KVPY Class-XI (...

If n is the smallest natural number such that n + 2n + 3n + … + 99n is a perfect square, then the number of digits in n² is

Let x, y and z be positive reals. Which of the following imply x = y = z?

I. x³ + y³ + z³ = 3xyz
II. x³ + y²z + yz² = 3xyz
III. x³ + y²z + z²x = 3xyz
IV. (x + y + z)³ = 27xyz

Let n > 1 be an integer. Which of the following sets of numbers necessarily contains the multiples of 3?

The number of distinct primes dividing 12! + 13! + 14! is

Methane is a greenhouse gas because

A parachutist with total weight 75 kg drops vertically onto a sandy ground with a speed of 2 ms^-1 and comes to a half over a distance of 0.25 m. The average force from the ground on her is close to

The beta particles of a radioactive metal originate from the

Mendeleev's periodic law states that the properties of elements are a periodic function of their

The gas released when baking soda is mixed with vinegar is:

The element which readily forms an ionic bond has the electronic configuration:

Among Mg, Cu, Fe, Zn, the metal that does not produce hydrogen gas on reaction with hydrochloric acid is

Excess salt inhibits bacterial growth in pickles by

Restriction endonucleases are enzymes that are used by bio-technologists to

Enzyme X extracted from the digestive system hydrolyses peptide bonds. Which of the following is a probable candidate to be enzyme X?

A person with blood group AB has

Glycolysis is the breakdown of glucose to pyruvic acid. How many molecules of pyruvic acid are formed from one molecule of glucose?

The process of transfer of electrons from glucose to molecular oxygen in bacteria and mitochondria is known as

Which one of the following cell types is a part of innate immunity?

Deficiency of which one of the following vitamins can cause impaired blood clotting?

Which one of the following is/are detrimental to soil fertility?

In which one of the following phyla is the body segmented?

Widal test is prescribed to diagnose

Which among grass, goat, tiger and vulture in the food chain, will have the maximum concentration of harmful chemicals in its body due to contamination of pesticides in the soil?

Considering the average molecular mass of a base to be 500 Da, what is the molecular mass of a double stranded DNA of 10 base pairs?

Which of the following pairs contains both polysaccharides?

Which one of the following is a modified leaf?

When 262 g of xenon (Atomic mass = 131) reacted completely with 152 g of fluorine (Atomic mass = 19), a mixture of XeF₂ and XeF₆ was produced. The molar ratio XeF₂ : XeF₆ is

Genomic DNA is digested with Alu I, a restriction enzyme which is a four base-pair cutter. What is the frequency with which it will cut the DNA assuming a random distribution of bases in the genome?

If rice is cooked in a pressure cooker on the Siachen glacier, at sea beach, and on Deccan plain, then which of the following is correct about the time taken for cooking rice?

What is the advantage of storing glucose as glycogen in animals instead of as monomeric glucose?

A line is drawn from the exterior of an animal cell to the centre of the nucleus, crossing through one mitochondrion. What is the minimum number of membrane bilayers that the line will cross?