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The number of 5-tuples (a, b, c, d, e) of positive integers, such that
I. a, b, c, d and e are the measures of angles of a convex pentagon in degrees; II. a ≤ b ≤ c ≤ d ≤ e; and III. a, b, c, d and e are in arithmetic progression, is
a + b + c + d + e = 540 Let's say first term = a Common difference = d n/2[2a + (n - 1)d] = 540 ⇒a + 2d = 108 Case-1: d = 0 a = 108 (108, 108, 108, 108, 108) Case-2: d = 1 (106, 107, 108, 109, 110) Similarly, it goes up to d = 35. For d > 35, interior angle > 180o; which is not possible. So, from d = 0 to d = 35, total 36 tuples are possible.
The distance s travelled by a particle in time t is s = ut - 1/2 gh2. The initial velocity of the particle was measured to be u = 1.11 ± 0.01 m/s and the time interval of the experiment was t = 1.01 ± 0.1 s. The acceleration was taken to be g = 9.8 ± 0.1 m/s2. With these measurements, the student estimates the total distance travelled. How should the student report the result?
This question is related to significant numbers as the question asks how the student reports the result. On analysing the values of u, t and g, the reported result must have two significant numbers.
Which of the following statements for air molecules in an air tight container is/are true?
(I) The average speed of molecules is larger than root mean square speed. (II) Mean free path of molecules is larger than the mean distance between molecules. (III) Mean free path of molecules increases with temperature. (IV) The rms speed of nitrogen molecule is smaller than oxygen molecule.
According to Kinetic Theory of Gases, for ideal gas, mean free path of molecules is larger than mean distance between molecules.
The most abundant metal ion present in the human body is
Calcium is the most abundant metal in the human body, found both in ionic form (necessary for metabolic functions) and in the mineral form in the bones and teeth as hydroxyapatite. The mineral form of calcium comprises half the weight of our bones and most of our teeth.
The complete hydrolysis of XeF6 results in the formation of
XeF6 + 3H2O → XeO3 + 6HF White explosive compound
Resting membrane potential of a neuron is approximately
The resting membrane potential of a neuron is about -70 mV. This means that the inside of the neuron is 70 mV less than the outside. At rest, there are relatively more sodium ions outside the neuron and more potassium ions inside that neuron.
Amphimixis is
Amphimixis is a type of sexual reproduction, involving the union or fusion of a male and a female gamete.
Activation of sympathetic nervous system
The sympathetic nervous system (SNS) releases the hormones (catecholamines - epinephrine and norepinephrine) to accelerate the heart rate.
At physiological temperature, sterols in biological membranes
Sterols are essential in all eukaryotic cell membranes. Sterols reduce membrane fluidity and increase membrane rigidity and strength.
Which of the following is a heteropolysaccharide?
Hyaluronic acid is a polymer of D-Gluconic acid and N-Acetyl D-Glucosamine. So, it is heteropolysaccharide.
Bacterial plasmids are genetic entities that
Bacterial plasmid is an extra chromosomal genetic material capable of independent replication.
Skin prick test on the forearm is conducted to identify the responsible allergen. This is because
Skin prick test measures specific IgE attached to mast cells in the skin. SPT is usually the first test recommended when an allergy is suspected.
Which of the following processes in E.coli does not directly involve RNA?
RNA primers are involved in DNA replication. Transcription and translation directly involve RNA molecules. DNA repair does not involve any RNA molecules.
Which of the following statements is incorrect for translation in cytoplasm?
One specific codon codes for only one amino acid. It cannot code for more than one amino acid.
Two homozygous parents harbouring two different alleles of a gene, exhibiting incomplete dominance for flower colour, were used for a genetic experiment. Which of the following statements is incorrect?
Both genotypic and phenotypic ratios obtained in F2 generation will be the same. It will be 1 : 2 : 1.
Which of the following conditions is essential for a population to be at Hardy-Weinberg equilibrium?
Five conditions are required for a population to remain at Hardy-Weinberg equilibrium.
1. A large breeding population 2. Random mating 3. No change in allelic frequency due to mutation 4. No immigration or emigration 5. No natural selection
Inbreeding in a population leads to
Inbreeding is the production of offspring from the mating or breeding of individuals or organisms that are closely related genetically. It leads to increase in homozygosity in the population.
If a pure chlorophyll solution is illuminated with ultraviolet light, then the solution appears
In isolation, some pigments (including chlorophyll) emit light as well as heat after absorbing photons. As excited electrons fall back to the ground state, photons are given off. This afterglow is called fluorescence. If a solution of chlorophyll is isolated from chloroplasts, it will fluoresce in the red-orange part of the spectrum and also give off heat.
Botanical names of plants are given in Column - I and the family/order names are given in Column - Il. Choose the appropriate combination from the options given below.
