Q.60 In an enzyme catalyzed first-order reaction, the substrate conversion follows an exponential pattern such that 80 % of the substrate is converted in 10 minutes. The first-order rate constant (in min-1) of the reaction, rounded off to THREE decimal places, is __________.

 Enzyme Catalyzed First-Order Reaction

Q.59 At a given time t, velocity (v) and acceleration (a) of a particle undergoing simple harmonic motion are given by v(t) = -100 sin(20t + π/3), a(t) = -2000 cos(20t + π/3). Assuming all quantities are in SI units, the amplitude of the oscillation is ________.

Amplitude of SHM from Velocity and Acceleration Equations

Q.58 Energy of the electron in hydrogen atom in its ground state is 13.6 eV. The energy required (in eV) to move the electron from its ground state to the first excited state, rounded off to TWO decimal places, is ________.

Energy Required to Move Electron from Ground State to First Excited State

Q.57 One point charge (q) each, is placed along a line at 3 different points x = 0, x = 2 nm and x = 6 nm. The force between two charges separated by 2 nm is 2 piconewton (pN). The magnitude of force (in pN) on the charge in the middle due to the other two charges is ________.

Force on Middle Charge

Q.56 A bouncing ball is dropped from an initial height of h meters above a flat surface. Each time the ball hits the surface, it rebounds a distance r × h meters and it bounces indefinitely. Consider the value of h = 5 meters and r = 1/3. The total vertical distance (up and down) travelled (in meters) by the ball is ______.

Bouncing Ball Total Vertical Distance

Q.55 The average value of function f(x) = 9 - ₓ² on [-3, 3], rounded off to TWO decimal places, is ________.

Average Value of f(x)=√(9−x²) on [-3,3]

Q.54 limₓ→₀ (ₓ² - 4ₓ) / (ₓ) The solution to the above limit is ________.

Limit \(\lim_{x\to 0}\frac{2-\sqrt{4-x}}{x}\)

Q.53 The length of transverse and conjugate axis in a hyperbola are 6 and 8, respectively. The eccentricity of the hyperbola, rounded off to TWO decimal places, is ________.

Hyperbola Eccentricity with Transverse Axis 6 and Conjugate Axis 8

Q.52 The vibrational frequency (expressed in wavenumber) of ¹H³⁵Cl is 2990.6 cm⁻¹. Assuming that the force constant is same in both the cases, vibrational frequency (in cm⁻¹) of ²D³⁵Cl is ________.

Vibrational Frequency of 2D35Cl from 1H35Cl

Q.51 A variable number of tandem repeats (VNTR) locus has 15 different alleles. The number of genotypes possible in a population for this VNTR is ________.

VNTR Locus 15 Alleles

Q.50 The median of Y in the following data is ________. Serial number 1 2 3 4 5 6 Y 22 12 10 14 16 20

Median of Y in the Data Set 22, 12, 10, 14, 16, 20

Q.49 The decimal reduction time (DRT or D value) of a bacterial culture is one minute. If a suspension of the bacterial culture contains an initial population of 10^6 cells, then the time (in minutes) required to reduce the number of bacteria to 10 by heat treatment is ________.

Decimal Reduction Time DRT D Value Bacterial Culture Calculation

Q.48 A compound microscope has its objective with linear magnification of 10. In order to achieve a final magnification of 100, the angular magnification of the eyepiece should be ________.

Compound Microscope Magnification

Q.47 The volume (in mL) required to prepare 350 mL of 1X buffer solution from a fifty times (50X) concentrated buffer stock solution is ________.

Volume Required for 50X to 1X Buffer Dilution

Q.46 In the following reaction, the values of ∆H and ∆S at temperature 25 oC are −13.7 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙𝑒 and −16.0 𝑐𝑎𝑙/(𝐾 ∙ 𝑚𝑜𝑙𝑒), respectively. Cd2+ + 4CH3NH2 → Cd(CH3NH2)42+ The value of ∆G (in 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙𝑒) of the reaction, rounded off to TWO decimal places, is ________.

Gibbs Free Energy Calculation for Cd²⁺ + 4CH₃NH₂ → Cd(CH₃NH₂)₄²⁺ at 25 °C

Q.45 Consider two particles, each of mass 20 g; the first particle is moving with a speed of 10 m/s along a one-dimensional track in the positive x-direction and collides with the second particle at rest. Assuming that the collision is elastic, the speed (in m/s) of the first particle after the collision is ________.

Elastic Collision One Dimensional Equal Mass Speed After Collision

Q.44 Truth table of a logic gate is given below: Input A Input B Output Y 0 0 1 0 1 1 1 1 0 1 0 X The value of X in the above table is __________.

Truth Table of NAND Gate

Q.43 Let sin θ cos θ cos θ sin θ and \( A + A^T - 2I = 0 \), where \( A^T \) is the transpose of \( A \) and \( I \) is the identity matrix. The value of \( \theta \) (in degrees) is ______.

Matrix angle problem

Q.42 The solution to the integral1 2 0 2 1y y dy , rounded off to TWO decimal places, is ________. The value of the integral \(\int_{0}^{1} 2y\sqrt{1+y^{2}}\,dy\) rounded to two decimal places is 1.22.

Exact Evaluation of ∫0¹ 2y√(1+y²) dy with Step‑by‑Step Solution

Q.41 The generation time of E. coli is 20 minutes. If there are 106 E. coli present in an exponentially growing synchronous culture, then the average time (in minutes) required to obtain a final population of 4×106 E. coli is ________.

E. coli Generation Time 20 Minutes

Q.40 Which of the following gas(es) function(s) as signaling molecule(s) in the human nervous system? (A) Nitric oxide (B) Carbon monoxide (C) Helium (D) Argon

Signaling Molecules in Human Nervous System

Q.39 Which of the following is(are) CORRECT? (A) Both glucose and fructose have the same molecular formula (B) The positions of the oxygen and carbon differ in the structures of glucose and fructose (C) Both glucose and fructose have the same physical properties (D) Both glucose and fructose are monosaccharides

 Glucose and Fructose

Q.38 Consider two bodies with equal masses of 1012 kg each and R distance apart. Let G be the gravitational constant and V0 be a constant with dimensions of energy. Which of the following represent(s) gravitational potential energy (V) between the bodies, such that Newton’s law of gravitation is valid?

Gravitational Potential Energy Between Two Equal Masses

Q.37 Which of the following curve/straight line equations will pass through the origin when plotted on a graph? (A) -x/2+y/2=0 (B)1+y+x=1 (C)xy=1 (D)2y-2x+2=0

Which Curve/Straight Line Equation Passes Through Origin?

Q.36 Protozoa are (A) unicellular (B) multicellular (C) eukaryotic (D) prokaryotic

Protozoa are Unicellular

Q.35 Which of the following is(are) CORRECT? (A) Light has wave nature only (B) Light can have both wave and particle nature (C) Photo electric effect shows that light can behave like particles (D) Interference experiments show that light behaves like particles

 Wave-Particle Duality of Light

Q.34 DNA and RNA are acidic in nature due to the presence of (A) pentose sugar (B) nitrogenous bases (C) phosphate groups (D) large number of hydrogen bonds

DNA and RNA Acidic Nature Due to Phosphate Groups

Q.33 Which of the following is(are) involved in the activation of cytotoxic T cells? (A) MHC I (B) FcR (C) T cell receptor (D) CTLA 4

Activation of Cytotoxic T Cells

Q.32 Which of the following is(are) TRUE about photosynthesis? (A) In C3 plants the first organic product of carbon fixation is 3-phosphoglycerate (B) In C4 plants the first organic product of carbon fixation is oxaloacetate (C) Crassulacean acid metabolism occurs in succulent plants living in arid conditions (D) Oxygen is generated from carbon dioxide

Photosynthesis in C3, C4, and CAM Plants

Q.31 Which of the following is(are) auxins? (A) 1-Naphthaleneacetic acid (B) Indole-3-butyric acid (C) 2,4-Dichlorophenoxyacetic acid (D) Indole-3-acetic acid

Which Compounds are Auxins?

Q.30 IR spectrum of a compound C5H10O shows a band at 1715 cm^-1. The same compound showed two signals, a triplet and a quartet, in its NMR spectrum. Identify the compound from the following.

IR band at 1715 cm⁻¹ and NMR triplet–quartet for C₅H₁₀O

Q.29 Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]. Assertion [a]: lac operon is an inducible operon. Reason [r]: lac operon is not induced when the repressor protein remains bound to operator DNA sequence. (A) Both [a] and [r] are true and [r] is the correct reason for [a] (B) Both [a] and [r] are true but [r] is not the correct reason for [a] (C) Both [a] and [r] are false (D) [a] is true but [r] is false

Lac Operon is Inducible Operon

Q.28 In the following reaction, X is an intermediate and Y is one of the end products. Which one of the following compounds is the end product Y?

Grignard Reaction of Acetone with Ethylmagnesium Iodide

Q.27 Which one of the following compounds is the simplest alkane that is optically active?

