KVPY Class-XI (...

The number of digits in the decimal expansion of 16⁵5¹⁶ is

Let t be a real number such that t² = at + b for some positive integers a and b. Then for any choice of positive integers a and b, t³ is never equal to

Consider the equation (1 + a + b)² = 3(1 + a² + b²), where a, b are real numbers. Then

Consider a cuboid, all of whose edges are integers and whose base is a square. Suppose the sum of all its edges is numerically equal to the sum of the areas of all its six faces. Find the sum of all its edges.

Find the number of all 2-digit numbers 'n', such that 'n' is equal to the sum of the square of digit in its tens place and the cube of the digit in its units place.

Let f be a function defined on the set of all positive integers such that f(xy) = f(x) + f(y) for all positive integers x and y. If f(12) = 24 and f(8) = 15, then the value of f(48) is

The primary and the secondary coil of a transformer contain 10 and 100 turns, respectively. The primary coil is connected to a battery that supplies a constant voltage of 1.5 volts. The voltage across the secondary coil is

Mercury is often used in clinical thermometers. Which one of the following properties of mercury is not a reason for this?

LiOH reacts with CO₂ to form Li₂CO₃ (atomic mass of Li = 7). The amount of CO₂ (in g) consumed by 1 g of LiOH is closest to

Among the elements Li, N, C and Be, one with the largest atomic radius is

What is the length of human DNA containing 6.6 x 10⁹ bp?

The Diptheria, Pertussis, Tetanus (DPT) vaccine consists of

Which of the following is NOT an enzyme?

The pH of the avian blood is maintained by

Podocyte layer that provides outer lining to the surface of glomerular capillaries is found in

If a dsDNA has 20% adenine, what would be its cytosine content?

Which one of the following is incapable of curing Pellagra?

In Escherichia coli, how many codons code for the standard amino-acids?

Bombyx mori (silk worm) belongs to the order

The source of mammalian hormone 'Relaxin' is

Which one of the following animals is a connecting link between reptiles and mammals?

What is the number of chromosomes in an individual with Turner's syndrome?

Chipko movement in the year 1974 in Garhwal Himalayas involved

Which of the following amino acids is NOT involved in gluconeogenesis?

Which of the following entities causes syphilis?

If 'a' is a positive real number such that a⁵ - a³ + a = 2, then

Consider the quadratic equation nx² - 7√nx + n = 0, where n is a positive integer. Which of the following statements is/are necessarily correct?

I. For any n, the roots are distinct.
II. There are infinitely many values of n for which both roots are real.
III. The product of the roots is necessarily an integer.

If a 3-digit number is randomly chosen, what is the probability that either the number itself or some permutation of the number (which is a 3-digit number) is divisible by 4 and 5?

The atmospheric pressure is 760 mm Hg at the sea level. Which of the following ranges is nearest to the partial pressure of CO₂ in mm Hg?

Match the different types of heart given in column A with organisms given in column B. Choose the correct combination.

Match the enzymes in Group I with the reactions in Group II. Select the correct combination.