KVPY SB/SX Mock Test - 5

Number of elements in B for a good set = n
So, number of good subsets of B = 2ⁿ - 1

a_n = 3a_{n - 1} + 1
a₂₀₁₀ = 3a₂₀₀₉ + 1

= 3(3a₂₀₀₈ + 1) + 1 = 3² a₂₀₀₈ + 3 + 1
= 3³ a₂₀₀₇ + 3 + 3 + 1
.
.
.
= 3²⁰¹⁰ a₀ + (3 + 3 + ... + 3) + 1
(2009 times)
= 0 + 6027 + 1 = 6028

Remainder = (6028/11)  = 0

There is no slide. So, V = ωR at the point of contact. Because of this, there will be no relative motion at this contact point. So, frictional force would be zero.

Using theory of entropy, as the temperature increases, randomness decreases.

As boron is trivalent impurity, it will produce p-type semiconductor.

For a first order reaction, half life period is independent of initial concentration of the reaction.

For CCP (cubic close packed arrangement):
Number of atoms per unit cell (Z) = 4
As we know, if total number of atoms = N
Then, number of tetrahedral voids = 2N
Number of octahedral voids = N
Hence, according to the question, metal M occupies half of the octahedral voids.
Then, the chemical formula is: M₂Y₄ or MY₂.

The plant hormone auxin is responsible for a plant's ability to grow towards the light. The cells on the plant that are the farthest from the light have a chemical called auxin, that reacts when phototropism occurs. This causes the plant to have elongated cells on the farthest side from the light.

DNA is a polymer. The monomer units of DNA are nucleotides and the polymer is known as a "polynucleotide". Each nucleotide consists of a 5-carbon sugar (deoxyribose), a nitrogen containing base attached to the sugar and a phosphate group.

Earthworms are bisexual but still cross-fertilisation is common. This is because spermatozoa and ova mature at different times in the same earthworm.

The process of adsorption of water by solid particles of a substance, without forming a solution, is called 'imbibition'. Wooden doors and windows adsorb water in humid rainy season and increase in their volume so that they are hard to open or close. This occurs by the process of imbibition.

Helicobacter pylori (H. pylori) is a bacteria that can cause a stomach infection and inflammation. This is the main organism that causes peptic ulcers.

Glucose is present in blood plasma and glomerular filtrate, but not present in urine (normally). This is because glucose is selectively reabsorbed in the proximal convoluted tubule. It is reabsorbed from the filtrate into the blood by active transport (symport with Na⁺ ions).

Tinospora has long, slender and hanging aerial adventitious roots. These roots are green and photosynthetic.

With increase in every trophic level, the amount of energy decreases. Hence, the energy cost of respiration will increase with every trophic level.

Rate of photosynthesis is fastest in blue and red lights. 

This happens because of higher blood circulation to the skin. This helps to release more heat from the body.

Bt crystal toxins include the Cry proteins (crystal toxins) and Cyt proteins (cytolytic toxins). When these crystal proteins are exposed to the alkaline environment of the gut of susceptible larvae, the crystals are solubilised and proteolytically processed at the N-terminus and/or the C-terminus by mid-gut proteases to yield the active protease-resistant toxin.

The mean conduction velocity of an action potential ranges from 1 metre per second (m/s) to over 100 m/s, and in general, increases with axonal diameter.

The sodium-potassium pump works by pumping two potassium ions into the cell and pumping out three sodium ions using the energy from an ATP molecule.

Immunosuppressive therapy used in transplantation prevents activation and proliferation of alloreactive T-lymphocytes.

Organogenesis begins with the process of neurulation. This neurulation begins with the formation of primitive streak in epiblast (ectoderm), which leads to the formation of neural tube (nerve cord).

When a nerve or muscle cell is at "rest", its membrane potential is called the resting membrane potential. In a typical neuron, this is about –70 millivolts (mV).

The process of meiosis involves two divisions of the genetic material. The first division is called the reduction division – or meiosis I – because it reduces the number of chromosomes from 46 chromosomes or 2n to 23 chromosomes or n (n describes a single chromosome set).

RuBisCo is a bifunctional enzyme. It possesses both carboxylase and oxygenase activities. Both the activities are found on the same active site. The enzyme acts as an oxygenase during photorespiration and as a carboxylase during photosynthesis.

The outer ovary wall in citrus fruits becomes the thick spongy layer of the rind, while the inner ovary wall becomes very juicy with several seeds.

Glycogen is a readily mobilised storage form of glucose. The two major sites of glycogen storage are the liver and skeletal muscles.

Since P''(x) ≠ 0 ⇒ a ≠ 0

P(x) = ax² + bx + c

P'(x) = 2ax + b

P''(x) = 2a

P(0) = c = 1

P'(0) = b = -1

Therefore, P(x) = ax² - x + 1

P(1) = a - 1 + 1 = a ≠ 0

6^m + 2^m+n.3^w + 2ⁿ = 332
Maximum possible value of m is 3 because if m = 4, then 6^m exceeds 332.
Checking for m = 3, 2 and 1, we get
m = 2, n = 3, w = 2
m² + mn + n² = 4 + 6 + 9 = 19

Total droplets = 2.4 x 10¹⁸
Total area = total droplets x area of one drop
= 2.4 x 10¹⁸ x 12.5 x 10¹⁶
= 12.5 x 2.4 x 10² m²
Energy consumption
= 0.03 x 12.5 x 2.4 x 10²
= 90 Joule

Cell membrane becomes more permeable at high temperature. E. coli has an optimal temperature of 37°C. At this temperature, all the processes required for synthesising new cells occur at maximal rate. 

Cells use a strategy called reaction coupling, in which an energetically favourable reaction (like ATP hydrolysis) is directly linked with an energetically unfavourable (endergonic) reaction. The linking often happens through a shared intermediate, meaning that a product of one reaction is "picked up" and used as a reactant in the second reaction.

Let's start with 10 kb fragment, and go through from one end to the other, and mark every time a 'G' occurs. Theoretically those could all be the beginning of EcoRI sites. There will be approximately 2500 such 'G's. Now to match the pattern, we need an 'A' in the second position, so mark all those sites that contain the dinucleotide 'GA', there will be about 2500 x 0.25 = 625 of them. The next match we need is position 3, another 'A', so in a similar fashion, let's go through the positions of all those GA dinucleotides, and just mark the ones that have an 'A' at the next position. So that will be about 625 x 0.25, or approximately 156 'GAA's distrubuted randomly along the 10 kb fragment.
If we continue, essentially filtering out more and more of those 'G' sites in our initial list, then we will find that on average, there are:
39 sites with GAAT.
10 sites with GAATT.
2 sites with GAATTC.

Change in preference of herbivores for plants has enabled the survival of plants for long.

Tree trunk growth is coordinated with the increase of tree height and width. When buds begin opening in the early Spring, cells in the trunk and limbs get the signal to increase in girth by dividing and in height by elongating.

DNA replication is semi conservative. Hence, when DNA is transferred to the normal medium, only one strand will be radioactive.

One complete 360 degree turn of the DNA helix covers 10 base in length and a physical distance of 34 angstrom.

An apicoplast is a derived non-photosynthetic plastid found in most Apicomplexa, including malaria parasites such as Plasmodium falciparum. It originated from an alga through secondary endosymbiosis.

Animals present as one large population are most susceptible to extinction due to infectious diseases.