# Recent questions tagged gate2018

If $x^2 + x – 1 = 0$ what is the value of $x^4 + \dfrac{1}{x^4}$? $1$ $5$ $7$ $9$
To pass a test, a candidate needs to answer at least $2$ out of $3$ questions correctly. A total of $6,30,000$ candidates appeared for the test. Question A was correctly answered by $3,30,000$ candidates. Question B was answered correctly by $2,50,000$ candidates. Question C ... as the number answering none, how many candidates failed to clear the test? $30,000$ $2,70,000$ $3,90,000$ $4,20,000$
A set of $4$ parallel lines intersect with another set of $5$ parallel lines. How many parallelograms are formed? $2$0486072$0 votes 0 answers 4 An automobile travels from city A to city B and returns to city A by the same route. The speed of the vehicle during the onward and return journeys were constant at$60$km/h and 90 km/h, respectively. What is the average speed in km/h for the entire journey?$72737475$0 votes 0 answers 5 In a detailed study of annual crow births in India, it was found that there was relatively no growth during the period$2002$to$2004$and a sudden spike from$2004$to$2005$. In another unrelated study, it was found that the revenue from cracker sales ... birth rate. If cracker sale declines, crow birth will decline. Increased birth rate of crows will cause an increase in the sale of crackers. 0 votes 0 answers 6 Arrange the following three-dimensional objects in the descending order of their volumes: A cuboid with dimensions$10$cm,$8$cm and$6$cm A cube of side$8$cm A cylinder with base radius$7$cm and height$7$cm A sphere of radius$7$cm (i), (ii), (iii), (iv) (ii), (i), (iv), (iii) (iii), (ii), (i), (iv) (iv), (iii), (ii), (i) 0 votes 0 answers 7 For$0 \leq x \leq 2\pi$,$\sin x$and$\cos x$are both decreasing functions in the interval __________.$\bigg( 0, \dfrac{\pi}{2} \bigg) \\\bigg( \dfrac{\pi}{2}, \pi \bigg) \\\bigg( \pi, \dfrac{3\pi}{2} \bigg) \\\bigg(\dfrac{3 \pi}{2}, 2 \pi \bigg)$0 votes 0 answers 8 The area of an equilateral triangle is$\sqrt{3}$. What is the perimeter of the triangle?$2468$0 votes 0 answers 9 In spite of being warned repeatedly, he failed to correct his _________ behaviour." The word that best fills the blank in the above sentence is rational reasonable errant good 0 votes 0 answers 10 "When she fell down the __________, she received many __________ but little help." The words that best fill the blanks in the above sentence are stairs, stares stairs, stairs stares, stairs stares, stares 0 votes 0 answers 11 A rod shaped bacterium has a length of$2 \: \mu m$, diameter of$1 \mu m$and density the same as that of water. If proteins constitute$15 \%$of the cell mass and the average protein has a mass of$50$kDa, the number of proteins in the cell is __________ ($1$Da$= 1.6 \times 10^{-24}$g) 0 votes 0 answers 12 The product of complete digestion of the plasmid shown below with EcoRI and HaeIII was purified and used as a template in a reaction containing Klenow fragment of DNA polymerase, dNTPs and$[\alpha -^{32}P]$-dATP in a suitable reaction buffer. The ... purified and subjected to gel electrophoresis followed by autoradiography. The number of bands that will appear on the X-ray film is _____________ 0 votes 0 answers 13 Consider a simple uni-substrate enzyme that follows Michaelis-Menten kinetics. When the enzyme catalyzed reaction was carried out in the presence of$10$nM concentration of an inhibitor, there was no change in the maximal velocity. However. the slope of the Lineweaver-Burk plot increased$3$-fold. The dissociation constant for the enzyme-inhibitor complex (in nM) is ____________ 0 votes 0 answers 14 First order deactivation rate constants for soluble and immobilized amyloglucosidase enzyme are$0.03 \text{ min}^{-1}$and$0.005 \text{ min}^{-1}, respectively. The ratio of half-life of the immobilized enzyme to that of the soluble enzyme is (rounded off to the nearest integer) ___________ 0 votes 1 answer 15 Consider the following alignment of two DNA sequences:\mathbf{AGTAAC} \\ \mathbf{AA}\text{- -}\mathbf{AC}$Assuming an affine gap scoring scheme of an identity matrix for substitution, a gap initiation penalty of$1$and a gap extension penalty of$0.1, the score of the alignment is (up to one decimal place) __________ 0 votes 1 answer 16 At the end of a batch culture, glucose solution is added at a flow rate of200 \: ml/h$. If the culture volume after$2$h of glucose addition is$1000$ml, the initial culture volume (in ml) is _________ 0 votes 0 answers 17 Yeast converts glucose to ethanol and carbon dioxide by glycolysis as per the following reaction:$C_6H_{12}O_6 \to 2C_2H_5OH + 2CO_2$Assuming complete conversion, the amount of ethanol produced (in$g$) from$200 \: g$of glucose is (up to two decimal places) ____________ 0 votes 0 answers 18 Mammalian cells in active growth phase were seeded at a density of$1 \times 10^5$cells/ml. After$72$hours,$1 \times 10^6$cells/ml were obtained. The population doubling time of the cells in hours is (up to two decimal places) ________________ 0 votes 0 answers 19 In a chemostat, the feed flow rate and culture volume are$100$ml/h and$1.0$L, respectively. With glucose as substrate, the values of$\mu_{\text{max}}$and$K_s$are$0.2 \: h^{-1}$and$1 \: g/L$, respectively. For a glucose concentration of$10 \: g/L$in the feed, the effluent substrate concentration (in$g/L$) is _______ 0 votes 0 answers 20 If$1+r + r^2+ r^3 +\dots \infty = 1.5$, then,$1 + 2r + 3r^2 + 4r^3 + \dots \infty = $(up to two dcimal places) ________ 0 votes 0 answers 21 The probability distribution for a discrete random variable$X$is given below.$\begin{array}{|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 \\ \hline P(X) & 0.3 & 0.4 & 0.2 & 0.1 \\ \hline \end{array}$The expectation value of$X$is (up to one decimal place) _____________ 0 votes 0 answers 22 Calculate the following integral (up to two decimal places)$\displaystyle \int_0^1 (x + 3)(x + 1)dx = \text{ ___________}$0 votes 0 answers 23 A microbial strain is cultured in a$100$L stirred fermenter for secondary metabolite production. If the specific rate of oxygen uptake is$0.4 \: h^{-1}$and the oxygen solubility in the broth is$8 $mg/L, then the volumetric mass transfer coefficient$(K_La)$(in$s^{-1}$) of oxygen required to achieve a maximum cell concentration of$12$g/L is (up to two decimal places) ___________ 0 votes 0 answers 24 An aqueous solution containing$6.8$mg/L of an antibiotic is extracted with amyl acetate. If the partition coefficient of the antibiotic is$170$and the ratio of water to solvent is$85$, then the extraction factor is ________ 0 votes 0 answers 25 Moist heat sterilization of spores at$121 ^\circ C$follows first order kinetics as per the expression:$\dfrac{dN}{dt}=-k_dN$where,$N$is the number of viable spores,$t$I is the time,$k_d$is the rate constant and$\dfrac{dN}{dt}$is the rate of change ... reduce the number of viable spores from an initial value of$10^{10}$to a final value of$1$is (up to two decimal places) __________ 0 votes 0 answers 26$5'$capping of mRNA transcripts in eukaryotes involves the following events: Addition of GMP on the$5'$end Removal of$\gamma$-phosphate of the triphosphate on first base at the$5'$end$5'-5'$linkage between GMP and the first base at$5'$end Addition of methyl group to$N7$position of ... of the following is the correct sequence of events? P, Q, R, S P, R, Q, S Q, P, R, S Q, P, S, R 0 votes 0 answers 27 Match the industrial products mentioned in Group I with their producer organisms in Group II ...