Simplest Optically Active Alkane

Q.26 The following carboxylic acids have a general formula, R-COOH. (i) HCOOH (ii) CH3 - COOH (iii) ClCH2 - COOH (iv) CF3 - COOH Which one of the following represents the decreasing order of their respective 𝑝𝐾𝑎 values? (A) i > ii > iii > iv (B) ii > i > iii > iv (C) iv > iii > i > ii (D) iv > iii > ii > i

Decreasing Order of pKa Values

Q.25 Match the techniques in Group I with their applications in Group II for protein analysis Group I                                                                                                                      Group II (P) Nuclear magnetic resonance spectroscopy                                              (1) Proximity between specific sites (Q) Fluorescence resonance energy transfer                                                  (2) Concentration (R) Ultraviolet absorption spectroscopy                                                          (3) Size (S) Dynamic light scattering                                                                              (4) Structure (A) P-3, Q-1, R-2, S-4 (B) P-4, Q-1, R-2, S-3 (C) P-2, Q-1, R-4, S-3 (D) P-3, Q-4, R-1, S-2

Protein Analysis Techniques Matching

Q.24 Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]. Assertion [a]: The difference in the respective melting points of butter and coconut oil is caused by the degrees of saturation of the corresponding fatty acid chain. Reason [r]: Unsaturated fatty acid chains in fats/lipids become solid more easily because they are relatively straight and thus able to pack together more closely than saturated chain. (A) Both [a] and [r] are true and [r] is the correct reason for [a] (B) Both [a] and [r] are true but [r] is not the correct reason for [a] (C) Both [a] and [r] are false (D) [a] is true but [r] is false

Butter vs Coconut Oil Melting Points

Q.23 Match the diseases in Group I with their causative organisms in Group II Group I                                                                          Group II (P) Syphilis                                                                  (1) Shigella dysenteriae (Q) Bacillary dysentery                                             (2) Bordetella pertusis (R) Gas gangrene                                                       (3) Treponema pallidum (S) Whooping cough                                                  (4) Clostridium perfringens (A) P-2, Q-1, R-4, S-3 (B) P-3, Q-4, R-2, S-1 (C) P-2, Q-3, R-4, S-1 (D) P-3, Q-1, R-4, S-2

 Syphilis, Bacillary Dysentery, Gas Gangrene, Whooping Cough Causative Organisms

Q.22 Consider monoatomic ideal gas molecules of equal mass 𝑚 in thermal equilibrium, at temperature 𝑇. Which one of the following equations is correct? (the angular brackets denote average, 𝑘𝐵 is Boltzmann constant, 𝑣 is velocity, and vx is the x-component of velocity)

Average Kinetic Energy of a Monatomic Ideal Gas at Temperature T

Q.21 Match the type of bacterial flagella in Group I with their definitions in Group II Group I                                                          Group II (P) Monotrichous                                        (1) Flagella only at both poles of the cell (Q) Peritrichous                                          (2) Two or more flagella at one pole of the cell (R) Lophotrichous                                      (3) Flagella distributed over the entire cell (S) Amphitrichous                                      (4) A single polar flagellum               (A) P-4, Q-1, R-2, S-3 (B) P-4, Q-3, R-2, S-1 (C) P-4, Q-3, R-1, S-2 (D) P-3, Q-1, R-4, S-2

Bacterial Flagella Types

Q.20 Consider a spherical particle of mass m and radius r moving in a medium. Its velocity at any time t is given by v=𝑣0 exp(-6𝜋xrt/m) ,where 𝑣0 is initial velocity of the particle. The dimensions of X are (A) MLT-1 (B) M-1LT (C) ML-1T-1 (D) Dimensionless

Dimensions of X in Spherical Particle Velocity Equation

Q.19 In a typical mammalian cell, the protein content is 20 % of its net weight. If the density and volume of the cell are 1.2 g/mL and 4 × 10−9 mL, respectively, then the concentration (in mg/mL) of the protein is (A) 60 (B) 600 (C) 166 (D) 240

Mammalian Cell Protein Concentration Calculation

Q.18 Match the RNAs in Group I with their corresponding function in Group II Group I                                                            Group II (P) snRNA                                                      (1) rRNA processing (Q) piRNA                                                      (2) RNA splicing (R) snoRNA                                                    (3) Selected mRNAs degradation (S) siRNA                                                        (4) Germ line protection from transposable elements (A) P-4, Q-3, R-2, S-1 (B) P-4, Q-1, R-3, S-2 (C) P-3, Q-2, R-1, S-4 (D) P-2, Q-4, R-1, S-3

snRNA piRNA snoRNA siRNA Functions Matching

Q.17 If a coin is tossed three times, what is the probability that NO two successive tosses show the same face? (A) 0.25 (B) 0.33 (C) 0.20 (D) 0.125

Probability Coin Tossed Three Times No Two Successive Same Face

Q.16 In ABO blood group testing, which one of the following is INCORRECT (A) A group – agglutination with anti-A antibodies (B) B group – agglutination with anti-B antibodies (C) AB group – no agglutination with either anti-A or anti-B antibodies (D) O group – no agglutination with either anti-A or anti-B antibodies

