at its center. What is the total electrostatic energy of the system? (Vacuum permittivity is denoted by ε0.) 15q 2 A. − 4πε0 L 15q 2 B. 4πε0 L 30q 2 C. − 4πε0 L 30q 2 D. 4πε0 L 53. The half life of a radioactive element is 2000 hours. Approximately how much time is required for the decay of 2/3 of its nuclei? A. 3170 hours B. 3000 hours C. 1170 hours D. 2830 hours 54. A 2-input exclusive OR (XOR) gate with inputs X and Y produces the output X̄Y + X Ȳ. In the Boolean circuit shown below, which values of the inputs P and Q will produce the output 0? XOR 1 P NAND AND 0 1 Q A. P = 0, Q = 1 B. P = 0, Q = 0 C. P = 1, Q = 0 D. P = 1, Q = 1 55. In an experiment on the photoelectric effect, the de Broglie wavelength of the emitted electron is λB. The energy of the photon incident on the metal is five times the work function. If h is Planck’s constant and me is the electron mass, then what is the work function? h2 A. 8me λ2B h2 B. 10me λ2B h2 C. 12me λ2B Page 18 h2 D. 4me λ2B 56. An ambulance traveling at a speed 20 m s−1 emits a sound of frequency 540 Hz from its siren. Sunanda is driving a car which approaches the ambulance from the opposite direction at a speed of 20 m s−1. What will be the change in detected frequency by Sunanda, as she crosses the ambulance? (Given, the speed of sound in air is 340 m s−1.) A. 127.5 Hz B. 128.8 Hz C. 135.5 Hz D. 72.00 Hz 57. Consider a Young’s double slit experiment with monochromatic light of wavelength 600 nm. The intensity of the light is I0 at a point on the screen where the path difference is 600 nm. What would be the intensity of light at a point on the screen where the path difference is 100 nm? 3 A. I0 4 1 B. I0 4 1 C. I0 2 √ 3 D. I0 2 58. Consider a mixture of O2 and N2 gases at temperature 27 ◦ C. Which of the following relations is correct? A. RMS speed of O2 molecules < RMS speed of N2 molecules B. Average kinetic energy of O2 molecules < Average kinetic energy of N2 molecules C. Average kinetic energy of O2 molecules > Average kinetic energy of N2 molecules D. RMS speed of O2 molecules > RMS speed of N2 molecules 59. Two identical objects A and B are at initial temperatures TA and TB (TA > TB ), respectively. The specific heat capacity of the material of these objects increases with temperature. If these two objects are brought in contact then their final equilibrium temperature is T. Assuming that there is no heat exchange with the surroundings, then TA + TB A. T >. 2 B. T > TA. TA + TB C. T =. 2 TA + TB D. T <. 2 60. Which one of the following expressions has the dimension of electrical resistance where e is the charge of an electron and h is Planck’s constant? Page 19 h A. e2 e2 B. h e C. h h D. e Page 20 IISER Aptitude Test 2019 Biology 1. Which of the following produces a dikaryotic phase in Basidiomycetes? A. Karyogamy B. Plasmogamy C. Apogamy D. Karyokinesis 2. In the standard nomenclature used for depicting floral formula, which type of flower is represented by K(5) ? A. Polysepalous B. Syncarpous C. Gamosepalous D. Gamopetalous 3. Which one of the following statements is TRUE? A. Blood is a connective tissue which does not secrete collagen B. Tendons are a type of dense, irregular connective tissue C. Adipose tissue is an example of a fluid connective tissue D. Saliva is secreted by an endocrine gland 4. Match the entries in column I and column II. Which one of the following choices is correct? Column I Column II (a) Haem (1) Cofactor (b) NAD (2) Vitamin (c) Zinc (3) Coenzyme (d) Niacin (4) Prosthetic group A. a-3, b-1, c-4, d-2 B. a-4, b-3, c-1, d-2 C. a-2, b-1, c-3, d-4 D. a-4, b-1, c-3, d-2 5. Which one of the following helps in bacterial motility? A. Centrioles B. Fimbriae C. Microtubules D. Flagella Page 1 