Q.60 A first order reaction is 87.5% complete at the end of 30 minutes. The half-life of the reaction is __________ minute(s).

First Order Reaction 87.5% Complete 30 Minutes Half-Life Calculation

Q.59 The number of axial C-H bond(s) in the major product (P) of the given reaction is ________.

Axial C–H Bonds in the Major Product

Q.58 The relationship between the applied force F(X) (in Newton) on a body and its displacement X (in metre) is given below. The total amount of work done in moving the body from X = 0 to X = 4 m is ___________ Joule.

Work Done from Force–Displacement Graph for Motion from 0 m to 4 m

Q.57 An ultrasound signal of frequency 50 KHz is sent vertically down into a medium. The signal gets reflected from a depth of 25 mm and returns to source 0.00005 seconds after it is emitted. The wavelength of the ultrasound signal in that medium is ________ cm.

Ultrasound Wavelength Calculation

Q.56 If A and B are events such that 𝑃𝑃(𝐴𝐴) = 0.3, 𝑃𝑃(𝐵𝐵) = 0.2 and 𝑃𝑃(𝐴𝐴 ∪ 𝐵𝐵) = 0.45, the value of 𝑃𝑃(𝐴𝐴 ∩ 𝐵𝐵�) is ___________.

Probability of A ∩ B̄ when P(A)=0.3, P(B)=0.2 and P(A ∪ B)=0.45

Q.55 For a = ________, the following simultaneous equations have an infinite number of solutions: 10𝑥𝑥 + 13𝑦𝑦 = 6 𝑎𝑎𝑥𝑥 + 32.5𝑦𝑦 = 15

Infinite Solutions for Simultaneous Equations

Q.54 For a 0.1 M aqueous solution of lysine, the pH at which it carries no net charge is ___________. (pKa values for: α-carboxylic group = 3.1, α-amino group = 8.0, ε-amino group = 10.8)

Lysine pI Calculation

Q.53 If a colour-blind woman marries a normal man, the chance that their boy child will be colour-blind is ________%.

Colour-Blind Woman Marries Normal Man

Q.52 A 100 nucleotide-long single stranded poly-(A) is synthesized from adenosine monophosphate (AMP) at physiological pH. (Atomic mass of C = 12, H = 1, O = 16, P = 31; at physiological pH, Molecular mass of AMP = 345). The molecular mass of the resulting poly-(A) at physiological pH is ___________.

Calculate Molecular Mass of 100 Nucleotide Poly-A from AMP at Physiological pH

Q.51 The concentration of a purified enzyme is 10 mg/mL. Ten microlitres of the enzyme solution in a total reaction volume of 1 mL catalyses the formation of 20 nanomoles of product in one minute under optimum conditions. The specific activity of the enzyme is _________ unit/mg.

Specific Activity of Purified Enzyme

Q.50 The mechanism of the following reaction involves the formation of a __________ membered ring.

Wittig Reaction Mechanism

Q.49 Oxidation state of Fe in the complex K3 [Fe(CN)5NO] is (+) __________.

Oxidation State of Fe in K3[Fe(CN)5NO] Complex

Q.48 The stability of the following carbocation arises from hyperconjugation with _________ number of hydrogen atoms.

Hyperconjugation in Isopropyl Carbocation

Q.47 The equivalent capacitance of following assembly of capacitors is ________ μF.

Equivalent Capacitance of Mixed Series and Parallel Capacitors

Q.46 The determinant of the matrix \(\begin{vmatrix} 1 & 3 & 0 \\ 2 & 6 & 4 \\ -1 & -1 & 2 \end{vmatrix}\) is _________.

Determinant of the Matrix [1 3 0; 2 6 4; -1 -1 2]

Q.45 The value of \(\log_n 4 - 16\) is \(-32\). The value of \(n\) is _________.

Logarithm Problem : Find n from logₙ 4⁻¹⁶ = -32

Q.44 The number of cycles required for complete degradation of Palmitic acid (16 Carbon) by β-oxidation is __________.