ABO Blood Group Testing

Q.15 Match the enzymes in Group I with the corresponding substrate in Group II Group I                                                          Group II (P) Amylase                                                  (1) Protein (Q) Pepsin                                                     (2) Fat (R) Lipase                                                      (3) RNA (S) Ribozyme                                                (4) Starch (A) P-2, Q-3, R-1, S-4 (B) P-4, Q-1, R-2, S-3 (C) P-3, Q-1, R-4, S-2 (D) P-4, Q-2, R-3, S-1

Amylase Pepsin Lipase Ribozyme Substrates

Q.14 Which one of the following ions has the maximum number of unpaired electrons? (A) Cu2+ (B) Na+ (C) Cr3+ (D) Fe3+

Which Ion Has Maximum Unpaired Electrons

Q.13 Eutrophication refers to an aging process from a (A) low production ecosystem to high production ecosystem due to availability of excess nutrients (B) high production ecosystem to low production ecosystem due to nutrient deficiency (C) high production ecosystem to low production ecosystem due to light scarcity (D) low production ecosystem to high production ecosystem due to light scarcity

Eutrophication: Aging Process from Low Production to High Production Ecosystem Due to Excess Nutrients

Q.12 Match the deficiency conditions in Group I with the corresponding vitamin in Group II Group I                                                                                Group II (P) Beriberi                                                                          (1) Ascorbic acid (Q) Scurvy                                                                            (2) Retinol (R) Birth defects                                                                  (3) Thiamine (S) Night blindness                                                             (4) Folic acid (A) P-3, Q-2, R-1, S-4 (B) P-2, Q-3, R-4, S-1 (C) P-3, Q-1, R-4, S-2 (D) P-1, Q-2, R-3, S-4

Vitamin Deficiency Matching

Q.11 During El Niño, (A) cold water of the north flowing Peru current is displaced by a low-nutrient warm southward current (B) warm water of the north flowing Peru current is displaced by a low-nutrient cold southward current (C) cold water of the south flowing Peru current is displaced by a warm northward current rich in nutrients (D) warm water of the south flowing Peru current is displaced by a cold northward current rich in nutrients

During El Niño

Q.10 For an ideal gas at room temperature, choose the CORRECT representation(s) of Boyle’s Law. (P = Pressure, V = Volume, T = Temperature) (A) only (i) (B) both (ii) and (iii) (C) only (iii) (D) both (iii) and (iv)

Boyle’s Law Graphs Explained

Q.9 The CORRECT sequence of evolution (simplest to complex) is (A) algae, bryophytes, ferns, angiosperms (B) algae, ferns, bryophytes, angiosperms (C) bryophytes, ferns, algae, angiosperms (D) bryophytes, algae, ferns, angiosperms

 Correct Sequence of Evolution

Q.8 The common component in crustacean exoskeleton and fungal cell wall is (A) lignin (B) cellulose (C) chitin (D) peptidoglycan

Crustacean Exoskeleton and Fungal Cell Wall

Q.7 In viruses, capsids are made up of (A) proteins (B) nucleic acids (C) lipids (D) sterols

Virus Capsids Made Up of Proteins

Q.6 The curve y=x^4-4x^3+4x^2-4 has tangents parallel to the x-axis at the following points (x,y) (A) (1, 4), (−2, 2) 𝑎𝑛𝑑 (0, −1) (B) (0, −4), (2, −4) 𝑎𝑛𝑑 (1, −3) (C) (−1, 2), (−2, 1) 𝑎𝑛𝑑 (1, −2) (D) (1, −4), (1, −3) 𝑎𝑛𝑑 (2, −4)

Tangents Parallel to the X‑Axis for the Curve y = x⁴ − 4x³ + 4x² − 4

Q.5 The CORRECT sequence of phases during mitosis is (A) prophase, metaphase, anaphase, telophase (B) prophase, anaphase, metaphase, telophase (C) anaphase, prophase, metaphase, telophase (D) anaphase, metaphase, prophase, telophase

Correct Sequence of Phases During Mitosis

Q.4 Protein that helps other proteins to fold correctly is (A) chaperone (B) proteasome (C) ubiquitin (D) desmosome

Protein That Helps Other Proteins Fold Correctly

Q.3 In humans, the testis temperature is maintained below the core body temperature with the help of (A) proximal tubule (B) loop of Henle (C) scrotum (D) seminal vesicles

Testis Temperature Regulation in Humans

Q.2 T cells and B cells are (A) lymphocytes (B) erythrocytes (C) epithelial cells (D) squamous cells

 T Cells and B Cells are Lymphocytes

Q.1 Deficiency of the enzyme phenylalanine hydroxylase causes Phenylketonuria. Phenylalanine hydroxylase converts phenylalanine to (A) tryptophan (B) alanine (C) tyrosine (D) threonine

Phenylalanine Hydroxylase Deficiency Causes Phenylketonuria

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