KVPY SB/SX Mock Test - 1

(x - 41)⁴⁹ + (x - 49)⁴¹ + (x - 2009)²⁰⁰⁹ = 0

f(x) = (x - 41)⁴⁹ + (x - 49)⁴¹ + (x - 2009)²⁰⁰⁹

f'(x) = 49(x - 41)⁴⁸ + 41(x - 49)⁴⁰ + 2009(x - 2009)⁴⁸ > 0

Hence, f(x) will cut x-axis only once.

[Co(dien)Cl₃] is an MA₃B₃ type complex. Therefore, it exhibits geometrical isomerism and exists in the cis and trans forms which in this case may also be referred to as fac and mer isomers.

On dilution, entropy change is positive, while there is no change in enthalpy.

Na⁺, Mg²⁺, F^- and O^2- are isoelectronic as all are 10 electron species.

Photolysis is a chemical reaction in which a chemical compound is broken down by photons. Photolysis of water results in the release of oxygen (as a by-product) and hydrogen.

Cellular differentiation is the process where a cell changes from one cell type to another. Most commonly, the cell changes to a more specialised type.

Fertilisation is the fusion of male and female gametes to produce a zygote. It usually takes place in the fallopian tube.

Blood contains red blood cells, white blood cells and platelets. Lymph is a whitish and clear liquid. It is generally similar to blood plasma, except that it does not contain red blood cells.

Rheumatoid arthritis is an autoimmune disease that causes chronic inflammation of the joints and other areas of the body.

The Cloverleaf model of tRNA is a model that depicts the molecular structure of tRNA. The model revealed that the chain of tRNA consists of two ends, sometimes called "business ends" and three arms. Two of the arms have a loop, D-loop (dihydro U loop) and Tψ-loop with a ribosome recognition site.

The hormones of the pituitary gland help regulate the functions of other endocrine glands. The hypothalamus sends signals to the pituitary to release or inhibit pituitary hormone production.

Night blindness, also called nyctalopia, means a person cannot see well at night or in poor light. Vitamin A deficiency is one of the reasons for night blindness. In this condition, the rhodopsin pigment of the rod cells becomes defective.

Within the ribosome, ribozymes function as part of the large sub-unit ribosomal RNA to link amino acids during protein synthesis. They also participate in a variety of RNA processing reactions, including RNA splicing, viral replication, and transfer RNA biosynthesis.

Pheromones help ants keep track of food and also direct each other through their environment. Hence, it is the chemical signal between the ants that helps them track their path.

Bacteriochlorophylls are photosynthetic pigments that occur in various phototrophic bacteria. None of the anoxygenic phototrophic bacteria has the ability to use water as an electron donor (or cannot oxidise water), and thus, perform photosynthesis using sulphide, hydrogen or organic substrates. Therefore, photosynthesis by these bacteria does not involve oxygen.

The conditions mentioned are appropriate for increasing the rate of respiration in the seeds. The heat released is due to the respiration of the seeds.

Neurofilaments (NF) are the 10 nanometer or intermediate filaments found in neurons. They are a major component of the neuronal cytoskeleton and are believed to function primarily to provide structural support for the axon and to regulate axon diameter.

M phase is the mitotic phase. The sister chromatid form is present in the M phase.

Saline drip is given to a cholera patient because sodium ions help in the retention of water in the body. This helps to prevent dehydration.

Polytene chromosomes are oversised chromosomes, which have developed from standard chromosomes and are commonly found in the salivary glands of Drosophila melanogaster. These represent transcriptionally active genes.

HbF has more affinity for oxygen than adult haemoglobin. This property helps in extracting oxygen from the mother.

The western blotting (sometimes called the protein immunoblot) is a widely used analytical technique used in molecular biology, immunogenetics and other molecular biology disciplines to detect specific proteins in a sample of tissue homogenate or extract.

CFCs destroy ozone layer. This allows the penetration of harmful UV rays to the Earth. UV rays damage DNA by causing thymine dimerisation.

The nitrogenase enzyme complex (the nitrogen fixing enzyme) is sensitive to O₂ and inactivates the enzyme.

p(x) = a₀ + a₁x + .........+ a_nx_n

p(0) = 7

a₀ = 7

p(1) = a₀ + a₁ +a₂ + ......... + a_n = 9

p(-1) = a₀ - a₁ + 2a₂ - ........... = 1

p(2) = a₀ + 2a₁ + 4a₂ ......... = 13

p(-2) = a₀ - 2a₁ + 4a₂ ......... = -15

p(1) + p(-1) = 2[a₀ + a₂ + ......] = 10

a₀ + a₂ + a₄ = 5 -----(1)

7 + a₂ + a₄ = 5

a₂ + a₄ = -2 ------(2)

p(2) + p(-2) = 13 - 15

2(a₀ + 4a₂ + ........) = -2

a₀ + 4a₂ + 16a₄ = -1

4a₂ + 16a₄ = -8 -----(2)

p(3) = 25

a₀ + 3a₁ + 9a₂ + ........ = 25

a₀ + 3a₁ + 9a₂ + 27a₃ + 81a₄ + 243a₅ = 25

From (1) and (2):

4a₂ + 4a₄ = -8

4a₂ + 16a₄ = -8

- - +
________________
a₄ = 0 and a₂ = -2

Therefore, smallest possible value of n is 3.

D₁ = 4a² - 4b² > 0

⇒ 4(a² - b²) > 0

a² - b² > 0 ---------(1)

D₂ = 4b² - 4c² > 0

⇒ b² - c² > 0 ----------(2)

= -4(b² - c² + a² - b²) = -4(D₁ + D₂)

Now, D = 4c² - 4a² = 4(c² - b² + b² - a²)

= Negative

Therefore, the equation has no real roots.

β-Lactam antibiotics are a broad class of antibiotics that includes penicillin derivatives, cephalosporins, monobactams, and carbapenems. β-Lactam antibiotics are bacteriocidal and act by inhibiting the synthesis of the peptidoglycan layer of bacterial cell walls.

This is because blood and most living cells contain the enzyme catalase, which attacks hydrogen peroxide and converts it into water and nascent oxygen. The frothing is caused due to the release of nascent oxygen.

Enzymes lower the activation energy of the reaction. This makes the reaction occur at a higher rate. The enzyme is recovered without any change.

Heritable bacterial endosymbionts are very common in insects. One important feature of all these symbionts is that most of them are exclusively or predominantly vertically (and usually maternally) transmitted, and thus heritable.

Not all bacterial symbionts influence the host's interactions with other species directly, and many of these bacterial species affect the reproductive system of their hosts by either causing female-biased sex ratios or impacting on the ability of pairs of individuals to produce offspring.

The sequence followed is:

Low [glucose] ⇒ low osmotic pressure ⇒ low pH ⇒ high pCO₂

At night, photosynthesis stops and glucose gets consumed. This leads to low osmotic pressure and a low pH as respiration starts in the plant cells. This increases the carbon dioxide concentration in the plant cell. This leads to closure of stomata.

Auxotrophy is the inability of an organism to synthesise a particular organic compound required for its growth. An auxotroph is an organism that displays this characteristic. A lysine auxotroph will grow only in a medium containing lysine.

The colonies resistant to penicillin will grow on agar plates containing penicillin.