GATE BT 2022 Question Paper & Solutions

Verbal Aptitude

You should _________ when to say _________.

Quantitative Aptitude

Two straight lines pass through the origin (𝑥଴, 𝑦଴) = (0,0). One of them passes through the point (𝑥ଵ, 𝑦ଵ) = (1,3) and the other passes through the point (𝑥ଶ, 𝑦ଶ) = (1,2). What is the area enclosed between the straight lines in the interval [0, 1] on the 𝑥-axis?

Quantitative Aptitude

If 𝑝∶𝑞= 1 ∶2 𝑞∶𝑟= 4 ∶3 𝑟∶𝑠= 4 ∶5 and 𝑢 is 50% more than 𝑠, what is the ratio 𝑝∶𝑢?

Analytical & Spatial Aptitude

Given the statements:  P is the sister of Q.  Q is the husband of R.  R is the mother of S.  T is the husband of P. Based on the above information, T is ______ of S.

Analytical & Spatial Aptitude

In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQT is

Verbal Aptitude

Healthy eating is a critical component of healthy aging. When should one start eating healthy? It turns out that it is never too early. For example, babies who start eating healthy in the first year are more likely to have better overall health as they get older. Which one of the following is the CORRECT logical inference based on the information in the above passage?

Quantitative Aptitude

P invested ₹ 5000 per month for 6 months of a year and Q invested ₹ 𝑥 per month for 8 months of the year in a partnership business. The profit is shared in proportion to the total investment made in that year. If at the end of that investment year, Q receives ସ ଽ of the total profit, what is the value of 𝑥 (in ₹)?

Quantitative Aptitude

The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam. From the data presented above, which one of the following is CORRECT?

Analytical & Spatial Aptitude

In the square grid shown on the left, a person standing at P2 position is required to move to P5 position. The only movement allowed for a step involves, “two moves along one direction followed by one move in a perpendicular direction”. The permissible directions for movement are shown as dotted arrows in the right. For example, a person at a given position Y can move only to the positions marked X on the right. Without occupying any of the shaded squares at the end of each step, the minimum number of steps required to go from P2 to P5 is 1 2 3 4 5 P Q R S T Example: Allowed steps for a person at Y

Analytical & Spatial Aptitude

Consider a cube made by folding a single sheet of paper of appropriate dimensions with face labels. The pair of opposite faces that cannot be adjacent is:

Differential Equations

What is the order of the differential equation given below? 2 4 3 2 6 3 2 2 d y x x x dx    

Linear Algebra

If the eigenvalues of a 2×2 matrix P are 4 and 2, then the eigenvalues of the matrix 1 P are

Biomolecules, enzyme kinetics

For a double-pipe heat exchanger, the inside and outside heat transfer coefficients are 100 and 200 W m-2 K-1, respectively. The thickness and thermal conductivity of the thin-walled inner pipe are 1 cm and 10 W m-1 K-1, respectively. The value of the overall heat transfer coefficient is ___________ W m-2 K-1.

Mass transfer in bioprocesses (kLa)

Match the media component (Column I) with its role (Column II). Column I Column II P. Sucrose 1. Anti-foam agent Q. Zinc chloride 2. Nitrogen source R. Ammonium sulphate 3. Carbon source S. Silicone oil 4. Trace element

Bioenergetics and Metabolism

The binding free energy of a ligand to its receptor protein is −11.5 kJ mol-1 at 300 K. What is the value of the equilibrium binding constant? Use R = 8.314 J mol-1 K-1.

Media Sterilization and Stoichiometry

The overall stoichiometry for an aerobic cell growth is 3C6H12O6 + 2.5NH3 + O2  1.5CaHbOcNd + 3CO2 + 5H2O What is the elemental composition formula of the biomass?

Biomolecules, enzyme kinetics

In binomial nomenclature, the name of a bacterial strain is written with the first letter of ___________ word(s) being capitalized.

