List of top Questions asked in GATE BT- 2023

Fabry disease in humans is a X-linked disease. The probability (in percentage) for a phenotypically normal father and a carrier mother to have a son with Fabry disease is ________________.

Temperature of a reaction with an activation energy value of 15 kcal mol\(^{-1}\) is increased from 300 K to 310 K. If the value of the ideal gas constant (R) is 1.9872 cal mol\(^{-1}\) K\(^{-1}\), the ratio of the reaction rate constants \(\left(\frac{k_{310}}{k_{300}}\right)\) (rounded off to two decimal places) is ____________.

References : __________ : Guidelines : Implement (By word meaning)

An enzyme (E) catalyzes the biochemical reaction \(A \rightarrow B\) with \(k_{\text{cat}}=500~\text{s}^{-1}\). If the initial reaction velocity \((V_0)\) is \(10~\mu\text{M}\cdot\text{s}^{-1}\) at the total enzyme concentration \([E_t]=30~\text{nM}\) and substrate concentration \([A]=40~\mu\text{M}\), the value of \(K_m\) (in \(\mu\text{M}\)) is ________________.

Match the immune tolerance mechanisms in Group I with their respective outcomes in Group II

Group I	Group II
P) Anergy	1) Elimination of activated T-cells after antigen clearance
Q) Activation-induced cell death	2) Inhibition of auto-reactive T-cells at periphery
R) Receptor editing	3) Unresponsiveness to antigens due to lack of co-stimulatory molecules
S) Regulatory T-cells	4) Elimination of auto-reactive B-cells

Match the type of bacteria in Group I with their respective growth properties in Group II

Group I	Group II
P) Halophile	1) Grows optimally between 20°C and 45°C
Q) Piezophile	2) Grows best at low water activity
R) Mesophile	3) Grows at high level of salt
S) Xerophile	4) Grows optimally at high hydrostatic pressure

E. coli cultivated at 298 K uptakes an uncharged compound (A) by passive diffusion. The intracellular and extracellular concentrations of A are 0.001 M and 0.1 M, respectively. If \(R=1.9872\ \mathrm{cal\ mol^{-1}\ K^{-1}}\), the free-energy change (in \(\mathrm{kcal\ mol^{-1}}\)) for this passive diffusion of A (rounded off to two decimal places) is ________________.

E. coli is cultivated in a chemostat operated at a dilution rate of 0.2 h\(^{-1}\). The values of biomass yield due to oxygen consumption and the steady state biomass concentration are 0.2 g g\(^{-1}\) and 10 g L\(^{-1}\), respectively. The oxygen transfer rate (in g L\(^{-1}\) h\(^{-1}\)) is ____________.

If \(f(x)=\dfrac{\sin x+\cos x}{\sin x-\cos x}\), the value of \(f'(x)\) at \(x=0\) is ________________.

A dNTP master-mix is prepared by combining \(40~\mu\text{L}\) of each \(20~\text{mM}\) dNTP stock (dATP, dCTP, dGTP and dTTP). \(4~\mu\text{L}\) of this dNTP master-mix is added to a PCR mix and the final volume is adjusted to \(50~\mu\text{L}\). The concentration (in \(\mu\text{M}\)) of total dNTPs in the PCR mix is ________________.

If \(A=\begin{pmatrix}1 & 2 \\ 3 & 5\end{pmatrix}\), the value of \(\left|A^{4}+3A^{2}-5A+6I\right|\) is ________________.

If \(f(2)=5\) and \(f(x)\,f(x+1)=3\) for all real \(x\), the value of \(f(10)\) is ________________.

Ten playing cards numbered \(1,\ldots,10\) are drawn with replacement. What is the probability that the second number is greater than the first (rounded to two decimal places)?

The values of the consistency index ‘\(K\)’ and the flow behavior index ‘\(n\)’ of a dilatant fluid are 0.415 (in CGS units) and 1.23, respectively. The value of the apparent viscosity (in \( g \cdot cm^{-1} \cdot s^{-1} \)) of this fluid at a shear rate of 60 \( s^{-1} \) (rounded off to the nearest integer) is __________________.

An evaporator is insulated using glass wool material of \(0.15\ \text{m}\) thickness. The inner most surface and the outer surface of the insulation are at \(700^{\circ}\text{C}\) and \(80^{\circ}\text{C}\), respectively. The mean thermal conductivity of the glass wool under these conditions is \(0.29\ \text{W}\,\text{m}^{-1}\,\text{K}^{-1}\). The rate of heat loss (in W) through \(1.2\ \text{m}^2\) of the evaporator wall surface (rounded off to the nearest integer) is ________________.

A proportional controller is used to control the temperature of an autoclave from \(60^{\circ}C\) to \(130^{\circ}C\). If the proportional band setting of the controller is 25%, the proportional gain value is ______________.

If there are three unrooted trees for four protein sequences, the number of rooted trees for the same number of sequences is ________________.

The number of different possible ways of forming five intramolecular disulfide bonds with ten cysteine residues of a protein is ________________.

The following schematic diagram shows a chemostat with cell recycle (feed flow rate \(F_0\) and recycle flow rate \(F_r\) in \(\mathrm{L\,h^{-1}}\)). The cell concentrations in the reactor, recycle stream, and product stream are \(X_1\), \(X_0\), and \(X\) (in \(\mathrm{g\,L^{-1}}\)), respectively. If \(\dfrac{X_0}{X_1}=1.5\), \(\dfrac{F_r}{F_0}=0.7\), and \(X_1=7.3~\mathrm{g\,L^{-1}}\), the value of \(X\) (in \(\mathrm{g\,L^{-1}}\), rounded off to one decimal place) is ________________.