KVPY (SA) Mock ...

The average of two non-negative integers x and y is 4. How many pairs of (x, y) satisfy this condition?

The number of real solution(s) of the equation -2 = x² - x = 2^x is

In a certain school, 71% students like cricket, 76% students like football and 82% students like tennis. Then, all the three sports are liked by at least

Find the time taken (in seconds) by two trains to cross each other if they are running at the speeds of 46 kmph and 54 kmph, respectively in the same direction. It is given that the length of one train is 210 m and of the other train is 270 m.

One of the factors of x³ + 8y³ + 27z³ – 18xyz is

Let t_n be the number of integral-sided triangles with distinct sides chosen from {1, 2, 3, ……., n}. Then, t₂₀ - t₁₉ equals

What is the difference of the perimeters of outer and inner boundaries of a park whose figure is given below?

The ratio of the radii of two circular cylinders A and B is 2 : 3 and that of their heights is 5 : 3. If the volume of cylinder B is 27 cm³, then the volume (in cc) of cylinder A is

The three different face diagonals of a cuboid (rectangular parallelepiped) have lengths 39, 40 and 41. The length of the main diagonal of the cuboid which joins a pair of opposite corners is

Consider a square ABCD of side 12, and let M and N be the midpoints of AB and CD, respectively. Take a point P on MN and let AP = r and PC = s. Then, the area of the triangle whose sides are r, s and 12 is

A and B together can complete a piece of work in 25 days. B and C together can complete the same work in 30 days. How many days would A and C take to complete the work?

The number of real roots of the equation (x² + 4x)² - (x + 2)² - 26 = 0 is

The sides of a quadrilateral are all positive integers and three of them are 5, 10, 20. How many possible values are there for the fourth side?

In a pair of two supplementary angles, the measure of the larger angle is 44° more than the measure of the smaller one. What are the measures of these angles?

The number of real roots of equation 3x¹⁰ + 7x⁶ + 5x⁴ + 2x² + 1 = 0 is

In the figure below, a ray of light travelling in a medium of refractive index passes through two different connected rectangular blocks of refractive indices and (> ).



The angle of incidence is increased slightly. The angle

From the top of a tower, a stone is thrown up and reaches the ground in time t₁ = 9 s. A second stone is thrown down with the same speed and reaches the ground in time t₂ = 4 s. A third stone is released from rest and reaches the ground in time t₃, which is equal to

The given blocks A, B and C of the same material are immersed in identical fluids. Volume of C > Volume of B > Volume of A. Which block experiences the greatest buoyant force?

Shyam was initially at a distance of 30 m towards 45° north of west from the school. Later, he was at a distance of 50 m towards 60° south of west from the school. Which of the following diagrams shows the direction of displacement vector correctly for Shyam?

A bomber plane is moving horizontally with a speed of 500 m/s and a bomb released from it strikes the ground in 10 seconds. The angle with the horizontal at which the bomb strikes the ground is (g = 10 m/s²)

The diameter of the pupil of an eye of a person in dim light was measured to be 7 mm. Which of the following cannot be the measurement of the diameter of his pupil in bright light?

Refractive index of glass with respect to air is . What is the refractive index of air with respect to glass?

A double convex thin lens made of glass (refractive index = 1.5) has both the radii of curvature of magnitude 20 cm. Incident light rays parallel to the axis of lens will converge at a distance 'd' cm such that

Consider the given V–I graph for two conductors A and B having resistances R₁ and R₂.



Which of the following relations is true?

Which of the following phenomena can be demonstrated by light, but not by sound waves in an air column?

If you are provided three resistances of 2Ω, 3Ω and 6Ω, how will you connect them so as to obtain the equivalent resistance of 4?

The work done in carrying a packet weighing 10 kg to the top of a building 14 m high is (g = 10 m/s²)

Two bulbs, one of 200 W and the other of 100 W, are connected in series with a 100 V battery which has no internal resistance. Then,

The frequency of a light ray is 6 × 10¹⁴ Hz. Its frequency when it propagates in a medium of refractive index 1.5 will be

A car was moving on a straight horizontal road with speed v. When brakes were applied to give a constant retardation a, the car was stopped at the shortest distance S. If the car is moving on the same road with speed 3v and the same retardation a is applied, then the shortest distance at which the car is stopped is given by

The IUPAC name of methyl alcohol (CH₃OH) is ________.

