KVPY Class-XI (SA) - 2012

Since the sides are in A.P let the sides be x , x + d and x + 2d.
Now since smallest side is 10

Therefore, x = 10
=> sides are 10, 10 + d and 10 + 2d

We know that sum of any two sides of a triangle is greater than the third side.
=> 20 + d > 10 +2d
=> 10 + d > 2d
Since, we know that the sign of d = +
Therefore, we can subtract d.
10 > d
=> d
Since the sides are positive integers.
Therefore ,
d can hold the values 1 , 2 ,3 …, 9

suppose a quadratic function is f(x) = ax² + bx + c

Since, f(2) = 10 this implies that 4a + 2b + c = 10 .........(i)

And f(-2) = - 2, this implies that 4a - 2b + c = -2 .....................(ii)

so from equation (i) & (ii)

(i) - (ii)

4b = 12 ⇒ b = 3

hence coefficient of x = 3

Taking all the number which gives remainder 3 and 4 and one of the number which gives remainder 0
A = {3, 4, 5, 8,9,13,14,18,19,23, 24,28,29,33,34,38,39}
and all the number which gives remainder 1 and 2 and one of the number which gives remainder 0
A = {1, 2, 5, 6, 7, 11, 12, 16, 17, 21, 22, 26, 27, 31, 32, 36, 37}
total number of element in set A = 17 (in both cases)

Out side the battery ,electrons flow from low potential to high potential where as inside the battery electrons flow from high potential to low potential.

Ice has low thermal conductivity so no exchange of heat takes place with outside surrounding.

On the basis of Rutherford's alpha particle scattering experiment, Rutherford put forward the model of an atom, which had the following features:
1) There is a positively charged centre in an atom called the nucleus.
2) Nearly all the mass of an atom resides in the nucleus.
3) The electrons revolve around the nucleus in well-defined orbits.
4) The size of the nucleus is very small as compared to the size of the atom.

Here stream of water gets deflected due to induction hence in both cases it will bend toward the girl.

The metallic oxides are basic in nature and non-metallic oxides are acidic in nature.
We know that metallic character decreases as we move from left to right in the periodic table. Therefore, among all, Na₂O is most basic in nature, while Al₂O₃ is amphoteric oxide, and P₂O₅ and SiO₂ are acidic oxides due to non-metallic in nature.

An intensive property is a bulk property of a system that does not depend on the system size or the amount of material in the system. These properties depends only upon the nature of the substance. Examples of intensive properties include temperature (T), density (ρ), pressure (P), Viscosity, refractive index, etc.

Formula is K₂SO₄ . Al₂(SO₄)₃ . 24H₂O
Empirical formula is KAl(SO₄)₂ . 12H₂O
So x = 2

A comparison of Q with K indicates which way the reaction shifts and which side of the reaction is favored:

(A) If Q>K, then the reaction favors the reactants. This means that in the Q equation, the ratio of the concentration or pressure of the products to the concentration or pressure of the reactants is larger than that for K, which means more products are present than there would be at equilibrium. Because reactions always tend toward equilibrium (Le Châtelier's Principle), the reaction produces more reactants from the excess products, therefore causing the system to shift to the left. This allows the system to reach equilibrium.

(B) If Q<K, then the reaction favors the products. The ratio of products to reactants is less than that for the system at equilibrium—the concentration or the pressure of the reactants is greater than the concentration or pressure of the products. Because the reaction tends toward reach equilibrium, the system shifts to the right to make more products.

(C) If Q=K, then the reaction is already at equilibrium. There is no tendency to form more reactants or more products at this point. No side is favored and no shift occurs.

Aspirin, also known as acetylsalicylic acid, is a medication used to treat pain, fever, and inflammation.

In diethyl ether, there is no available H-atoms directly bonded to the O-atom in the ether, Thus it cannot have hydrogen bonding between molecules.

Neutrophils are by far the most numerous of the leukocytes. They are characterized by a nucleus that is segmented into three to five lobes that are joined by slender strands.The name neutrophil derives from staining characteristics on hematoxylin and eosin (H&E) histological or cytological preparations.

Transduction is the process by which a virus transfers genetic material from one bacterium to another. Viruses called bacteriophages are able to infect bacterial cells and use them as hosts to make more viruses.

Glycolysis is the metabolic process that serves as the foundation for both aerobic and anaerobic cellular respiration. In glycolysis, glucose is converted into pyruvate. The process occurs in the cytoplasm.

Huntington's disease (HD), also known as Huntington's chorea, is an inherited disorder that results in death of brain cells

Endosmoasis:- The movement of liquid from outside to inside is known as endosmosis. It takes place in hypotonic solution. The highest will be when the cell is kept in distilled water.

When touched, this sensitive leaf reacts to stimulus as there is a higher pressure at that point and the water in the vacuoles of the cells of the leaf lose water to the adjacent cell. All the water escapes the leaf (via the pulvinus) which then becomes flaccid.

The Sundarbans mangrove forest, one of the largest such forests in the world (140,000 ha), lies on the delta of the Ganges, Brahmaputra and Meghna rivers on the Bay of Bengal

Myeloid tissue is a biologic tissue with the ability to perform hematopoiesis. It is mainly found as the red bone marrow in bones.

Amphibians have a heart that consists of a single ventricle and two atria.

Overproduction of growth hormone causes excessive growth. In children, the condition is called gigantism. In adults, it is called acromegaly. Excessive growth hormone is almost always caused by a noncancerous (benign) pituitary tumor.

Mitochondria is a semi autonomous organelle having its own DNA and ribosomes.Hence it can produce its own proteins.

Maltose is a disacchride made up of two glucose units .

Mycorrhizae are symbiotic relationships that form between fungi and plants. The fungi colonize the root system of a host plant, providing increased water and nutrient absorption capabilities while the plant provides the fungus with carbohydrates formed from photosynthesis.

The probability of finding fossils of more complex organisms is highest in the upper layers of the strata. It increases from lower to upper strata.

Color blindness, also known as color vision deficiency, is the decreased ability to see color or differences in color. This is due to deficiency in cone cells.

The pleural membrane is thin, moist, slippery and has two layers. The outer, or parietal, pleura lines the inside of the rib cage and the diaphragm while the inner, visceral or pulmonary, layer covers the lungs. Pleural membranes reduce the friction between the ribs and the lungs.

S-phase (synthesis phase) is the part of the cell cycle in which DNA is replicated, occurring between G1 phase and G2 phase. The main enzyme required for replication is DNA Polymerase.

Muscles produce lactic acid during intense exercise. It's a metabolic byproduct that makes no contribution to exercise performance. It causes muscle fatigue and post-exercise muscle soreness

The optimum temperature for most enzymes to function is the body temperature which is around 37⁰C.