KVPY (SA) Mock ...

The number of non-negative real roots of 2^x - x - 1 = 0 is

The sides of a triangle ABC are positive integers. The smallest side has length 1. Which of the following statements is true?

The real numbers 'x' satisfying > 1 are precisely those which satisfy

Two trains start at the same time from station A and station B and proceed towards each other at the speeds of 16 km/hr and 21 km/hr, respectively. When they meet, it is found that one train has travelled 60 km more than the other. What is the distance between the two stations?

If a³ + b³ + c³ = 3abc, then a + b is equal to

In the figure given below, angle RQM = angle PSR. Further, it is also known that PS = 5 cm, SR = 5 cm, RQ = 6 cm and PQ = 4 cm. What is the approximate area of quadrilateral PQRS (in cm²)?

What will be the volume of frustum in the given figure?

A cube has a volume of 128 cm³. It is divided into 8 equal cubes. Then, the ratio of an edge of a smaller cube to an edge of the original cube is

What is the difference between the volume of a cone with r = 4 cm, h = 4 cm and the volume of a cone with r = 2 cm and h = 2 cm?

If the volume of a sphere increases by 72.8%, then its surface area increases by

A and B can complete a piece of work in 20 and 30 days, respectively. A and B started the work and after 10 days, A left the job and then C joined B and completed the job by taking 1 day more than the estimated time. How many days would C take to complete the work independently?

If one root of the equation ax² + bx + c = 0 is twice the other, then

If 2 + i is a root of the quadratic equation x² + ax + b = 0, where a, b ∈ R, then the values of a and b are respectively.

Let S_n be the sum of all integers 'k' such that 2ⁿ < k < 20^{n + 1}, for n 1. Then, 9 divides S_n if and only if

The inequality |z - 2| < |z - 4| represents the half plane

Two charges of the same magnitude move in two circles of radii R₁ = R and R₂ = 2R in a region of constant uniform magnetic field . The works W₁ and W₂ done by the magnetic field in the two cases, respectively, are such that

Two projectiles are fired from the same point with the same speed at angles of projection of 60° and 30°. Which one of the following is true?

Two blocks of the same volume with densities ₁ and ₂, such that ₁ > ₂ > _w, are immersed in water (density = _w). If the buoyant force experienced by m₁ is F₁ and that by m₂ is F₂, then

Directions: A body is moving in a circle as shown in the figure starting from point A clock–wise.


It completes one cycle in 20 s.

What will be the average velocity as it starts from A and reaches C after completing two cycles (take the line joining the origin and C as south and the origin and A as west)?

The projectile attains maximum height when the projection angle is

A torch welder is working without his safety glasses. Which of the following parts of his eyes is most likely to get affected?

Which one of the following graphs correctly represents the distance-time variation for a body released vertically downward from the top of a building?

A vessel consists of two plane mirrors at a right angle (as shown in figure). The vessel is filled with water. The total deviation in the incident ray is

The temperature of a metal coin is increased by 100°C and its diameter increases by 0.15%. Its area increases by nearly

A solid cube and a solid sphere of identical material and equal masses are heated to the same temperature and left to cool in the same surroundings. Then

A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. The potential at a distance of 2 cm from the centre of the sphere is

A total of 4,900 J. was expended in lifting a mass of 50 kg. The mass was raised to a height of (g = 10 m/s²)

A planet of mass m is moving around a star of mass M and radius R in a circular orbit of radius r. The star abruptly shrinks to half its radius without any loss of mass. What change will be there in the orbit of the planet?

The Earth moves in an elliptical orbit with the sun S at one of foci as shown in the figure. Its rotational kinetic energy is maximum at the point

Figure (a) below shows a Wheatstone bridge in which P, Q, R and S are fixed resistances, G is a galvanometer and B is a battery. For this particular case, the galvanometer shows zero deflection. Now, only the positions of B and G are interchanged, as shown in figure (b). The new deflection of the galvanometer

The IUPAC name of acetaldehyde (CH₃CHO) is ________.

Which of the following can behave both as an acid and a base according to both the Arrhenius and the Bronsted concept?

Which of the following does not have an sp² hybridised carbon?

Which of the following elements has the greatest tendency to lose electrons?

