If A(n) represents the area bounded by the curve \[y=n.\ell nx,\] where \[n\,\,\in \,\,N\] and n > 1, the x-axis and the lines x = 1 and x = e, then the value of \[A(n)+nA(n-1)\] is equal to -
If \[p({{x}_{1}},{{y}_{1}}),\]\[Q({{x}_{2}},{{y}_{2}}),\]\[R({{x}_{3}},{{y}_{3}}),\] and \[S({{x}_{4}},{{y}_{4}})\] are four cyclic points on a rectangular hyperbola \[ay\text{ }=\text{ }{{c}^{2}}\] the coordinate of the orthocenter of the APQ are -
If \[\underset{x\to 0}{\mathop{Lim}}\,\,\,\frac{{{729}^{x}}-{{243}^{x}}-{{81}^{x}}+{{9}^{x}}+{{3}^{x}}-1}{{{x}^{3}}}=K{{(\ell n3)}^{3}}\] then K is equal to -
If \[{{\vec{e}}_{1}}\] & \[{{\vec{e}}_{2}}\] are two unit vectors and \[\theta \] is the angle between them, then sin \[\left( \frac{\theta }{2} \right)\] is -
A pulley system with frictionless massless puller and ideal string is used to lift a weight of 100 N. F is the force that is sufficient to lift the load.
Water flows out from a beaker through a capillary of length 200 mm and diameter 2 mm.
Density of water is \[1000\,kg\,{{m}^{-\,3}}\]and its viscosity is 0.8 centipoise. If a level of 5 cm is continuously maintained in the beaker, then flow rate through capillary is nearly
Let's assume that our atmosphere consists only of nitrogen gas with molecular mass is nearly \[4.5\times {{10}^{-26}}\,kg.\] If mean temperature of earth is taken as \[27{}^\circ C,\] then height of our atmosphere is nearly
A container is separated into two chambers A and B of equal volumes by a conducting wall.
Heat cannot leave or enters the chambers A and B from outer boundary except through partition AB. Compartment A is filled with hot gas and compartment B is filled with same cold gas in equal amount. Hot gas cool down from \[65{}^\circ C\] to \[63{}^\circ C,\]choose correct,
Consider a block held stationary over a rough incline by applying a force F parallel to the incline as shown below.
Force applied is initially, \[{{F}_{i}}=mg\,(\sin \theta -{{\mu }_{s}}\cos \theta )\] and is increased finally to \[{{F}_{f}}=mg\,(\sin \theta -{{\mu }_{K}}\cos \theta ),\]
where \[{{\mu }_{s}}\] and \[{{\mu }_{K}}\] are coefficient of friction and \[\theta \] is angle of inclination. Now, correct graph of F (Force) versus f (friction) is
A typical atomic nucleus is about \[5\times {{10}^{-15}}m\] in radius. Using uncertainty principle, the least value of energy of an electron so that it resides in nucleus is around (Use \[\frac{h}{2\pi }=1.054\times {{10}^{-\,34}}Js)\]
A long copper wire carries a steady current. Force on an electron moving with drift speed on surface of wire will be take current in wire \[I=10A,\] radius of wire \[a=0.5\,mm\] and number of conduction electrons in wire \[n=5\times {{10}^{28}}{{m}^{-\,3}}.\]
A thin metallic disc of radius R is rotating with constant angular velocity co about a vertical axis that is perpendicular to plane of disc and passes through its centre.
Rotation causes free electrons in the disc to redistribute. If there is no external electric or magnetic field is present, then potential difference between centre and rim of disc is
An ideal gas is adiabatically compressed to one tenth of its initial volume. Ratio of final temperatures \[{{T}_{A}}\] and \[{{T}_{B}}\] will be (where, in case A a monoatomic gas is taken and in case B a diatomic gas is taken)
In a wind tunnel used to test drag force on car using their models a 20 cm high car model is used for testing a car 550 cm high. Let you want to calculate drag force on car, when it is moving at \[15\,m{{s}^{-1}}\] in still air. Wind speed in the tunnel must be kept around
The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383 K is: (Specific heat of water liquid and water vapours are 4.2 \[{{\text{K}}^{-1}}\]\[\text{k}{{\text{g}}^{-1}}\] and 2.0 kJ \[{{\text{K}}^{-1}}\]\[{{\text{k}}^{-1}}\] heat of liquid fusion and vapourisation of water are 334 kJ \[\text{k}{{\text{g}}^{-1}}\]and 2491 kJ \[\text{k}{{\text{g}}^{-1}}\]respectively) (log 273 = 2.436, log 373 = 2.572, log 383 = 2.583)
For the following reaction the mass of water produced from 445 \[{{C}_{57}}{{H}_{110}}{{O}_{6}}\] is \[2{{C}_{57}}{{H}_{110}}{{O}_{6}}(s)+163{{O}_{2}}(g)\to 114C{{O}_{2}}(g)+110{{H}_{2}}O(l)\]
For the reaction, \[2A+B\to \] products, when the concentrations of A and B both were doubled, the rate of the reaction increased from 0.3 mol \[{{L}^{-\,1}}{{s}^{-\,1}}\] to 2.4 mol \[{{L}^{-\,1}}{{s}^{-\,1}}.\] When the concentration of A alone is doubled, the rate increased from 0.3 mol \[{{L}^{-\,1}}{{s}^{-\,1}}\] 0.6 mol \[{{L}^{-\,1}}{{s}^{-\,1}}.\] Which one of the following statements is correct?
If the standard electrode potential for a cell is V at 300 K, the equilibrium constant (K) for the reaction \[Zn(s)+C{{u}^{2+}}(aq)Z{{n}^{2+}}(aq)+Cu(s)\] At 300 K is approximately \[(R=8j{{K}^{-\,1}}mo{{l}^{-\,1}},F=96000Cmo{{l}^{-1}})\]
Assume a thylakoid is somehow punctured so that the interior of the thylakoid is no longer separated from the stroma. This damage will have the most direct effect on which of the following processes?
A)
Splitting of water.
doneclear
B)
Absorption of light energy by chlorophyll.
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C)
Flow of electrons from photosystem II to photosystem I.
Because of the relatively high altitude of Antonito, Colorado, the town has a normal barometric pressure of about 600 mm Hg rather than 760 mm Hg at sea level. The partial pressure of oxygen in Antonito's air is approximately
If you could selectively neutralise the active transport mechanisms at the axon terminals of a neuron, which of the following processes would you most significantly impact?
A)
Fusion of synaptic vesicles with the presynaptic membrane.
doneclear
B)
Uptake of released neurotransmitter by the presynaptic cell.
Ecologists and evolutionary biologists have proposed various hypothesis; some important ones are:
(I) Speciation is generally a function of time.
These regions have witnessed frequent\ glaciations in the past-A
(II) Areas that have remained relatively undisturbed for millions of years and thus had a long evolutionary time for species diversification - B
(III) An environment which is less seasonal, relatively more constant and predictable. Such constant environments promote niche specialisation and lead to a greater species diversity-C
(IV) There is more solar energy available in the _D_. It contributes to higher productivity this in turn might contribute indirectly to greater diversity.
One chromosome of a homologous pair carries the genes J and K. The other chromosome of the pair carries the genes j and k at corresponding loci. Crossing over results in exchange of chromosome segments and production of gametes with new combinations of genes. A recombinant type gamete resulting from this crossover might contain:
The graph shows the amount of product formed by a standard concentration of enzyme and a standard concentration of substrate at a temperature of \[20{}^\circ C.\]
Which graph shows the effect on the activity of the enzyme of decreasing the temperature to\[15{}^\circ C\]?
In human ABO blood group system, there are six possible genotypes but only four phenotypes. An explanation of this is that the ABO blood groups are controlled by
A)
One gene locus with three incompletely dominant (co-dominant) alleles.
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B)
One gene locus with two incompletely dominant (co-dominant) alleles and two recessive alleles.
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C)
One gene locus with two incompletely dominant (co-dominant) alleles and one recessive allele.
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D)
Two unlinked gene loci each with two alleles, one dominant and one recessive.
In addition to the normal process of oxidation of carbohydrates through glycolysis and Krebs cycle, there is another process by which plants could oxidise carbohydrates to obtain energy. In this process, hexose sugars undergo oxidative degradation through 5-C sugar intermediates and hence it is known as pentose phosphate pathway (PPP). Which of the following statements is not true with regard to PPP?
A)
It is an alternative to glycolysis and also acts as a safety valve or shunt to glycolysis.