Number of Cycles Required for Complete Degradation of Palmitic Acid (16 Carbon) by β-Oxidation

Q.43 Both strands of a DNA molecule are labeled with radioactive thymidine and are allowed to duplicate in an environment containing non-radioactive thymidine. The number of DNA molecules that will contain radioactive thymidine after three duplications is _________.

DNA Molecules with Radioactive Thymidine After Three Duplications

Q.42 A healthy individual has the cardiac output of 5.5 L and heart rate of 72 beats per minute. The stroke volume of the individual is _________ mL.

Stroke Volume Calculation

Q.41 The total number of genetically different types of gametes that will be produced by a heterozygous plant carrying the genotypes AABbCc is _________.

Number of Genetically Different Gametes from AABbCc Genotype in Plants

Q.40 Which of the following pairs of compounds can be distinguished by iodoform test performed in ammonium hydroxide? (A) CH3 COCH3 and C 2 H5 OH (B) C 2 H5 OH and CH3 OH (C) CH3 COCH3 and C6 H5 COCH3 (D) C 6 H5 COCH3 and C2H5 OH

Iodoform Test in Ammonium Hydroxide to Distinguish Compounds

Q.39 Which of the following statements is/are CORRECT? (A) Absorption occurs at all wavelengths if light passes through a given solution. (B) The efficiency of a photochemical process is often expressed in terms of quantum yield. (C) The unit of molar extinction coefficient is litre mole-1 cm. (D) The extent of absorption in a dilute solution would be the same if the concentration is doubled and the path-length of light passing through solution is halved.

Molar Extinction Coefficient Beer-Lambert Law Quantum Yield Absorption

Q.38 If an optician prescribes a corrective lens of power -2.0 D, the required lens (A) is a concave lens. (B) is a convex lens. (C) has a focal length of +50 cm. (D) has a focal length of -50 cm.

Corrective Lens Power -2.0 D

Q.37 Which of the following statements is/are CORRECT regarding self-inductance of a long solenoid having cross sectional area (𝐴𝐴), length (𝑙𝑙) and having 𝑛𝑛 turns per unit length filled with material of relative permeability 𝜇𝜇𝑟𝑟 ? (A) It depends on the geometry of solenoid. (B) It does not depend on geometry of solenoid. (C) It depends on cross sectional area of solenoid. (D) It depends on relative permeability of the medium.

Self-Inductance of Long Solenoid

Q.36 Consider the equation \( x^3 - 1 = 0 \). If one of the solutions to this equation is 1, the other solution(s) is/are (A) ( -\frac{1}{2} + \frac{\sqrt{3}}{2} i \) (B) ( i \) (C) ( -i \) (D) ( -\frac{1}{2} - \frac{\sqrt{3}}{2} i \)

Solving x3 – 1 = 0

Q.35 In a double stranded DNA, which of the following ratios is/are always equal to 1? A, T, G and C denote the number of bases. (A) (A+T)/(G+C) (B) (A+G)/(T+C) (C) A/G (D) (G+T)/(A+C)

Double Stranded DNA Base Ratios Always Equal to 1

Q.34 Glucose is incubated with enzymes of the glycolytic pathway (except pyruvate kinase), γ32P-ATP, and unlabeled inorganic phosphate. Which of the following products is/are formed?

Gamma 32P‑ATP labeling in glycolysis

Q.33 Which of the following statements is/are CORRECT for G protein–coupled receptor (GPCR) mediated signaling? (A) GPCRs contain seven membrane spanning regions. (B) GPCRs are linked to heterotrimeric G protein consisting of α, β and γ subunits. (C) In the absence of GPCR interacting ligand, α subunit of G protein is bound to GTP and complexed with βγ subunits. (D) In the presence of GPCR interacting ligand, GTP is displaced from α subunit of G protein by GDP, GDP bound α subunit dissociates from βγ dimer and activates the effector.

