Recent questions without answers

A value of $k$ for which the linear equations $(k-1) x+3 y=0$ and $2 x+k y=0$ have a non-zero solution is $\_\_\_\_\_\_\_$.$1$$2$$3$$4$

The value of the series $1+\sin x+\cos ^{2} x+\sin ^{3} x+\cdots$ at $x=\frac{\pi}{4}$ is $\_\_\_\_\_\_\_$.$\frac{1}{\sqrt{2}+1}$$\frac{\sqrt{2}}{\sqrt{2}+1}$$\frac{1}{\s...

The solution of the differential equation $\frac{d y}{d x}=y+e^{-x}$ that satisfies $y(0)=-\frac{1}{2}$ is $\_\_\_\_\_\_\_$.$-\frac{1}{2} e^{-\frac{x}{2}}$$-\frac{1}{2} e...

The six faces of a cube (die) are numbered as $1,2,3,4,5$ and $6$, and it is rolled once. An outcome is the observed number on the top face. If the probability of getting...

Match the industrial enzyme (Column I) with its application (Column II).\begin{array}{|c|c|c|}\hline \text{Column I} & \text{Column II} \\\hline \text{P. Lipase} & 1. \...

Match the enzyme (Column I) with its corresponding function (Column II).\begin{array}{|c|c|c|}\hline & \text{Column I} & \text{Column II} \\\hline & \text{P. Primase} & 1...

Match the item (Column I) with its corresponding use (Column II).\begin{array}{|c|c|c|}\hline \text{Column I} & \text{Column II} \\\hline \text{P. Glutamine} & 1. \text{D...

Match the chemical (Column I) with its use (Column II).\begin{array}{|c|c|c|}\hline \text{Column I} & \text{Column II} \\\hline \text{P. Diethylpyrocarbonate} & 1. \text{...

Match the item in Column I with the corresponding technique in Column II.\begin{array}{|c|c|c|}\hline & \text{Column I} & \text{Column II} \\\hline & \text{P. Blue laser}...

Match the genetic disorder (Column I) with its molecular basis (Column II).\begin{array}{|c|c|c|}\hline \text{Column I} & \text{Column II} \\\hline \text{P. Sickle-cell a...

The evolution of wings in bats and insects is an example of $\_\_\_\_\_\_\_$ evolution.convergentdivergentneutralparallel

Which of the following statements is/are correct about an uncompetitive inhibitor of an enzyme?It binds to the substrate binding site of the enzyme onlyIt binds to the en...

Which of the following plant-based secondary metabolites belong(s) to the class of alkaloids? Ajmalicine $\left(\mathrm{C}_{21} \mathrm{H}_{24} \mathrm{~N}_2 \mathrm{O}_3...

Which of the following features help(s) in distinguishing alleles using restriction fragment length polymorphism (RFLP)?Differences in the number of recognition sites for...

Which of the following is/are considered as biotic elicitor(s) in plant cell culture?CellulaseChitinChitosanMercuric chloride

Under which of the following conditions, a mammalian somatic cell fails to undergo mitosis during cell cycle?Initiation of cell plate formationIncomplete DNA replicationC...

Which of the following is/are synthetic auxin(s) that does/do NOT occur naturally?$2,4$-Dichlorophenoxyacetic acid Indole-$3$-acetic acidIndole-$3$-butyric acid$1$-Naphth...

Which of the following statements regarding the below mentioned mRNA sequence is/are TRUE?$5'-\text{UGAUGAGCCUUAACCGGGAACGAAUUUAAG}-3'$It contains nine codons in the read...

Which of the following conditions induce(s) the expression of $\beta$-galactosidase gene in the lac operon?Absence of glucoseAbsence of lactosePresence of glucosePresence...

Which of the following factors can affect the growth of a microbial culture in a batch cultivation process?$\mathrm{pH}$ of the medium Osmolarity of the mediumSubstrate c...

Under complete cell washout condition in a chemostat with sterile feed, which of the following statements is/are correct?Biomass concentration in the reactor is maximumS...

Aspergillus niger is grown in a $10,000$ L stirred batch bioreactor under aerated conditions to produce citric acid. At steady state oxygen transfer conditions, the speci...

Ethanol is produced in a $10,000$ L stirred bioreactor using an impeller of diameter $1 \mathrm{~m}$. The density and viscosity of fermentation broth are $1000 \mathrm{~k...

The free energy change of ATP hydrolysis at $25^{\circ} \mathrm{C}$ is $-32.2 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The free energy change for hydrolysis of $\alpha$-glycerop...

A fermentor is filled with medium at a rate of $1 \mathrm{~L} \mathrm{~min}^{-1}$. A leak develops at the bottom of the fermentor when the medium in the fermentor reaches...

Consider scale-up of fungal fermentation from a $20 \mathrm{~L}$ model-type to $20,000 \mathrm{~L}$ prototype stirred tank reactor. The model-type and prototype have the ...

The value of the limit $\lim _{x \rightarrow \infty} \frac{x}{2} \ln \left(1+\frac{2024}{x}\right)$ is $\_\_\_\_\_\_\_\_$.

Let $y(x)=x^2 \ln x$ for $x>0$, be a solution of $x^2 \frac{d^2 y}{d x^2}+4 y=\alpha x \frac{d y}{d x}$. Then the value of $\alpha$ is $\_\_\_\_\_\_\_\_\_$.

The absolute relative error in evaluating the integral $\int_0^1 x^2 d x$ by the trapezoidal rule with the step size $0.25$ is $\%$ $\_\_\_\_\_\_\_\_$ (rounded off to $2$...

If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words $[$ dry $\rightarrow$ arid $\rightarrow$ parched] is analogous to [diet $\righta...

In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks.Steve was advised to keep his head __(i)_ before heading _(ii)__ to bat; for...

A rectangular paper sheet of dimensions $54 \mathrm{~cm} \times 4 \mathrm{~cm}$ is taken. The two longer edges of the sheet are joined together to create a cylindrical tu...

The pie chart presents the percentage contribution of different macronutrients to a typical $2,000$ $\mathrm{kcal}$ diet of a person.The typical energy density $(\mathrm{...

A rectangular paper of $20 \mathrm{~cm} \times 8 \mathrm{~cm}$ is folded $3$ times. Each fold is made along the line of symmetry, which is perpendicular to its long edge....

The least number of squares to be added in the figure to make AB a line of symmetry is$6$$4$ $5$ $7$

A batch cultivation of E. coli follows zeroth order Monod’s growth kinetics. The cell growth is terminated when the residual dissolved oxygen concentration attains 10% of...

Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that th...

The World Bank has declared that it does not plan to offer new financing to Sri Lanka, which is battling its worst economic crisis in decades, until the country has an ad...

The coefficient of $x^{4}$ in the polynomial $(x-1)^{3}(x-2)^{3}$ is equal to __________.$33$$-3$$30$$21$

Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spa...