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B)
It is common in plants and occurs in certain specialised tissues of animal body e.g., liver, adipose tissue, testes, ovary, adrenal cortex, lactating mammary gland, eye lens and cornea.
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C)
It occurs only in cytoplasm but not in any cell organelle. .
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D)
It is also called as Hexose Monophosphate shunt (HMP pathway).
If the protein hormone insulin from several mammalian species has similar activity in regulating sugar metabolism when injected into another species, which of the following is most appropriate?
A)
Primary structures of insulin from different species are identical.
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B)
Somewhat different amino acid sequences may yield similar 3- dimensional conformations.
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C)
Three-dimensional conformation has little relation to biological activity.
Which of the following statements about the life cycle of the HIV (Human Immunodeficiency Virus) are false?
(I) The HIV particles recognise the host cell through the sialic acid containing proteins or lipids on the membrane of the host cell.
(II) Upon entry of the HIV into the host cell, a drop of pH will result in a conformational change in the HIV structure, consequently releasing the viral genome into the host cell.
(III) The viral DNA which enters the host cell's nucleus will be integrated into the genetic material of the host cell using the host cell's enzyme, integrase.
(IV) The viruses are released from the host cell by exocytosis.
The leaf colour of certain plants is controlled by one gene. For that gene, the allele G = orange and g - green. You have a plant with orange leaves but do not know whether that plant's genotypes is GG or Gg. If you cross your unknown plant with one of the plants whose genotype is listed below, you will be able to determine your unknown's genotype. With which plant would you cross it?
Two tubes labelled 'P' and 'Q' contain food stuff. Tube 'P' gave positive test with Benedict's solution while tube 'Q' gave positive test with nitric acid. Which of the following is correct?
A)
Tube 'P' contains sugar, tube 'Q' contains protein
A couple have been trying to conceive a child for over a year without success. Recently, the man's doctor informed him that his seminal vesicles are defective. This means that
A)
The man makes functional sperm but they are not delivered because he is unable to ejaculate.
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B)
The man's sperm lack functional flagella.
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C)
The fluid needed to lubricate the man's urethra for easier sperm travel is defective.
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D)
The man's semen lacks the fructose fuel needed for the sperm to swim.
To study the genetic basis of the inherited human disease sickle-cell anemia, a biologist must first isolate DNA from an affected individual's cells. The next step is to use
A)
Restriction enzymes that break the DNA into small pieces at known points.
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B)
Gel electrophoresis to separate the DNA from other cell fragments.
If \[\left| \,z-4+3i\, \right|\le 1\,\,and\,\,\alpha \,\,and\,\,\beta \] and a and p be the least and greatest values of \[\left| \,z\, \right|\] and \[k\] be the least value of \[\frac{{{x}^{4}}+{{x}^{2}}+4}{x}\] on the x interval \[(0,\infty )\] then k is equal to-
There are twenty bags each containing 10 bulbs and it is known that no bag contains more than 5 defective bulbs and 3 bags have 5 defective bulbs. 4 bags have atleast 4 defective bulbs, 5 bags have atleast 3 defective bulbs, 6 bags have atleast 2 defective bulbs and 7 bags have atleast 1 defective bulb. Then the ratio of total defective bulbs is to non-defective bulbs is ?