One mole of nitrogen gas, on reaction with 3.01 10²³ molecules of hydrogen gas, produces

Which of the following compounds has the highest value of dipole moment?

How many atoms are present in 12 10²³ g of C?

Compressibility of gas is less than unity at S.T.P, therefore

The aqueous solution of which of the following compounds neutralises an aqueous solution of caustic soda?

The EMF of the cell is related to the equilibrium constant of the cell reactions as

In bleaching powder (CaOCl₂), the oxidation number of two chlorine atoms is

Which of the following is the correct decreasing order of reactivity of the elements?

What are the main products of the oxidation of alkene with ozone?

Which of the following reactions is not possible?

Since the enthalpy of elements in their standard state is taken to be zero, the heat of formation of a compound

Besides urination, another important activity in which water is substantially lost from the body is

Which part of the nerve cell contains a nucleus?

A human male bearing an allele for a trait on the X chromosome is termed as

For a cross between a tall plant with round seeds (TTRR) and a short plant with wrinkled seeds (ttrr), the F₁ plants will be

In the cell cycle, when will the synthesis of RNA be stopped?

Gram-positive bacteria are those which

Match the following:

A diabetic patient is on insulin. Which of the following cells might have been damaged in this person?

Haemodialysis is a treatment option for patients with malfunctions of

Bile salts

Which of the following pairs is a mismatch?

Lacteals are tiny lymphatic vessels. Where are these found in the body?

Hyposecretion of which hormone causes diabetes?

Which of the following structures will not be visible in the section of a hyaline cartilage?

Which of the following cell structures is/are associated with oxidative phosphorylation?

If f(x) = x³ - 4x + p and f(0) and f(1) have opposite signs, then which of the following is necessarily true?

Given four lines with equations x + 2y – 3 = 0, 3x + 4y – 7 = 0, 2x + 3y – 4 = 0 and 4x + 5y – 6 = 0. Then

In the given figure, O is the centre of the circle and AE is a diameter. If AB = BC and BFC = 25°, find the value of ABC.

In the figure given below, AB is a diameter of the circle, TD is a tangent to the circle and AB = 2AD. If AHD = 36° and DBA = 30°, then what is the measure of CDT?

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

The quadratic equation with rational coefficients, whose one root is i - 1, is

A solid square plate is spun around different axes with the same angular speed. In which of the following choices of axis of rotation will the kinetic energy of the plate be the largest?

An object is placed 0.40 m from one of the two lenses L₁ and L₂ of focal lengths 0.20 m and 0.10 m, respectively as depicted in the figure. The separation between the lenses is 0.30 m.



^{The final image formed by this two lens system is at}

Directions: Study the given electric circuit diagram.



If the voltage between points A and B is 10 V. The voltage between B and C will be

A gun fires bullets each of mass 1 g with velocity of 10 ms^-1 by exerting a constant force of 5 g weight. Then the number of bullets fired per second is
(Take g = 10 ms^-2)

The excess of pressure inside the first soap bubble is three times that inside the second bubble. The ratio of volume of the first to that of the second bubble is

BF₃ is a

Identify product 'Z' in the following reaction scheme:

C₆H₅NH₂

a K₂Cr ₂O₇ + b KCl + c H₂SO₄ x CrO₂Cl₂ + y KHSO₄ + z H₂O

The above equation gets balanced when

The percentage of s character of the hybrid orbitals of carbon in ethane, ethene and ethyne, respectively is

One mole of a compound AB reacts with one mole of a compound CD according to the equation AB + CD AD + CB. When equilibrium was established, it was found that 3/4 mol each of reactants AB and CD had been converted to AD and CB, respectively. There was no change in volume. The equilibrium constant for the reaction is

Which of the following is the correct set of vestigial organs?

A couple has a daughter suffering from Tay Sachs disease, and 4 normal children. Neither parent nor any of the four biological grandparents of the affected daughter had this disease. The most likely genetic condition leading to Tay Sachs disease is

What is the pattern of connection of two strands of DNA?

Mr. X, while drowning, simply failed to try to save himself, even though he was a good swimmer. He must have suffered from ________ neurological disorder.

Which of the following is the inflammation of the lining of the rectal mucosa?