Biomolecules, enzyme kinetics

The type of nucleic acid present in phage is

Biomolecules, enzyme kinetics

Which of the following statements about reversible enzyme inhibitors are P. Uncompetitive inhibitors bind only to the enzyme-substrate complex Q. Non-competitive inhibitors bind only at a different site from the substrate R. Competitive inhibitors bind to the same site as the substrate

Mass transfer in bioprocesses (kLa)

Match the component of eukaryotic cells (Column I) with its respective function (Column II). Column I Column II P. Lysosome 1. Digestion of macromolecules Q. Peroxisome 2. Detoxification of harmful compounds R. Glyoxysome 3. Conversion of fatty acids to sugar S. Cytoskeleton 4. Involvement in cell motility

DNA replication, transcription, translation

In animal cells, the endogenously produced miRNAs silence gene expression by

Biomolecules, enzyme kinetics

Terpenoids are made of ___________ units

Biomolecules, enzyme kinetics

Match the microbial product (Column I) with its respective application (Column II). Column I Column II P. Methane 1. Biosurfactant Q. Glycolipids 2. Bioplastic R. Polyhydroxy alkanoate 3. Biofuel

Biomolecules, enzyme kinetics

Which of the following is NOT used for generating an optimal alignment of two nucleotide sequences?

Mass transfer in bioprocesses (kLa)

The recognition sequences of four Type-II restriction enzymes (RE) are given below. The symbol (↓) indicates the cleavage site. Identify the RE that generates sticky ends.

Recombinant DNA technology

Among individuals in a human population, minor variations exist in nucleotide sequences of chromosomes. These variations can lead to gain or loss of sites for specific restriction enzymes. Which of the following technique is used to identify such variations?

Biomolecules, enzyme kinetics

Assuming independent assortment and no recombination, the number of different combinations of maternal and paternal chromosomes in gametes of an organism with a diploid number of 12 is _________________.

Bioreactor types, scale-up

A microorganism is grown in a batch culture using glucose as a carbon source. The apparent growth yield is 0.5 ୥ ୠ୧୭୫ୟୱୱ ୥ ୱ୳ୠୱ୲୰ୟ୲ୣ. The initial concentrations of biomass and substrate are 2 g L-1 and 200 g L-1, respectively. Assuming that there is no endogenous metabolism, the maximum biomass concentration that can be achieved is _________________ g L-1.

Media Sterilization and Stoichiometry

The degree of reduction of lactic acid (C3H6O3) is ________________.

Calculus

Consider a nonlinear algebraic equation, xlnx + x - 1 = 0. Using the Newton- Raphson method, with the initial guess of x଴ = 3, the value of x after one iteration (rounded off to one decimal place) is __________.

Probability and Statistics

The probability density function of a random variable X is 2 ( ) 2 x p x e  . The probability (1 2) P X   (rounded off to two decimal places) is __________.

Calculus

The maximum value of the function 2 3 ( ) 3 2 f x x x   for 0 x  is ___________.

Bioreactor types, scale-up

The specific growth rate of a yeast having a doubling time of 0.693 h (rounded off to nearest integer) is___________h-1.

Bioreactor types, scale-up

A fermentation broth of density 1000 kg m-3 and viscosity 10-3 kg m-1 s-1 is mixed in a 100 L fermenter using a 0.1 m diameter impeller, rotating at a speed of 2 s-1. The impeller Reynolds number is ____________. .35 For a pure species, the slope of the melting line ௗ௉ ௗ் at -2 ˚C is -5.0665×106 Pa K-1. The difference between the molar volumes of the liquid and solid phase at -2 ˚C is -4.5×10-6 m3 mol-1. The value of the latent heat of fusion (rounded off to nearest integer) is __________ J mol-1. .36 - Q.65 Carry TWO marks each.

Biomolecules, enzyme kinetics

For a pure species, the slope of the melting line ௗ௉ ௗ் at −2 ˚C is −5.0665×106 Pa K-1. The difference between the molar volumes of the liquid and solid phase at −2 ˚C is −4.5×10-6 m3 mol-1. The value of the latent heat of fusion (rounded off to nearest integer) is __________ J mol-1.