$\text{P-2, Q- 1, R- 4, S-3}\text{P- 3, Q- 1, R- 4, S-2}$0 votes 1 answer 28 A pedigree of an inheritable disease is shown below. What type of inheritance does the disease follow? Autosomal dominant X-linked dominant X-linked recessive Autosomal recessive 0 votes 1 answer 29 An analysis of DNA-protein interactions was carried out using all DNA-protein complexes in the protein data bank (PDB). The frequency distribution of four amino acid residues, represented as P, Q, R and S, occurring in non-covalent interactions between the protein and DNA backbone is shown below. Which one of the ... P-Gln, Q-Glu, R-Lys, S-Arg P-Asn, Q-Asp, R-Arg, S-Lys P-His, Q-Glu, R-Gln, S-Lys 0 votes 0 answers 30 Shear stress versus shear rate behavior of four different types of fluids (I, II, III and IV) are shown in the figure below. Which one of the following options is correct? I-Newtonian, II-Bingham plastic, III-Dilatant, IV-Pseudoplastic I-Pseudoplastic ... -Bingham plastic I-Newtonian, II-Pseudoplastic, III-Bingham plastic, IV-Dilatant I-Newtonian, II-Bingham plastic, III-Pseudoplastic, IV-Dilatant 0 votes 0 answers 31 Which of the following are true with regard to anaerobic respiration in bacteria? The final electron acceptor is an inorganic substance other than molecular oxygen The number of ATP molecules produced per glucose molecule is more than that produced in aerobic respiration The number of ATP molecules ... phosphorylation is used to generate ATP P and S only Q and S only P and R only P, Q and S only 0 votes 0 answers 32 Which of the following are true about bacterial superoxide dismutase? Present in obligate aerobes Present in facultative anaerobes Present in aerotolerant anaerobes Absent in obligate aerobes P and Q only P, Q and R only P and R only Q and S only 0 votes 0 answers 33 Which one of the following statements is true with regard to processing and presentation of protein antigens? In the class II MHC pathway, protein antigens in the cytosol are processed by proteasomes In the class I MHC pathway, extracellular protein antigens ... generated in the cytosol Invariant chain in endoplasmic reticulum is involved in transport of peptides and loading of class I MHC 0 votes 0 answers 34 Which one of the combinations of the following statements is true about antibody structure? Limited proteolysis of rabbit IgG with the enzyme pepsin generates two antigen-binding regions (Fab) and an Fc fragment. Limited proteolysis of rabbit IgG with the enzyme papain generates a single bivalent ... is composed of both light and heavy chains. P and Q only P and R only R and S only Q and S only 0 votes 0 answers 35 Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]: Assertion: The association constant in water for the G-C base pair is three times lower than that for the A-T base pair. Reason: There are three hydrogen bonds in the G-C base pair and two in the A-T ... r] is true Both [a] and [r] are false Both [a] and [r] are tme and [r] is not the correct reason for [a] 0 votes 0 answers 36 Which one of the following amino acids is catalyzed by activated macrophages to produce reactive nitrogen species? Arginine Asparagine Cysteine Histidine 0 votes 1 answer 37 Determine the correctness or otherwise of the following Assertion [a] and the Reason [r] Assertion: Ab initio gene finding algorithms that predict protein coding genes in eukaryotic genomes are not completely accurate. Reason: Eukaryotic splice sites are difficult to predict. Both [a] and [r] are ... is the correct reason for [a] Both [a] and [r] are true but [r] is not the correct reason for [a] 0 votes 0 answers 38 Match the classes of RNA molecules in$\text{Group I}$with their functions in$\text{Group II}$...$\text{P-1, Q-3, R-2, S-5}\text{P-1, Q-4, R-5, S-2}\text{P-4, Q-1, R-2, S-5}$0 votes 0 answers 39 The variable$z$has a standard normal distribution. If$P(0 \leq z \leq 1)= 0.34$then$P(z^2 > 1)$is equal to (up to two decimal places) ____________ 0 votes 0 answers 40 The determinant of the matrix$\begin{pmatrix} 4 & -6 \\ -3 & 2 \end{pmatrix}\$ is _________