Directions: The following question has four choices, out of which ONLY ONE is correct.

C-Cl bond is stronger than C-I bond because

The correct sequence of hybridisation of methane, ethene and acetylene is

To which group of the periodic table does the element with electronic configuration 1s², 2s², 2p⁶, 3s², 3p⁶, 3d¹⁰, 4s², 4p⁶, 4d¹⁰, 5s², 5p³ belong?

An element has mass number 40 and has two neutrons in excess of the number of electrons. Find the number of neutrons, if it forms a cation having a unit positive charge and its electronic configuration is equal to that of Argon?

Which of the following is a non-polar molecule?

How many atoms are present in 20 g of Ca?

A real gas most closely approaches the behaviour of an ideal gas at

Sodium zincate is produced when zinc is heated with

Two moles of PCl₅ were heated to 400°C in a 2-litre closed vessel. At equilibrium, 40% of PCl₅ was dissociated into PCl₃ and Cl₂. Its K_C will be

For the reaction ⇌ is equal to

Which of the following is the correct increasing order of reactivities of elements?

Which of the following orders of the isomers of pentane is correct in terms of increasing melting points?

A metal 'M' is positioned between sodium and aluminium in the reactivity series. Which of the following metals can displace 'M' from its salt solution?

If the rate of diffusion of gas 'A' is five times that of gas 'B', what will be the density ratio of A and B?

What is the pH value of human urine?

Which of the following organs is the organ of olfactory receptors?

AIDS is a ______ disease, that causes damage to the _________.

Ascorbic acid is a/an

Which of the following modes of arrangement of sepals/petals is seen in pea and bean flowers?

The part of the brain which acts as a relay centre is

The sequence of different phases of cell cycle is

The softening of ripened fruits can be done by

Unlike humans, dogs cannot perspire to get rid of excess metabolic heat. They lose metabolic heat by

Seedlings grown in dark

The epithelium tissues forming the lining of kidney tubules are

Pick odd one out of the following

Which of the following plant hormones is gaseous in nature?

Which of the following is a synthetic plant hormone?

Pachytene occurs during

The number of solutions of the equation |x² - 4| = 4 + x² is

The points A (2, 3), B (3, 5), C (7, 7) and D (4, 5) are such that

Let p and q be the roots of the quadratic equation x² - (α - 2) x - α - 1 = 0. What is the minimum possible value of p² + q²?

ABC is a right-angled triangle with angle A = 90° and 2s = a + b + c, where a > b > c. The notations have their usual meanings. Which of the following relations is correct?

If sin α and cos α are the roots of ax² + bx + c = 0, then

In the figure, what is the equivalent resistance between A and B?

What is the escape velocity for a body on the surface of a planet on which the acceleration due to gravity is (3.1)² ms^-2 and whose radius is 8100 km?

Two identical cells, whether connected in parallel or in series, give the same current when connected to an external resistance of 1.5. Find the value of internal resistance of each cell.

An electron enters a uniform electric field maintained by parallel plates and value of E = Vm^-1; with a velocity v ms^-1. If the plates are separated by a distance d metre, then acceleration of the electron in the field is:

Two wires with the same dimensions and resistivities ₁ and ₂ are connected in series. The equivalent resistivity of the combination is

For Zn²⁺/Zn = - 0.76 V, Cl₂/Cl^- = 1.36 V, H⁺/H₂ = 0 V and Fe³⁺/Fe²⁺ = 0.77 V, the increasing order of strengths as a reducing agent is

Which of the following is the least basic?

The maximum number of structural isomers possible for the hydrocarbon having the molecular formula C₄H₆ is

The empirical formula of a compound is CH₂. The mass of one mole of this compound is 42 g. Its molecular formula is

PCl₃ (g) + Cl₂ (g) PCl₅ (g) K_c (250°C) for this reaction is 26. The value of K_p at the same temperature is

The type of epithelium which lines the inner surfaces of fallopian tubes, bronchioles and small bronchi is known as

In a cross between a white-eyed female dragonfly and red-eyed male, how many female progenies will inherit white eyes? (White eyes are X-linked recessive)

With which of the following functions are chromosomes primarily concerned with?

An intrapetiolar type of stipule is present in

In which of the following can erythroblastosis foetalis occur?