 GPCR Mediated Signaling

Q.32 Plasmid mediated antibiotic resistances in bacteria are acquired by (A) hydrolysis by β-lactamase (penicillin resistance). (B) expression of aminoglycoside modifying enzyme (kanamycin resistance). (C) mutation in DNA gyrase (quinolone resistance). (D) overproduction of dihydrofolate reductase (trimethoprim resistance).

 Plasmid Mediated Antibiotic Resistance in Bacteria

Q.31 Antibody binds to antigen in solution through (A) ionic interactions. (B) hydrogen bonds. (C) van der Waals interactions. (D) hydrophobic interactions.

Antibody Binds to Antigen in Solution Through

Q.30 In the 1 H NMR spectrum, which one of the following compounds will show a triplet?

Ethyl Acetate NMR

Q.29 Which one of the following statements is CORRECT? (A) BF3 is a stronger Lewis acid than BI3 . (B) CO and CN- are good π-accepting ligands. (C) cis-Diamminedichloroplatinum (II) has zero dipole moment. (D) Central atom in BCl 3 is sp3 hybridized.

BF3 vs BI3 Lewis Acid Strength

Q.28 Match the entries in Group I with those in Group II Group I Group II P) Proline 1) Artificial sweetener Q) Oxytocin 2) Cyclic amino acid R) Aspartame 3) β-Lactam S) Penicillin 4) Peptide hormone Options: (A) P-2, Q-4, R-1, S-3 (B) P-3, Q-1, R-4, S-2 (C) P-4, Q-3, R-1, S-2 (D) P-2, Q-1, R-4, S-3 Q.28 Match the entries in Group I with those in Group II Group I Group II P) Proline 1) Artificial sweetener Q) Oxytocin 2) Cyclic amino acid R) Aspartame 3) β-Lactam S) Penicillin 4) Peptide hormone Options: (A) P-2, Q-4, R-1, S-3 (B) P-3, Q-1, R-4, S-2 (C) P-4, Q-3, R-1, S-2 (D) P-2, Q-1, R-4, S-3

Amino Acids, Hormones, Sweeteners and Antibiotics

Q.27 The achiral molecules among the following (I, II, III and IV) are (A) I and III (B) II and IV (C) III and IV (D) I and IV

Achiral Molecules Among I, II, III and IV

Q.26 Match the entries in Group I (Mechanical system) with analogous quantities in Group II (Electrical system) Group I Group II P) Mass 1) Current Q) Spring constant 2) Voltage R) Displacement 3) Reciprocal capacitance S) Velocity 4) Charge 5) Inductance (A) P-3, Q-5, R-4, S-1 (B) P-5, Q-3, R-4, S-2 (C) P-3, Q-5, R-4, S-2 (D) P-5, Q-3, R-4, S-1

Mechanical–Electrical Analogies

Q.25 A 30 μF capacitor is connected to a 240 V, 50 Hz source. If the frequency of the source is changed from 50 Hz to 200 Hz, the capacitive reactance of the capacitor will (A) increase by a factor of two. (B) increase by a factor of four. (C) decrease by a factor of four. (D) decrease by a factor of two.

Capacitive Reactance

Q.24 Which one of the following shows the CORRECT relationship among velocity of light in a medium (\( v \)), permittivity of medium (\( \varepsilon \)) and magnetic permeability of medium (\( \mu \))? (A) \( v = \frac{1}{\mu \varepsilon} \) (B) \( v = \frac{1}{(\mu \varepsilon)^2} \) (C) \( v = \frac{1}{(\mu \varepsilon)^{-2}} \) (D) \( v = \frac{1}{\sqrt{\mu \varepsilon}} \)

Correct relationship between velocity of light, permittivity and permeability in a medium

Q.23 Nucleus of a radioactive material can undergo beta decay with half life of 4 minutes. Suppose beta decay starts with 4096 nuclei at \( t = 0 \), the number of nuclei left after 20 minutes would be (A) 1024 (B) 128 (C) 512 (D) 256

Beta Decay Half Life Calculation

Q.22 The area of an equilateral triangle with sides of length \( \alpha \) is (A) \( \frac{\sqrt{3}}{4} \alpha^2 \) (B) \( \frac{\sqrt{3}}{2} \alpha^2 \) (C) \( \frac{1}{2} \alpha^2 \) (D) \( \frac{1}{\sqrt{2}} \alpha^2 \)