IISER Aptitude Test 2019 6. During light reaction in chloroplasts of tobacco plants, where is the proton gradient generated? A. Between stroma and intermembrane space of chloroplasts B. Between thylakoid lumen and intermembrane space of chloroplasts C. Between stroma and thylakoid lumen D. Between inner and outer chloroplast membranes 7. Which of the following will NOT be triggered by the release of acetyl choline in the synapse at the neuromuscular junction during muscle contraction? A. Generation of an action potential in the muscles B. Release of Ca2+ from the sarcoplasmic reticulum C. Binding of ATP molecules to the myosin head D. Shifting of tropomyosin to expose the myosin binding sites on actin filaments 8. The diagram below shows a typical ECG. If the AV node is not functional, which of the following options correctly represents the changes seen in the ECG? A. P wave will sustain longer with smaller amplitude B. The QRS complex will be absent C. The T wave will sustain longer with smaller amplitude D. The distance between the P wave and the QRS complex will be smaller 9. Listed below are different plant reproductive strategies. I. Parthenocarpy II. Syngamy III. Apomixis IV. Polyembryony Which of them can give rise to a clonal progeny having the same genotype as that of the mother plant? A. III and IV B. I and II C. II and III D. I and IV Page 2 IISER Aptitude Test 2019 10. The diagram below represents the pedigree of a certain genetic disease (affected individuals are shaded). What is the mode of inheritance of the gene responsible for this disease? A. X-linked recessive B. Y-linked C. X-linked dominant D. Mitochondrial 11. An E. coli whose DNA is fully labeled by 15 N is grown in a medium containing 14 NH4 Cl. What will be the percentage of hybrid (15 N/14 N) and light (14 N/14 N) DNA molecules at the end of 80 minutes (assume that doubling time of E. coli is 20 minutes)? A. 25% hybrid and 75% light B. 50% hybrid and 50% light C. 0% hybrid and 100% light D. 12.5% hybrid and 87.5% light 12. The following plots represent the body size distributions of a fruit fly population. Dashed lines represent the ancestral distributions and continuous lines represent the distributions after a few generations. If the larger individuals have better survival as well as higher reproductive rates, which diagram below best represents the expected change in the distribution of body size (X-axis represents body size while Y-axis represents frequency)? A. B. C. Page 3 IISER Aptitude Test 2019 D. 13. What are the types of immunity acquired by i) transfer of antibodies to the foetus via the placenta and ii) vaccination of an infant? A. Both are active immunity B. Both are passive immunity C. Active and passive immunity, respectively D. Passive and active immunity, respectively 14. Which among the following correctly represents the sequence of events for a normal polymerase chain reaction? A. Denaturation, annealing, extension B. Annealing, denaturation, extension C. Extension, annealing, denaturation D. Denaturation, extension, annealing 15. Loss of biodiversity occurs due to the growth of carrot grass (Parthenium sp.). This is an example of? A. Alien-species invasion B. Co-extinction C. Over-exploitation D. Habitat loss and fragmentation Page 4 IISER Aptitude Test 2019 Chemistry 16. What are the correct orders of bond lengths dX−X and bond dissociation enthalpies BDEX−X for F2 and Cl2 ? (where X = F or Cl) A. dF −F < dCl−Cl and BDEF −F < BDECl−Cl B. dF −F > dCl−Cl and BDEF −F > BDECl−Cl C. dF −F < dCl−Cl and BDEF −F > BDECl−Cl D. dF −F > dCl−Cl and BDEF −F < BDECl−Cl 17. Which is the appropriate combination of spin configuration and colour for the anionic complex [Co(L)6 ]3− (L is