List of top Questions asked in GATE XL

Imagine a population of diploid species in Hardy-Weinberg equilibrium. The population has two alleles for a gene which are ‘a’ and ‘A’. The number of individuals with ‘aa’ genotype in this population is 1 in 10000. The frequency of the allele ‘A’ in the population is ............ (up to two decimal places)
The \( F_{121} \) value of a known microorganism with \( Z \) value of \( 11^\circ C \) is 2.4 min for 99.9999% inactivation. For a 12D inactivation of the said microorganism at \( 143^\circ C \), the \( F \) value (in min) is .......... {(rounded off to 3 decimal places)}
In a typical grinding operation, 80% of the feed material passes through a sieve opening of 4.75 mm; whereas, 80% of the ground product passes through 0.5 mm opening. If the power required to grind 2 tonnes/h of the feed material is 3.8 kW, the work index of the material is ........ (rounded off to 2 decimal places)
The true density and bulk density of wheat grains are 1280 kg/m\(^3\) and 740 kg/m\(^3\), respectively. The porosity of the grains is ......... (rounded off to 2 decimal places).
A PCR was setup to amplify a 500 nucleotides-long DNA. The dNTPs in the reaction mixture were radiolabeled. The percentage (%) of radiolabeled single-stranded DNA after three cycles will be ............ (up to one decimal place)
The mother and the father of five children are carriers (heterozygous) of an autosomal recessive allele that causes cystic fibrosis. The probability of having exactly three normal children among five is ........ (up to two decimal places).
An enzyme, which follows Michaelis-Menten equation, catalyzes the reaction A\(\rightarrow\)B. When enzyme and substrate concentrations are 15 nM and 10 \(\mu\)M, respectively, the reaction velocity is 5 \(\mu\)M s\(^{-1}\). If \(K_m\) for the substrate A is 5 \(\mu\)M, the kinetic efficiency of the enzyme will be ______ \(\times 10^6\) M\(^{-1}\) s\(^{-1}\) (in integer).
The true density and bulk density of wheat grains are 1280 kg/m\(^3\) and 740 kg/m\(^3\), respectively. The porosity of the grains is ......... (rounded off to 2 decimal places).
The \( F_{121} \) value of a known microorganism with \( Z \) value of \( 11^\circ C \) is 2.4 min for 99.9999% inactivation. For a 12D inactivation of the said microorganism at \( 143^\circ C \), the \( F \) value (in min) is .......... {(rounded off to 3 decimal places)}
In a typical grinding operation, 80% of the feed material passes through a sieve opening of 4.75 mm; whereas, 80% of the ground product passes through 0.5 mm opening. If the power required to grind 2 tonnes/h of the feed material is 3.8 kW, the work index of the material is ........ (rounded off to 2 decimal places)
E. coli is grown exclusively in a medium containing \(^{15}NH_4Cl\) as the sole nitrogen source. Subsequently, the cells were shifted to a medium containing \(^{14}NH_4Cl\). The molar ratio of hybrid DNA (\(^{15}N-^{14}N\)) to light DNA (\(^{14}N-^{14}N\)) after four generations (rounded off to two decimal places) will be .......
If an egg cell of a diploid plant species has 10 chromosomes, the expected number of chromosomes in a double trisomic somatic cell of this species would be ............. (Answer in integer).
In a genetic cross between a true-breeding tall parent bearing red flowers and a true-breeding dwarf parent bearing white flowers, only tall plants with red flowers are obtained in the F$_1$ population. Considering these two traits segregate independently, if one tall individual is selected from the F$_2$ population, the probability that it would be genotypically homozygous for plant height and make red flowers is ........... {(Round off to two decimal places)}
The doubling time of {Escherichia coli is 30 minutes in a culture medium containing glucose and yeast extract. Phage T7 has a life cycle of 20 minutes and a burst size of 200 phage per infected {E. coli} cell. Phage absorption is instantaneous and occurs at 1 multiplicity of infection (MOI). Bacteria infected with multiple or single phage give the same burst. 5000 plaque forming units of T7 phage are added to a culture of \( 2 \times 10^7 \) {E. coli} cells. Assuming normal division, the {E. coli} culture will lyse completely by ........ full cycles of bacterial division. (Answer in integer)}
A polymerase chain reaction (PCR) based diagnosis test was performed on a bacterial sample targeting a specific gene. There are 3 copies of this gene in the bacterial genome. Prior to DNA extraction, the bacteria were incubated to allow one cycle of growth. 3072 amplicon copies were obtained after 9 cycles of the PCR. Assume 100% efficiency at each step. The initial bacterial count in the sample was ....... (Answer in integer)
Consider the two \( pK_a \) values of valine as 2.32 and 9.62. The isoelectric point (pI) of this amino acid is ....... (rounded off to two decimal places)
Energy of the transition from \( n_h = 4 \) to \( n_l = 2 \) for hydrogen atom is \( E \times 10^3 \) cm\(^{-1}\).
Given: Rydberg constant for hydrogen: \( 1.097 \times 10^7 \, {m}^{-1} \)
Value of E is ............... (rounded off to two decimal places)
A non-volatile solute has a molecular weight of 180 g mol\(^{-1}\). Assume that the solute does not associate or dissociate in water, and the boiling-point constant (ebullioscopic constant) of water is 0.51 K kg mol\(^{-1}\).
The amount (in g) of solute added to 500 g of water to elevate the boiling point by 0.153 K is ............... (answer in integer)
The standard potentials (\( E^\circ \)) for the Fe\(^{3+}\)/Fe and Fe\(^{3+}\)/Fe\(^{2+}\) couples are -0.04 V and +0.76 V, respectively.
Given: Faraday constant = 96500 C mol\(^{-1}\)
The value for \( E^\circ \) (Fe\(^{2+}\)/Fe) in V is ............... (rounded off to two decimal places)
The equilibrium dissociation constant of acetic acid is \( 1.74 \times 10^{-5} \) M. The \( pK_a \) of acetic acid (rounded off to one decimal place) is ......
The DNA double helix measures 0.34 nm/bp. The diameter of a nucleosome core particle is 11 nm. If the ratio of wrapped DNA length to nucleosome diameter is 4.51, the length of DNA around the nucleosome (to the nearest integer) is ...... bp.
The temperature dependence of reaction rates is generally given by the Arrhenius equation. A plot of \( \ln k_r \) against \( 1/T \) is a straight line from which the pre-exponential factor ‘\( A \)’ and the activation energy ‘\( E_a \)’ can be determined.
The CORRECT option regarding this plot is:

An electricity utility company charges ₹7 per kWh. If a 40-watt desk light is left on for 10 hours each night for 180 days, what would be the cost of energy consumption? If the desk light is on for 2 more hours each night for the 180 days, what would be the percentage-increase in the cost of energy consumption?
 

The \( F_{121} \) value of a known microorganism with \( Z \) value of \( 11^\circ C \) is 2.4 min for 99.9999% inactivation. For a 12D inactivation of the said microorganism at \( 143^\circ C \), the \( F \) value (in min) is .......... (rounded off to 3 decimal places)

Consider a five-digit number PQRST that has distinct digits P, Q, R, S, and T, and satisfies the following conditions:
1. \( P<Q \)
2. \( S>P>T \)
3. \( R<T \)
If integers 1 through 5 are used to construct such a number, the value of P is: