# Recent questions tagged gate2020

1
The number of molecules of a nucleotide of molecular weight $300\:g$/mol present in $10$ picomoles is ____________ $\times10^{12}$ (round off to $2$ decimal places).
2
To facilitate mass transfer from a gas to a liquid phase, a gas bubble of radius $r$ is introduced into the liquid. The gas bubble then breaks into $8$ bubbles of equal radius. Upon this change, the ratio of the interfacial surface area to the gas phase volume for the system changes from $3/r$ to $3n/r$. The value of $n$ is _____________________.
3
The largest eigenvalue of the matrix $\begin{bmatrix} 4 &1 \\ -2& 1 \end{bmatrix}$ is ______________.
4
A normal random variable has mean equal to $0$, and standard deviation equal to $3$. The probability that on a random draw the value of this random variable is greater than $0$ is __________ (round off to $2$ decimal places).
5
A variable $Y$ is a function of $t$. Given that $Y\left ( t=0 \right )=1$ and $Y\left ( t=1 \right )=2,\dfrac{dY}{dt}$ in the interval $t=\left [ 0,1 \right ]$ can be approximated as _________________.
6
A block of ice at $0 \:^{\circ}C$ is supplied heat at a constant rate to convert ice to superheated steam. Which one of the following trajectories correctly represents the trend of the temperature of the system with time? Assume that the Specific heat of $H_{2}O$ is not a function of temperature.
7
The $DNA$ sequence shown below is to be amplified by $PCR$: $5{}'$ GCTAAGATCTGAATTTTCC$\dots\dots$TTGGGCAATAATGTAGCGC$3{}'$ $3{}'$ CGATTCTAGACTTAAAAGG$\dots\dots$AACCCGTTATTACATCGCG$3{}'$ Which one of the following pair of primers can be used for this amplification? $5{}'$ ... $5{}'$ GCGCTACATTATTGCCCA$3{}'$ $5{}'$ GCTAAGATCTGAATTTTC$3{}'$ and $5{}'$ TGGGCAATAATGTAGCGC$3{}'$
8
Which of the following statements about immune response are $CORRECT$? $T$ cells are activated by antigen-presenting cells Foreign peptides are not presented to helper $T$ cells by Class $II$ $MHC$ proteins Dendritic cells are referred to as professional antigen- presenting cells $P$ and $R$ only $P$ and $Q$ only $Q$ and $R$ only $P, Q$ and $R$
9
Which of the following statemets are $CORRECT$ about eukaryotic cell cycle? $CDKs$ can phosphorylate proteins in the absence of cyclins $CDKs$ can be inactivated by phosphorylation Degradation of cyclins is required for cell cycle progression $CDKs$ are not involved in chromosome condensation $P$ and $R$ only $P$ and $S$ only $P, Q$ and $R$ only $Q$ and $R$ only
10
$W,X$ and $Y$ are the intermediates in a biochemical pathway as shown below: $S \cdots \cdots \rightarrow W\rightarrow X\rightarrow Y\rightarrow Z$ Mutants auxotrophic for $Z$ are found in four different complementation groups, namely $Z1$, $Z2$, $Z3$ and $Z4$. The ... $S \cdots \cdots \overset{Z4}{\rightarrow}W\overset{Z1}{\rightarrow}X\overset{Z2}{\rightarrow} Y\overset{Z3}{\rightarrow}Z$
11
In tomato plant, red ($R$) is dominant over yellow ($r$) for fruit color and purple ($P$) is dominant over green ($p$) for stem color. Fruit color and stem color assort independently. The number of progeny plants of different fruit/stem colors obtained from a mating ... the genotypes of the parent plants in this mating? $RrPp \times Rrpp$ $RrPp \times RrPp$ $RRPP \times rrpp$ $RrPP \times Rrpp$
12
Some of the cytokinins used in plant tissue culture media are given below: $BAP$ Zeatin Kinetin $2iP$ Which of these are synthetic analogs? $P$ and $Q$ only $Q$ and $S$ only $R$ and $S$ only $P$ and $R$ only
13
Carl Woese used the gene sequence of which one of the following for phylogenetic taxonomy of prokaryotes? A ribosomal $RNA$ of large ribosomal subunit A ribosomal $RNA$ of small ribosomal subunit A ribosomal protein of large ribosomal subunit A ribosomal protein of small ribosomal subunit
14
A list of pathogens $(Group\; I)$ and a list of anti-microbial agents $(Group\; II)$ ... $P-5, Q-2, R-4, S-1$ $P-2, Q-3, R-4, S-1$ $P-2, Q-3, R-1, S-5$
15
Determine the correctness or otherwise of the following Assertion [$a$] and the Reason [$r$]. Assertion [$a$]: Dam methylase protects $E$. coli $DNA$ from phage endonucleases Reason [$r$]: $E$. coli Dam methylase methylates the adenosine residue in the sequence "$GATC$" Both [$a$] and [$r$] ... $a$] Both [$a$] and [$r$] are false [$a$] is false but [$r$] is true
16
Determine the correctness or otherwise of the following Assertion [$a$] and the Reason [$r$]. Assertion [$a$]: Embryonic stem cells are suitable for developing knockout mice Reason [$r$]: Homologous recombination is more frequent in embryonic stem cells than that in somatic cells Both [$a$] and [$r$] ... $r$] are true, but [$r$] is not the correct reason for [$a$] [$a$] is true. but [$r$] is false
17
The schematic of a plasmid with a gap in one of the strands is shown below: Which of the following enzyme(s) is/are required to fill the gap and generate a covalently closed circular plasmid? $DNA$ ligase AIkaline phosphatase $DNA$ polymerase Polynucleotide kinase $P$ only $P, R$ and $S$ only $P$ and $R$ only $P, Q$ and $R$ only
18
Match sub-cellular organelles listed in $Group\; I$ with their features listed in $Group\; II$ ... $P-2, Q-3, R-4, S-1$ $P-3, Q-4, R-2, S-1$ $P-3, Q-1, R-4, S-2$
19
Which of the following strategies are used by cells for metabolic regulation? Phosphorylation-dephosphorylation Allostery Feedback inhibition $P$ and $Q$ only $P$ and $R$ only $Q$ and $R$ only $P, Q$ and $R$
20
Determine the correctness or otherwise of the following Assertion [$a$] and the Reason [$r$]. Assertion [$a$]: A zygote and its immediate descendant cells are unspecialized and are called totipotent Reason [$r$]: Totipotent cells retain the capacity to differentiate into only a few cell types Both [$a$ ... [$r$] are true and [$r$] is the correct reason for [$a$] [$a$] is true but [$r$] is false
21
Which of the following statements about gene therapy are CORRECT? Affected individuals, but not their progeny, can be cured through germline gene therapy Affected individuals, as well as their progeny, can be cured through germline gene therapy Affected individuals, but not their progeny, can be cured through ... gene therapy $P$ and $R$ only $P$ and $S$ only $Q$ and $R$ only $Q$ and $S$ only
22
Determine the correctness or otherwise of the following Assertion [$a$] and the Reason [$r$]. Assertion [$a$]: A genetically engineered rice that produces beta-carotene in the rice grain is called Golden rice Reason [$r$ ... [$r$] are true and [$r$] is the correct reason for [$a$] [$a$] is true but [$r$] is false
23
The sequence of a $1$ $Mb$ long $DNA$ is random. This $DNA$ has all four bases occurring in equal proportion. The number of nucleotides, on average, between two successive $EcoRI$ recognition site $GAATTC$ is ____________.
24
$E$ coli was grown in $^{15}N$ medium for several generations. Cells were then transferred to $^{14}N$ medium, allowed to grow for $4$ generations and $DNA$ was isolated immediately. The proportion of total $DNA$ with intermediate density is ___________ (round off to $2$ decimal places).
25
A batch reactor is inoculated with $1 \:g/L$ biomass. Under these conditions, cells exhibit a lag phase of $30$ min. If the specific growth rate in the log phase is $0.00417\;min^{-1}$, the time taken for the biomass to increase to $8 \:g/L$ is ________________ min (round off to $2$ decimal places).
26
The system of linear equations $cx+y=5$ $3x+3y=6$ has no solution when $c$ is equal to _______________________.
27
The amino acid sequence of a peptide is $Phe-Leu-lle-Met-Ser-Leu$. The number of codons that encode the amino acids present in this peptide is given below: Phe: $2$ codons Leu: $6$ codons Ile: $3$ codons Met: $1$ codon Ser: $4$ codons The number of unique $DNA$ sequences that can encode this peptide is ___________.
28
Assume that a cell culture was started with five human fibroblast cells. Two cells did not divide even once whereas the other three cells completed three rounds of cell division. At this stage, the total number of kinetochores in all the cells put together is ___________________.
29
Growth of an organism on glucose in a chemostat is characterized by Monod model with specific growth rate = $0.45 \:h^{-1}$ and $K_{s}= 0.5 \:g/L$. Biomass from the substrate is generated as $Y_{XS}=0.4 \:g/g$. The chemostat volume is $0.9\:L$ and media is fed at $1\:L/h$ and contains $20 \:g/L$ of glucose. At steady state, the concentration of biomass in the chemostat is _________________ $g/L$.
30
A function $f$ is given as : $f(X)=4X-X^{2}$ The function $f$ is maximized when $X$ is equal to _________________.
31
An infinite series $S$ is given as: $S=1+2/3+3/9+4/27+5/81+\:.\dots$ (to infinity) The value of $S$ is ______________________ (round off to $2$ decimal places).
32
Protein $A$ and protein $B$ form a covalent complex. Gel filtration chromatography of this complex showed a peak corresponding to $200 \:kDa$. $SDS-PAGE$ ... that the molecular weight of protein $A$ is $25 \:kDa$, the molecular weight of protein $B$ is ________________ $kDa$.
33
The concentrations of $ATP$, $ADP$ and inorganic phosphate in a cell are $2.59, \:0.73$ and $2.72 \:mM$, respectively. Under these conditions, free energy change for the synthesis of $ATP$ at $37^{\circ}C$ is $kJ$/mol (round off to $2$ decimal places). Given: free energy change for $ATP$ hydrolysis under standard conditions is $-30.5$ $kJ$/mol and $R=8.315$ $kJ/mol.K$
34
An algorithm was designed to find globins in protein sequence databases. A database which has $78$ globin sequences was searched using this algorithm. The algorithm retrieved $72$ sequences of which only $65$ were globins. The sensitivity of this algorithm is ___________ $\%$ (round off to $2$ decimal places).
35
The mitochondrial electron transfer chain oxidizes $NADH$ with oxygen being the terminal electron acceptor. The redox potentials for the two half-reactions are given below: $NAD^{+}+H^{+}+2e^{-}\rightarrow NADH,E^{0}{}'=-0.32V$ ... of electrons from $NADH$ to $O_{2}$ is _________________ $kJ/mol$ (round off to $2$ decimal places). Given: $F=96500\:C$/mol.
36
Hit by floods, the kharif (summer sown) crops in various parts of the country have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its ... target cannot be met due to floods. Officials hope that the food-grain production target will be met due to a good rabi produce.
37
The difference between the sum of the first $2n$ natural numbers and the sum of the first $n$ odd natural numbers is ______ $n^2-n$ $n^2+n$ $2n^2-n$ $2n^2+n$
Repo rate is the rate at which Reserve Bank of India $\text{(RBI)}$ lends commercial banks, and reverse repo rate is the rate at which $\text{(RBI)}$ borrows money from commercial banks. Which of the following statements can be inferred from ... of borrowing and decrease lending by commercial banks. Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.
$P,Q,R,S,T,U,V,$ and $W$ are seated around a circular table. $S$ is seated opposite to $W$ $U$ is seated at the second place to the right of $R$ $T$ is seated at the third place to the left of $R$ $V$ is a neighbour of $S$ Which of the following must be true? $P$ is a neighbour of $R$ $Q$ is a neighbour of $R$ $P$ is not seated opposite to $Q$ $R$ is the left neighbour of $S$
The distance between Delhi and Agra is $233$ km. A car $P$ started travelling from Delhi to Agra and another car $Q$ started from Agra to Delhi along the same road $1$ hour after the car $P$ started. The two cars crossed each other $75$ minutes after the car $Q$ started. Both ... car $Q$. How many kilometers the car $Q$ had travelled when the cars crossed each other? $66.6$ $75.2$ $88.2$ $116.5$