a monodentate and monoanionic ligand)? A. high-spin and green B. low-spin and green C. low-spin and blue D. high-spin and yellow 18. Which of the following combination of elements forms interstitial hydrides? A. Na and Mg B. Yb and Ti C. Fe and Mn D. B and Al 19. How many geometrical isomers are possible for the square planar complex [Pd(py)(Cl)(Br)(NH3 )] (py = pyridine)? A. 2 B. 4 C. 5 D. 3 20. A molecular adduct is formed between BF3 and Et2 O. Which of the following values describe the coordination number (CN), valency (V) and oxidation state (OS) of B atom in this adduct? A. CN = 4, V = 4 and OS = +3 B. CN = 4, V = 3 and OS = +4 C. CN = 4, V = 3 and OS = +3 D. CN = 3, V = 3 and OS = +4 Page 5 IISER Aptitude Test 2019 21. While making paneer (cottage cheese) from milk by adding dilute acetic acid, the milk proteins undergo A. solubilization B. degradation C. denaturation D. polymerization 22. What is the final major product of the following reaction? A. B. C. D. 23. Identify the final major product in the following reaction sequence. A. B. C. D. Page 6 IISER Aptitude Test 2019 24. Identify the compound [X] in the following reaction. A. CH3 COOH B. OHC-CHO C. CH3 CH2 OCH2 CH2 Cl D. CH3 CHO 25. Which one among the following compounds is aromatic? A. B. C. D. 26. Using the Arrhenius equation, find out the value of k at T→ ∞? A. A B. -A C. eA D. e−A 27. Which one of the following is NOT an example of heterogeneous equilibrium? A. Equilibrium between water vapour and liquid water in a closed container B. Equilibrium attained during acid catalysed hydrolysis of ethyl acetate C. Equilibrium between solid Ca(OH)2 and its saturated solution D. Equilibrium attained on heating solid CaCO3 in a closed container 28. At 60 ◦ C, 50% of N2 O4 (g) is dissociated to NO2 (g). What is the standard Gibbs free energy change at 60 ◦ C and 1 atm pressure for this process? (R = 8.314 JK−1 mol−1 ) A. 763 Jmol−1 B. -790 Jmol−1 C. -863 Jmol−1 D. 500 Jmol−1 Page 7 IISER Aptitude Test 2019 29. For a cell Ag|Ag+ ,Cl− |AgCl(s)|Ag, E◦Red for the half cells are given as: E◦Ag+ |Ag = 0.79 V, E◦Cl− |AgCl(s)|Ag = 0.22 V at 25 ◦ C. What is the value of lnK, where K is the equilibrium constant for the reaction AgCl(s) ! Ag + + Cl− ? Given, 1 F = 96485 C. A. -22.2 B. -18.5 C. -29.3 D. -26.8 30. Match the following: i) Ge doped with In 1. n-type semiconductor ii) Si doped with N 2. Schottky defect iii) ZnS 3. p-type semiconductor iv) CsCl 4. Frenkel defect A. i−1, ii−3, iii−2, iv−4 B. i−1, ii−3, iii−4, iv−2 C. i−3, ii−1, iii−2, iv−4 D. i−3, ii−1, iii−4, iv−2 Page 8 IISER Aptitude Test 2019 Mathematics 31. Let 1, ζ2 , ζ3 ,... , ζn be the roots of the equation xn = 1, for n ≥ 3. Then, the sum 1 1 1 + + ··· + 2 − ζ2 2 − ζ3 2 − ζn equals to A. 1+(n−2)2n 2n −1. B. 1+n2n−1 −2n 2n −1. C. 1+n2n−1 −2n 2n−1 +1. D. 1+(n−1)2n −2n−1 2n−1 +1. 32. How many solutions does the equation sin2 x − 15 sin x cos x + 50 cos2 x = 0 have in the interval [0, 2π]? A. 4. B. 0. C. 1. D. 2. 33. Let A be a 4 × 4 matrix with real entries. Consider the sets         x1 x1 0         x x   : A  =   , 2 2 0 K = x 3  x 3  0       x4 x4 0          c 1 c 1 y 1          c c y J =  2  2 : c 3  c 3  = A  2 y 3  , for some y , y , 1 2 3 4y , y ∈ R.       c4 c4 y4 Suppose K = J. Then, which one of the following statements is necessarily true? A. A2 = 0. B. A is symmetric. C. A is skew symmetric. D. A2 = A. Page 9 IISER Aptitude Test 2019 34. Consider 5 straight lines in a plane such that no two of them are parallel and no three of them intersect at a point. Then, the number of disjoint regions into which the plane is divided by these lines equals to A. 17. B. 18. C. 16. D. 20. 35. Consider the circle C that passes through the points (1, 0) and (0, 1) having the smallest area. Then, the equation of the tangent to the circle C at (0, 1) is A. y = −x + 1. B. y = x − 1. C. y = x. D. y = x + 1. 36. Let f : [−1, 1] → R be a continuous function. Consider the region. / S = (x, y) : −1 ≤ x ≤ 1 and 0 ≤ y ≤ f (x). For which one of the following functions f , the area of the region S is the largest? A. f (x) = π x | sin πx|. B. f (x) = π x | cos πx|. 0 1 12 C. f (x) = π x 1 + 1tan πx 1. 10 D. f (x) = πx |x|+1. 37. Let f : R → R be a continuous function. Then, f is surjective if A. lim f (x) = ∞ and lim f (x) = ∞. x→∞ x→−∞ B. lim f (x) = 0 and lim f (x) = ∞. x→∞ x→−∞ C. lim f (x) = 0 and lim f (x) = −∞. x→∞ x→−∞ D. lim f (x) = −∞ and lim f (x) = ∞. x→∞ x→−∞ 3 n 38. The limit lim 1 n2020 k 2019 n→∞ k=1 A. is 1 2018. B. is 1 2020. C. is 1 2019. D. does not exist. Page 10 IISER Aptitude Test 2019 39. The sum of n consecutive terms of an arithmetic progression consisting of integers is 161. Then, a possible value of n is A. 5. B. 7. C. 6. D. 8. 40. Let f : R → R be a non-zero even function such that 4 1 f (x)dx = α. −1 Then, the value of the integral 4 1 f (x) dx −1 1 + ex is A. α. B. αe−α. C. α 2. D. e−α 2. 41. What is the mean deviation about the mean for the following data? xi 1 2 3 4 fi 5 10 15 20 A. 4 5. B. 3 5. C. 2 5. D. 1. 42. Let S be a non-empty set such that the total number of subsets of S containing at most two elements is equal to 16. Then, the number of elements in S equals to A. 5. B. 6. C. 16. D. 7. Page 11 IISER Aptitude Test 2019 43. Consider the parallelogram ABCD as shown in the figure, where AE AB = CF CD = n1 , for some positive integer n. D F C X Y A E B Suppose the length of AC is a, then the length of XY is A. a n. B. na n+1. C. (n−1)a n+1. D. (n−1)a n. 44. Let 5i, 5 j and 5 k denote the standard unit vectors in R3 along the x-axis, y-axis and z-axis, respectively. Consider the sets 6 7 X = ai + bj + ck : a, b, c ∈ {−1, 0, 1} and 5 5 5 Y = {($v1 , $v2 , $v3 ) : $v1 , $v2 , $v3 ∈ X and $v1 , $v2 , $v3 are mutually perpendicular unit vectors}. Then, the number of elements in Y is A. 27. B. 24. C. 36. D. 48. 45. What is the probability that 3 randomly chosen elements x, y, z from the set {1, 2,... , 10} satisfy x + y + z = 5? A. 3 1000. B. 1 200. C. 1 1000. D. 3 500. Page 12 IISER Aptitude Test 2019 Physics 46. A particle of mass m is rotating in a circular orbit of radius r under the action of gravity in the presence of another stationary particle of very large mass M (M ( m). Consider that the gravitational potential energy is zero at infinite separation. If the total energy of the rotating particle is E, then, which of the following expressions correctly represents the angular momentum of the particle? √ A. r 2Em √ B. r −2Em 8 C. r −Em/2 8 D. r Em/2 47. A point electric charge Q is placed at a corner of a cube as shown in the figure. What is the electric flux passing through the shaded surface ABCD of the cube? (%◦ is permittivity of free space) Q A. 18%◦ Q B. 12%◦ Q C. 6%◦ Q D. 24%◦ 48. Neutral gas molecules, each of mass m, are at a temperature T in a container at zero gravity. How does the average de Broglie wavelength λ of a molecule depend on T ? √ A. λ ∝ T B. λ ∝ 1/T 2 3 √ C. λ ∝ 1/ T D. λ ∝ T 2 3 Page 13 IISER Aptitude Test 2019 49. Consider a particle of unit mass being thrown with an initial velocity v◦ making an angle φ with the horizontal ground. What is the magnitude of the angular momentum of the particle about the point of projection at a time t after its projection while it is in flight? A. 2gt2 v◦ cos φ B. 1 2 2 gt v◦ cos φ C. 2gt2 v◦ sin φ D. 1 2 2 gt v◦ sin φ 50. Consider two long thin conductors A and B each carrying cur

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