Bioreactor types, scale-up

Which of the following conditions will contribute to the stability of a gene pool in a natural population? P. Large population Q. No net mutation R. Non-random mating S. No selection

Bioreactor types, scale-up

Match the media component used in mammalian cell culture (Column I) with its respective role (Column II). Column I Column II P. Hydrocortisone 1. Mitogen Q. Fibronectin 2. Vitamin R. Epidermal growth factor 3. Hormone S. Riboflavin 4. Cell attachment

Mass transfer in bioprocesses (kLa)

Match the cell type (Column I) with its function (Column II). Column I Column II P. B cells 1. Humoral immunity Q. Neutrophils 2. Cytotoxicity R. T cells 3. Histamine-associated allergy S. Mast cells 4. Phagocytosis

Linear Algebra

A 2×2 matrix P has an eigenvalue 𝜆ଵ= 2 with eigenvector 𝑥ଵ= 1 0    and another eigenvalue 𝜆ଶ= 5, with eigenvector 𝑥ଶ= 1 1    . The matrix P is

Linear Algebra

Match the stationary phase (Column I) with its corresponding chromatography technique (Column II). Column I Column II P. Protein A 1. Size exclusion chromatography Q. Sephadex 2. Ion-exchange chromatography R. Phenylsepharose 3. Affinity chromatography S. Diethylaminoethyl cellulose 4. Hydrophobic interaction chromatography

Calculus

Which of the following statements are CORRECT for a controller? P. In a proportional controller, a control action is proportional to the error Q. In an integral controller, a control action is proportional to the derivative of the error R. There is no “offset” in the response of the closed-loop first-order process with a proportional controller S. There is no “offset” in the response of the closed-loop first-order process with a proportional-integral controller

Biomolecules, enzyme kinetics

Which of the following are CORRECT about protein structure? P. Secondary structure is formed by a repeating pattern of interactions among the polypeptide backbone atoms Q. Tertiary structure is the three-dimensional arrangement of the polypeptide backbone atoms only R. Quaternary structure refers to an assembly of multiple polypeptide subunits

Recombinant DNA technology

The enzymes involved in ubiquitinylation of cell-cycle proteins are

Recombinant DNA technology

The maximum parsimony method is used to construct a phylogenetic tree for a set of sequences. Which one of the following statements about the method is CORRECT?

Biomolecules, enzyme kinetics

Which of the following spectroscopic technique(s) can be used to identify all the functional groups of an antibiotic contaminant in food? P. Infrared Q. Circular dichroism R. Nuclear magnetic resonance S. UV-Visible

Recombinant DNA technology

Adenine can undergo a spontaneous change to hypoxanthine in a cell, leading to a DNA base pair mismatch. The CORRECT combination of enzymes that are involved in repairing this damage is

Differential Equations

Consider the ordinary differential equation 2 2 ( , ) 2 dy f x y x y dx    . If (1) 1 y , the value(s) of (1.5) y , using the Euler’s implicit method [𝑦௡ାଵ= 𝑦௡+ ℎ𝑓(𝑥௡ାଵ, 𝑦௡ାଵ)] with a step size of h = 0.5, is (are)

Mass transfer in bioprocesses (kLa)

Which of the following statements are CORRECT for an enzyme entrapped in a spherical particle?

Downstream processing (chromatography, filtration)

Which of the following is(are) COMMON feature(s) for both aerobic and anaerobic bacterial cultures?

Biomolecules, enzyme kinetics

Which of the following plot(s) is(are) CORRECT for an enzyme that obeys Michaelis-Menten kinetics in the presence of a competitive inhibitor?

DNA replication, transcription, translation

Which of the following statement(s) is(are) CORRECT regarding the lac operon in E. coli when grown in the presence of glucose and lactose?

Recombinant DNA technology

Emerging viruses such as SARS-CoV2 cause epidemics. Which of the following process(es) contribute to the rise of such viruses?

Recombinant DNA technology

Introduction of foreign genes into plant cells can be carried out using

Probability and Statistics

Which of the following statement(s) regarding trafficking in eukaryotic cells is(are) CORRECT?

Probability and Statistics

Consider a random variable X with mean 𝜇௑= 0.1 and variance 𝜎௑ ଶ= 0.2. A new random variable 𝑌= 2𝑋+ 1 is defined. The variance of the random variable Y (rounded off to one decimal place) is _________________.

Biomolecules, enzyme kinetics

For 1 0x  and 2 0x  , the value of 1 2 1 2 1 2 2 lim ln x x x x xx x        is __________. .57 Figure below depicts simplified metabolic and transport reactions taking place in the production of B from A in a cell. The subscript ' i' refers to intracellular metabolites. rj is the jth reaction flux in ୥ (୥ ୢ୰୷ ୫ୟୱୱ) ୦. Under pseudo-steady-state condition, the following reaction fluxes are available. r1 = 4, r3 = 1 and r6 = 1. The transport flux of B, r4, is _____________ ୥ (୥ ୢ୰୷ ୫ୟୱୱ) ୦.

Biomolecules, enzyme kinetics

Figure below depicts simplified metabolic and transport reactions taking place in the production of B from A in a cell. The subscript ‘i’ refers to intracellular metabolites. rj is the jth reaction flux in ୥ (୥ ୢ୰୷ ୫ୟୱୱ) ୦. Under pseudo-steady-state condition, the following reaction fluxes are available. r1 = 4, r3 = 1 and r6 = 1. The transport flux of B, r4, is _____________ ୥ (୥ ୢ୰୷ ୫ୟୱୱ) ୦.

Bioreactor types, scale-up

The amount of biomass in a reactor at the end of the batch process is 50 g. Fed- batch operation is initiated by feeding the substrate solution at a constant rate of 1 L h -1. The concentration of substrate in the feed is 50 g L -1. The maximum biomass yield (Y௑ௌ ெ) is 0.4 ୥ ୠ୧୭୫ୟୱୱ ୥ ୱ୳ୠୱ୲୰ୟ୲ୣ. Assuming the system is at quasi-steady state, the maximum amount of biomass after 5 h of feeding is _____________ g. .59 An enzyme catalyzes the conversion of substrate A into product B. The rate equation for this reaction is 5 A A A Cr C   mol L-1 min-1 Substrate A at an initial concentration of 10 mol L -1 enters an ideal mixed flow reactor (MFR) at a flow rate of 10 L min-1. The volume of the MFR required for 50% conversion of substrate to product is ___________ L.

Biomolecules, enzyme kinetics

An enzyme catalyzes the conversion of substrate A into product B. The rate equation for this reaction is 5 A A A C r C    mol L-1 min-1 Substrate A at an initial concentration of 10 mol L-1 enters an ideal mixed flow reactor (MFR) at a flow rate of 10 L min-1. The volume of the MFR required for 50% conversion of substrate to product is ___________ L.

Bioreactor types, scale-up

Liquid-phase mass transfer coefficient ( kL) is measured in a stirred tank vessel using steady-state method by sparging air. Oxygen uptake by the microorganism is measured. The bulk concentration of O 2 is 10 -4 mol L -1. Solubility of O 2 in water at 25 ˚C is 10-3 mol L-1. If the oxygen consumption rate is 9×10 -4 mol L -1 s-1, and interfacial area is 100 m2/m3, the value of kL is __________cm s-1. .61 Consider a piston-cylinder assembly shown in the figure below. The walls of the cylinder are insulated. The cylinder contains 1 mole of an ideal gas at 300 K and the piston is held initially at the position z 1 using a stopper. After the stopper is removed, the piston suddenly rises against atmospheric pressure (1.013×10 5 Pa) to the new position z2 where it is held by another stopper. The heat capacity (Cv) of the gas is 12.5 J mol -1 K-1. The cross-sectional area of the cylinder is 10-3 m2. Assume the piston is weightless and frictionless. If zଶ - zଵ = 1 m, the final temperature of the gas (rounded off to nearest integer) is ___________K. .62 Consider the growth of S. cerevisiae under aerobic condition in a bioreactor and the specific growth rate of yeast is 0.5 h-1. The overall reaction of the process is 2C6H12O6 +0.2NH3+10.35O2  CH1.8O0.5N0.2+0.2C2H6O+10.6CO2+10.8H2O The heat of combustion values for different compounds are tabulated below with the reference to CO2, H2O, O2, and N2 at standard conditions. Compound Heat of combustion (kJ mol-1) C6H12O6 2802 NH3 383 CH1.8O0.5N0.2 560 C2H6O 1366 The specific rate of heat production (rounded off to nearest integer) is _____________ kJ mol-1 h-1. .63 A pilot sterilization was carried out in a vessel containing 100 m 3 medium with an initial spore concentration of 10 8 spores/ml. The accepted level of contamination after sterilization is 1 spore in the entire vessel. The specific death rate constant for the spore is 2 min -1 at 121 ˚C. Assuming no death takes place during the heating and cooling cycles, the holding time at 121 ˚C (rounded off to nearest integer) is _____________min.

Biomolecules, enzyme kinetics

Consider a piston-cylinder assembly shown in the figure below. The walls of the cylinder are insulated. The cylinder contains 1 mole of an ideal gas at 300 K and the piston is held initially at the position z1 using a stopper. After the stopper is removed, the piston suddenly rises against atmospheric pressure (1.013×105 Pa) to the new position z2 where it is held by another stopper. The heat capacity (Cv) of the gas is 12.5 J mol-1 K-1. The cross-sectional area of the cylinder is 10-3 m2. Assume the piston is weightless and frictionless. If 𝑧ଶ− 𝑧ଵ = 1 m, the final temperature of the gas (rounded off to nearest integer) is ___________K.

Bioreactor types, scale-up

Consider the growth of S. cerevisiae under aerobic condition in a bioreactor and the specific growth rate of yeast is 0.5 h-1. The overall reaction of the process is 2C6H12O6 +0.2NH3+10.35O2  CH1.8O0.5N0.2+0.2C2H6O+10.6CO2+10.8H2O The heat of combustion values for different compounds are tabulated below with the reference to CO2, H2O, O2, and N2 at standard conditions. Compound Heat of combustion (kJ mol-1) C6H12O6 2802 NH3 383 CH1.8O0.5N0.2 560 C2H6O 1366 The specific rate of heat production (rounded off to nearest integer) is _____________ kJ mol-1 h-1.

Media Sterilization and Stoichiometry

A pilot sterilization was carried out in a vessel containing 100 m3 medium with an initial spore concentration of 108 spores/ml. The accepted level of contamination after sterilization is 1 spore in the entire vessel. The specific death rate constant for the spore is 2 min-1 at 121 ˚C. Assuming no death takes place during the heating and cooling cycles, the holding time at 121 ˚C (rounded off to nearest integer) is _____________min.

CRISPR-Cas9 gene editing

A circular plasmid has three different but unique restriction sites for enzymes 'a', 'b' and 'c.' When enzymes 'a' and 'b' are used together, two fragments of equal size are generated. Enzyme 'c' creates fragments of equal size only from one of the fragments generated by those cleaved by 'a' and 'b'. The plasmid is treated with a mixture of 'a', 'b' and 'c' and analysed by agarose gel electrophoresis. The number of bands observed in the gel is __________.

Mass transfer in bioprocesses (kLa)

A bacterial strain is grown in nutrient medium at 37 ˚C under aerobic conditions. The medium is inoculated with 102 cells from a seed culture. If the number of cells in the culture is 105 after 10 hours of growth, the doubling time of the strain (rounded off to nearest integer) is ____________h.