Area of an Equilateral Triangle with Side a

Q.21 What is the solution of \( \int \frac{x}{x^2 \ln x} \, dx \)? Given \( C \) is an arbitrary constant. (A) \( \frac{x^3}{3} \ln x - \frac{x^3}{9} + C \) (B) \( \frac{x^3}{3} \ln x + \frac{x^3}{9} + C \) (C) \( -\frac{x^3}{9} \ln x + \frac{x^3}{9} + C \) (D) \( \frac{x^3}{9} \ln x - \frac{x^3}{3} + C \)

Integration of \(x^2 \ln x\)

Q.20 The number of three letter words, with or without meaning, which can be formed using letters of the word 'VIRUS' without repetition of letters is (A) 30 (B) 40 (C) 60 (D) 120

Number of Three Letter Words from VIRUS Without Repetition

Q.19 If φ(x) = x² and ψ(x) = 2x, then ψ(φ(x)) is (A) 2x² (B) x² (C) 2²x (D) x²x

 If φ(x) = x² and ψ(x) = 2x

Q.18 Match the entries in Group I with that in Group II Group I Group II P) Vitamin B1 1) Co-enzyme A Q) Vitamin B2 2) Flavin mononucleotide R) Vitamin B5 3) Pyridoxal phosphate S) Vitamin B6 4) Thiamine pyrophosphate (A) P-4, Q-3, R-2, S-1 (B) P-3, Q-1, R-4, S-2 (C) P-1, Q-2, R-3, S-4 (D) P-4, Q-2, R-1, S-3

Match the entries in Group I with that in Group II

Q.17 Match the entries in Group I with that in Group II Group I Group II P) Fehling's test 1) α-Amino acid Q) Ninhydrin reaction 2) Reducing sugar R) Biuret reaction 3) Sulfhydryl group S) Nitroprusside reaction 4) Peptide linkage (A) P-1, Q-2, R-3, S-4 (B) P-3, Q-4, R-1, S-2 (C) P-2, Q-1, R-4, S-3 (D) P-4, Q-1, R-2, S-3

Fehling’s, Ninhydrin, Biuret and Nitroprusside Tests

Q.16 Match the hormones in Group I with their functions in Group II Group I Group II P) Aldosterone 1) Stimulates the synthesis and secretion of androgens from the testis Q) Luteinizing hormone (LH) 2) Helps in the re-absorption of Na⁺ and water from the kidney R) Atrial natriuretic factor (ANF) 3) Increases the heart rate and the strength of heart contraction. S) Epinephrine 4) Causes dilation of blood vessels and reduction of blood pressure (A) P-2, Q-3, R-4, S-1 (B) P-2, Q-1, R-4, S-3 (C) P-1, Q-2, R-3, S-4 (D) P-3, Q-4, R-2, S-1

Endocrine Physiology MCQ

Q.15 When bacteria are grown in glucose-depleted media containing high concentration of lactose, expression of lac operon genes is activated by (A) the binding of lac repressor in the operator site and cAMP-CAP complex in the CAP site. (B) the dissociation of bound lac repressor from the operator site and binding of cAMP-CAP complex in the CAP site. (C) the dissociation of bound lac repressor only from the operator site. (D) the dissociation of both bound lac repressor from operator site and cAMP-CAP complex from CAP site.