Nitrogen fixation is inhibited by oxygen. However, in aerobic nitrogen fixing bacteria, nitrogen is fixed in the presence of oxygen. Nitrogenase in such organisms is protected by
In nodules where nitrogen-fixation occurs, the plant tissues contain the oxygen-scavenging molecule (leghaemoglobin). The function of this molecule in nodules is to reduce the amount of free oxygen and to protect the nitrogen-fixing enzyme nitrogenase, which is irreversibly inactivated by oxygen.
Frederick Griffith performed an experiment where mice were killed when injected with a mixture of heat killed S-type Streptococcus (HKS) and live R-type Streptococcus (LRS), but not with HKS or LRS separately. The mice were killed because
Transformation occurs when DNA is taken up by R-strain from dead S-strain.
In diabetic patients, the pH of blood plasma can decrease. This leads to acidosis. It occurs because tissues catabolise
In diabetic patients, excessive breakdown of fatty acids occurs. This leads to the production of acetoacetic acid and β-hydroxy butyric acid which decreases pH of blood.
If the number of alveoli in an individual is doubled without changing the total alveolar volume, then the gas exchange capacity of the lungs will
With increase in the number of alveoli, the surface area will increase. Hence, the gas exchange capacity will increase for both oxygen and carbon dioxide.
In an experiment, bacteria were infected with 32P labelled viruses in the ratio 5 : 1. The culture was rigorously shaken, followed by centrifugation. Radioactivity was
The experiment mentioned in the question is in accordance with the Hershay and Chase blending experiment. 32P activity is found in the pellet and 35S activity is found in the supernatant.
Let A be a set of all permutations a1, a2, ..., a6 of 1, 2, ..., 6 such that a1, a2, ..., ak is not a permutation of 1, 2, .., k for any k, 1 ≤ k ≤ 5. Then, the number of elements in A is
Let f(x) be a polynomial with integer coefficients satisfying f(1) = 5 and f(2) = 7. The smallest possible positive value of f(12) is
f(x) = ax + b 5 = a + b ...(i) 7 = 2a + b ...(ii) Solving, a = 2 and b = 3 f(x) = 2x + 3 f(12) = 24 + 3 f(12) = 27
Consider the following statements regarding the photoelectric effect experiment. (I) Photoelectrons are emitted as soon as the metal is exposed to light. (II) There is a minimum frequency below which no photo-current is observed. (III) The stopping potential is proportional to the frequency of light. (IV) The photo-current varies linearly with the intensity of light. Which of the above statements indicate that light consists of quanta (photons) with energy proportional to frequency?
(I) Photoelectrons are emitted as soon as the metal is exposed to light. (II) There is a minimum frequency below which no photo-current is observed. (III) The stopping potential is proportional to the frequency of light.
Suppose, non-linked autosomal genes A, B and C control coat colour in an animal, the dominant alleles A, B and C are responsible for dark colour and the recessive alleles a, b and c are responsible for light colour. If a cross between a male of AABBCC genotype and a female of aabbcc genotype produces 640 offsprings in the F2 generation, then how many of them are likely to be of the parental genotype?
In a trihybrid cross, a total of 64 progeny are produced. Out of these, 8 are of parental genotype. In the problem given, 640 progeny are formed. Hence, 8/64 × 640 = 80
In a population of families having three children each, the percentage of population of families having both boys and girls is
Probability of 2 boys and 1 girl = 3/8 Probability of 1 girl and 2 boys = 3/8 Total probability = 3/8 + 3/8 = 6/8 = 75%
Matthew Meselson and Franklin Stahl grew E.coli (doubling time is 20 mm) in a medium containing 15NH4CI for many generations. Then, it was transferred to a medium containing 14NH4CI. After 40 minutes, the cells were harvested and DNA was extracted and subjected to cesium chloride density gradient centrifugation. The proportion of light and hybrid DNA densities will be
DNA replication is semiconservative.
Which of the following statements is correct in a population interaction between the species X and the species Y?
Both species benefit in mutualism.
The protein P, the oligosaccharide O and the oligonucleotide N are composed of 100 amino acid residues, 100 hexose residues and 100 nucleotides, respectively. Which of the following orders of molecular weights is correct?
Monomer of protein is amino acid, oligosaccharide is of sugar and oligonucleotide is of nucleotides. Order of its molecular weight is nucleotide > monosaccharide > amino acid.
An octapeptide (NH2-Asn-Glu-Tyr-Lys-Trp-Met-Glu-Gly) is subjected to complete protease and chemical digestion. Choose the incorrect option.
When an octapeptide (NH2-Asn-Glu-Tyr-Lys-Trp-Met-Glu-Gly) is subjected to complete protease and chemical digestion,the products are formed depending upon the cleavage sites given below:- For trypsin - After Lys and Arg For chymotrypsin - After Phe, Trp or Tyr For cyanogen bromide - After Met
Match the enzymes in Column - I with their respective biochemical reactions in Column - Il.
Correct -
Wrong -
Skipped -
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