If S be the sum of coefficients in the expansion of \[{{(px+qy-rz)}^{n}}\] (where p, q, r > 0) then the value of \[\underset{n\to \infty }{\mathop{\lim }}\,\,\,\,\frac{S}{{{({{S}^{1/n}}+1)}^{n}}},\] is:
If A, B and C are exhaustive events satisfying \[P\,\,((A\cup B)\cap \overline{C}=\frac{1}{5},\]\[P\,\,(B\,\cap \,C)-P\,\,(A\,\cap \,B\,\cap \,C)=\frac{1}{15}\] and \[P\,\,(A\,\cap \,C)\frac{1}{10},\] then \[P\,\,(C\,\cap \,\,(A\,\cup \,B))\] equal to-
Coordinate of the vertices B and C of a triangle ABC are (2, 0) and (8, 0) respectively. The vertex A is varying in such a way that \[4\,\,\tan \,\,\frac{B}{2}\,\,\tan \,\,\frac{C}{2}=1.\]The locus of A is -
If \[g(x)\] is a differential real valued function satisfying \[g''(x)-3g'(x)>3\,\,\forall \,\,x\,\,\ge 0\,\] and \[g'(0)=-\,1,\] then \[\frac{d}{dx}(g'(x){{e}^{-\,3x}})>3.\,{{e}^{-\,3x}}\] is-
If matrix \[A={{[{{a}_{ij}}]}_{3\times 3}},\] matrix \[B={{[{{b}_{ij}}]}_{3\times 3}},\] where \[{{a}_{ij}}+{{a}_{ij}}=0\] and \[{{b}_{ij}}-{{b}_{ij}}=0\] then \[{{A}^{4}}.\,{{B}^{3}}\] is -
If \[f(x)=a{{e}^{2x}}+b{{e}^{x}}+cx\] satisfies the conditions \[f\left( 0 \right)=-\,1,\] \[f'(\log \,\,2)=31\] & \[\int\limits_{0}^{\ell n4}{f(x)-cx)\,\,dx=\frac{39}{2}},\] then -
Moment of inertia of a rod of mass M and length L that rotated about its centre along an axis, which makes angle of \[30{}^\circ \] with the length of rod will be
A uniform rod of length L is placed over a horizontal frictionless surface. It is pulled over the surface by applying a force F on one of its end. Area of rod is A
Stress in the rod at a distance L/3 from the end, where the force is applied is
A rigid massless rod of length L connects two particles each of mass m. The rod lies over a horizontal frictionless table. Another particle of mass m and velocity \[{{v}_{0}}\] struck one of two particles attached with rod.
Angular velocity of rod about its centre of mass just after collision will be (take, collision elastic)
A square loop of area \[100c{{m}^{2}}\] with sides parallel to X and Y-axes is moved with velocity \[8\,\,cm{{s}^{-1}}\] in positive direction of X-axis. A magnetic field exists in region which points in z-direction. Magnetic field decreases along negative x-direction at rate of \[0.1\,T{{m}^{-1}}\] and also decreases in time at a rate of \[{{10}^{-\,3}}T{{s}^{-\,1}}.\] Emf induced in the loop is
At \[100{}^\circ C,\] copper (Cu) has FCC unit cell structure with cell edge length \[x\overset{o}{\mathop{A}}\,.\] What is the approximate density of Cu \[(in\,g\,C{{m}^{-\,\,3}})\] at this temperature? [Atomic mass of\[Cu=63.55u\]]
A solution containing 62 g ethylene glycol in 250 water is cooled to \[-10{}^\circ C.\] If \[{{K}_{f}}\] for water is 1.86 K kg \[mo{{l}^{-\,1}}\] the amount of water (in g) separated as ice is :
Homoleptic octahedral complexes of a metal ion 'M with three monodentate ligands \[{{L}_{1}},\]\[{{L}_{2}}\] and \[{{L}_{3}},\] absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is
The famous experiment by Avery, MacLeod and McCarty showed that neither heat killed S-type nor live R-type pneumococci could kill mice (experiment 1) but simultaneous injection of both killed the mice just as efficiently as the live S-type (experiment 2). S-type pneumococci are known to possess a capsule structure outermost to the cell wall. Structurally, capsule is a linear homopolymer of sialic acid residues. Apart from the capsule, there are other virulence factors present in these bacteria such as adhesion proteins that recognise a wide range of molecular motifs and provide targeting of the bacteria to specific tissue surfaces in the host.
(I) one can hypothesise that sialic acid residues are likely to be poorly immunogenic if the same homopolymer is a structural component of the host.
(II) If the capsular deficient mutants are used in place of S-type bacteria and adhesion deficient mutants in place of R-type in the Avery, MacLeod and McCarty experiment, mice would be killed.
(III) If genomic DNA from S-type is extracted and injected sub-cutaneously into the mice, most of the mice would be killed.
(IV) In the experiments performed by Avery,
MacLeod and McCarty, all types of live R strains recovered from dead mice would also be virulent.
In an experiment, the \[{{\operatorname{PO}}_{4}}\] groups of the phospholipids facing the lumen of the endoplasmic reticulum (ER) are labelled. If in the course of time, the ER buds off vesicles which fuse with the cell membrane, the label will be found:
A)
On the \[{{\operatorname{PO}}_{4}}\] groups of cell membrane facing extracellular fluid.
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B)
On the \[{{\operatorname{PO}}_{4}}\] groups of cell membrane facing cytosol.
