KVPY Class-XI (...

A quadrilateral has distinct integer side lengths. If the second-largest side has length 10, then the maximum possible length of the largest side is

Let S be the set of all ordered pairs (x, y) of positive integers satisfying the condition x² - y² = 12345678. Then,

If 72^x.48^y = 6^xy, where x and y are non-zero rational numbers, then (x + y) equals

It is given that the number 43361 can be written as a product of two distinct prime numbers p₁ and p₂. Further, assume that there are 42900 numbers which are less than 43361 and are co-prime to it. Then, p₁ + p₂ is equal to

The sum of all non-integer roots of the equation x⁵ - 6x⁴ + 11x³ - 5x² - 3x + 2 = 0 is

Consider the following statements:
(Here, X and Y stand for two different elements.)

(I) ₃₂X⁶⁵ and ₃₃Y⁶⁵ are isotopes.
(II) ₄₂X⁸⁶ and ₄₂Y⁸⁵ are isotopes.
(III) ₈₅X¹⁷⁴ and ₈₈Y¹⁷⁷ have same number of neutrons.
(IV) ₉₂X²³⁵ and ₉₄Y²³⁵ are isobars.

Which of the above statements are correct?

A student studying the similarities and differences between a camera and the human eye makes the following observations:

(I) Both the eye and the camera have convex lenses.
(II) In order to focus, the eye lens expands or contracts, while the camera lens moves forward or backward.
(Ill) The camera lens produces upside down real images, while the eye lens produces only upright real image.
(IV) A screen in camera is equivalent to the retina in the eyes.
(V) A camera adjusts the amount of light entering in it by adjusting the aperture of the lens. In the eye, the cornea controls the amount of light.

The correct statements are:

The first ionisation energy of Na, B, N and O atoms follows the order:

Among P₂O₅, As₂O₃, Sb₂O₃ and Bi₂O₃, the most acidic oxide is

Among K, Mg, Au and Cu, the one which is extracted by heating its ore in air is

The metal ion with total number of electrons same as S^2- is

The maximum number of electrons that can be filled in the shell with the principal quantum number n = 3 is

The atomic radii of Li, F, Na and Si follow the order:

The major excretory product of birds is

Codon degeneracy means that

In a cell cycle, during interphase,

Transfer of genetic material between populations is best defined as

Which ONE of the following statements is CORRECT about the tobacco mosaic virus?

Which ONE of the following statements is CORRECT about placenta?

Which ONE of the following statements is INCORRECT about nucleosomes?

The immediate precursor of thyroxine is

The maximum number of oxygen molecules that can bind to one molecule of haemoglobin is

Which ONE of the following biomolecules is synthesised in smooth endoplasmic reticulum?

The products of light reaction during photosynthesis include

Hypothalamus directly controls the production of the hormones

Which ONE of the following drugs is NOT obtained from fungal or plant sources?

Jean-Baptiste Lamarck explained evolution based on

Consider the set A = {1, 2, 3, ..., 30}. The number of ways in which one can choose three distinct numbers from A so that the product of the chosen numbers is divisible by 9 is

The nucleus of a diploid organism contains 3 ng of DNA in G₁ phase. Which ONE of the following statements describes the state of the cell at the end of S phase?

Three cellular processes are listed below. Choose the correct combination of processes that involve proton gradient across the membrane.

(i) Photosynthesis
(ii) Aerobic respiration
(iii) Anaerobic respiration

Given that tidal volume is 600 ml, inspiratory reserve volume is 2500 ml, and expiratory reserve volume is 800 ml, what is the value of vital capacity of lung?

Which of the following organisms produce sperm without involving meiosis?