Lac Operon Activation in Glucose-Depleted Lactose Media

Q.14 Proenzyme pepsinogen is secreted from 'P' of gastric mucosa and converted into active enzyme pepsin on exposure to 'Q' secreted from 'R'. Choose the CORRECT combination of P, Q and R. (A) P - chief cells Q - hydrochloric acid R - oxyntic cells (B) P - parietal cells Q - enterokinase R - chief cells (C) P - oxyntic cells Q - hydrochloric acid R - parietal cells (D) P - peptic cells Q - gastrin R - oxyntic cells

Role of Chief Cells, Hydrochloric Acid and Oxyntic Cells in Pepsinogen Activation

Q.13 Match the entries in Group I with that in Group II. Group I Group II P) Cholera toxin 1) Endotoxin Q) Diphtheria toxin 2) Neurotoxin R) Lipopolysaccharide 3) Enterotoxin S) Tetanus toxin 4) Cytotoxin (A) P-1, Q-2, R-3, S-4 (B) P-3, Q-2, R-1, S-4 (C) P-3, Q-4, R-1, S-2 (D) P-4, Q-1, R-2, S-3

Match the Entries in Group I with Group II

Q.12 Which of the following feature(s) should be present in a protein to generate strong immune response (antibody production) in an animal? I. At least one B-cell epitope II. At least one T-cell epitope III. Proteolytic cleavage site(s) (A) I only (B) II and III (C) I and III (D) I, II and III

Protein Features for Strong Immune Response

Q.11 Viral capsids are made up of morphological subunits called capsomeres. One of the common capsomeres is icosahedral. The icosahedron is a regular polyhedron with (A) 16 triangular facets and 12 vertices. (B) 20 triangular facets and 12 vertices. (C) 16 triangular facets and 16 vertices. (D) 20 triangular facets and 16 vertices.

Icosahedron Viral Capsids

Q.10 The reaction of 11-cis-retinal with the lysine residue of a specific protein forms the light- sensitive pigment in the cells of retina. The light-sensitive pigment is an (A) amide.         (B) acid. (C) anhydride. (D) imine.

11‑cis‑retinal and lysine reaction

Q.9 The logic operation (OR, AND, NOR or NAND) carried out by following circuit is (A) AND (B) NOR (C) OR (D) NAND

How to Identify the Logic Operation of a Bubbled OR–AND Circuit

Q.8 Three vectors are as follows: \(\vec{a} = 3\hat{i} - 10\hat{j} + 7\hat{k}\) \(\vec{b} = -9\hat{i} + 6\hat{j} - 47\hat{k}\) \(\vec{c} = 11\hat{i} - 17\hat{k}\) The value of \((\vec{a} + \vec{b}) \cdot \vec{c}\) is (A) 614 (B) 746 (C) 2 (D) 134

Step‑by‑Step Solution of \(( \vec{a} + \vec{b} ) \cdot \vec{c}\)

Q.7 The value of \(\lim_{n\to\infty} \frac{3n^2 + 5n + 4}{4 + 2n^2}\) is (A) 0 (B) 0.75 (C) 1.5 (D) 3

The limit limn→∞(3n2+5n+4)/(4+2n2) equals 1.5

Q.6 What is the source of electrons in photosynthesis? (A) Carbohydrates (B) Water (C) CO2 (D) NADH

 Source of Electrons in Photosynthesis

Q.5 In the feedback regulation of an enzyme, the end product binds to the (A) active site of the enzyme. (B) allosteric site of the enzyme. (C) enzyme-substrate complex. (D) substrate.

 Feedback Regulation of Enzyme

Q.4 Pyramid of energy in a forest ecosystem is (A) always inverted. (B) dumb-bell shaped. (C) spindle shaped. (D) always upright.

 Pyramid of Energy in a Forest Ecosystem

Q.3 Which one of the following organelles is enclosed by a single membrane? (A) Ribosome (B) Mitochondria (C) Endoplasmic reticulum (D) Centrosome

Which Organelle is Enclosed by a Single Membrane?

Q.2 Which one of the following statements is CORRECT for Mycoplasma? (A) Their cells are of definite shape. (B) They are resistant to lysis by osmotic shock. (C) Their growth is not inhibited by penicillin. (D) They are nonpathogenic to human.

Mycoplasma Characteristics

Q.1 Which one of the following protozoan parasites belongs to the phylum Apicomplexa? (A) Toxoplasma gondii (B) Leishmania donovani (C) Entamoeba histolytica (D) Trichomonas vaginalis

Protozoan Parasites Phylum Apicomplexa

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