A bacterial cell is \[la{{c}^{-}}\]\[ga{{l}^{+}}\] and contains F plasmid that is \[la{{c}^{+}}\]. The plasmid has temperature sensitive mutation in its replication system such that above \[40{}^\circ C\] the replication is blocked. A few statements are made about the growth of these organisms in different conditions.
(I) the cells will grow normally in media containing galactose as the sole source of carbon and incubation temperature as \[42{}^\circ C.\]
(II) The cells will grow normally only if media contains both galactose and lactose irrespective of temperature.
(III) The cells will grow normally in media containing lactose as the sole source of carbon and incubation temperature of \[42{}^\circ C.\]
(IV) If the cells are grown at \[37{}^\circ C.\], lactose should be added to the medium and if the cells are grown at \[42{}^\circ C\], galactose should be added to the medium.
A two month study on a population of 500 rats showed that the emigration of individuals from the population was 1.5 times the rate of immigration. At the same time the birth rate was found to be two times the rate of death. If the number of emigrants during the period of study was 75 and the birth rate was 10%, what would be the number of rat individuals in the population at the end of the study?
Four DNA molecules are shown below. These molecules were denatured by heating and then cooled and allowed to renature. Which of the four molecules will show highest melting temperature?
Two biomolecules (P and Q) which can act as carbon sources were added to a bacterial culture. When their initial rates of entries into the bacterial cell were measured, the following data was obtained.
Carbon source (mM)
Initial rate of transport \[\mathbf{(}\mu \,\,\,\mathbf{moles/min)}\]
P
Q
0.1
2
18
0.3
6
46
1
20
100
3
60
150
10
200
162
What can be deduced from this data?
A)
P is transported by a channel protein while, Q is transported by a carrier protein.
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B)
P is transported by a carrier protein while Q is transported by passive diffusion.
Silky fur is a recessive trait in a breed of cats. An amateur breeder has procured a stock of 1000 cats of which 160 are silky-furred. As he is away, his wife happily sells all these 160 cats for a handsome price. On his return, the husband is upset and has no option but to breed the remaining stock. What percentage of the next generation will be silky-furred?
Assuming that histone octamer forms a cylinder 9 nm in diameter and 5 nm in height and that the human gemone forms 32 million nucleosomes, what fraction (approximately) of the volume of nucleus (6 \[\mu \]m diameter) is occupied by histone octamers?
The chemicals such as urea and betamercaptoethanol denature proteins. Betamercaptoethanol oxidises disulphide linkages, while urea breaks all the non-covalent bonds found in the native protein molecule. To understand the quaternary structure of a protein, the purified protein was treated with different agents and separated using a gel-filtration column and the following results were obtained: select the incorrect statement.
A)
The 100 kDa subunit is a homodimer of 50 kDa polypeptide, whereas the 60 kDa subunit is a homotetramer of 15 kDa polypeptide.
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B)
Disulphide bonds are responsible for multimerisation of 50 and 15 kDa polypeptides into 100 and 60 kDa subunits, respectively.
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C)
Protein is heteromeric.
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D)
The protein is a dimer of two polypeptide chains that have relative molecular mass of 100 and 60 kDa each.
The \[{{C}_{3}}\], \[{{C}_{4}}\] and CAM pathways are the major \[C{{O}_{2}}\] fixing pathways present in plants given in Column-II. Column-I has a few statements relating to one or more of the pathway.
Column-I
Column-II
P.
The Calvin cycle operates in the chloroplast
(i)
\[{{\operatorname{C}}_{3}}\]
Q.
The primary carboxylation is catalyzed by RuBisCO
(ii)
\[{{\operatorname{C}}_{4}}\] pathway
R.
The atmospheric \[{{\operatorname{CO}}_{2}}\] is first fixed during the day
(iii)
CAM pathway
S.
The whole process of \[{{\operatorname{CO}}_{2}}\] uptake and its fixation take place in a single cell
Select the option with correct combination of pathway pain ways and statement
A)
P - (III), Q - (I) and (II), R - (I) and (II), S-(I) and (III)
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B)
P - (I), (II) and (III), Q - (I), R- (I) and (II), S-(I) and (III)
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C)
P-(I), (II) and (III), Q-(I) and (III).R-(I), S-(I) and (II)
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D)
P-(I), (II) and (III), Q-(I) and (III), R-(I), S-(I) and (II)