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KVPY Mock Test – SB / SX (Quiz)
Number of questions  20 
Type of questions  Multiple Choice Question with single answer correct 
Time limit (duration of exam)  45 minutes 
Mock Test for  KVPY SA Stream 
Marks for correct answer in Part I  +1 
Marks for correct answer in Part II  +2 
Maximum Marks  40 
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Question 1 of 32
1. Question
Category: MathsLet f(x) = √2 xx^{2} and g(x) = cos x. Which of the following statements are true?
(I) Domain of f((g(x))^{2}) = Domain of f(g(x))
(II) Domain of f(g(x)) + g(f(x)) = Domain of g(f(x))
(III) Domain of f(g(x)) = Domain of f(g(x))
(IV) Domain of g((f(x))^{3}) = Domain of f(g(x)) 
Question 2 of 32
2. Question
Category: MathsFor real x with 10 ≤ x ≤ 10 define f(x) = where for a real number r we denote by [r] the largest integer less than or equal to r. The number of points of discontinutiy of f in the interval (10,10) is

Question 3 of 32
3. Question
Category: MathsFor a real number x let [x] denote the largest integer less than or equal to x and {x} = x [x]. The smallest possible integer value of n for which exceeds 2013 is

Question 4 of 32
4. Question
Category: MathsThe area bounded by the curve y = cos x, the line joining (π/4, cos(π/4)) and (0, 2) and the line joining (π/ 4, cos(π/4)) and (0, 2) is

Question 5 of 32
5. Question
Category: MathsA box contains coupons labeled 1, 2, 3….n. A coupon is picked at random and the number x is noted. The coupon is put back into the box and a new coupon is picked at random. The new number is y. Then the probability that one of the numbers x, y divides the other is (in the options below [r] denotes the largest integer less than or equal to r)

Question 6 of 32
6. Question
Category: MathsLet n ≥ 3. Alist of numbers 0 < x_{1} < x_{2} < … < x_{n} has mean μ and standard deviatiion σ.Anew list of numbers is made as follows : y_{1} = 0, y_{2} = x_{2}, ….,y_{n1} = x_{n1}, y_{n} = x_{1} + x_{n}. The mean and the standard deviation of the new list are and . Which of the following is necessarily true?

Question 7 of 32
7. Question
Category: Physics“Two species of radioactive atoms aremixed in equal number. The disintegration of the first species is λ and of the second is λ/3. After a long time the mixture will behave as a species with mean life of approximately”

Question 8 of 32
8. Question
Category: PhysicsThe bulk modulus of a gas is defined as B = VdP/dV. For an adiabatic process the variation of B is proportional to P^{n}. For an idea gas, n is

Question 9 of 32
9. Question
Category: PhysicsPhotons of energy 7 eV are incident on two metals A and B with work functions 6 eV and 3 eV respectively. Theminimum de Broglie wavelengths of the emitted photoelectrons withmaximum energies are λA and λB, respectivelywhere λA/λB is nearly

Question 10 of 32
10. Question
Category: PhysicsAn electron enters a chamber in which a uniform magnetic field is present as shown. Ignore gravity.
During its motion inside the chamber

Question 11 of 32
11. Question
Category: PhysicsA ray of light incident on a glass sphere (refractive index √3 ) suffers total internal reflection before emerging out exactly parallel to the incident ray. The angle of incidence was

Question 12 of 32
12. Question
Category: PhysicsYoungLaplace law states that the excess pressure inside a soap bubble of radius R is given by ΔP = 4σ/R where σ is the coefficient of surface tension of the soap. The number E_{0} is a dimensionless number that is used to describe the shape of bubbles rising through a surrounding fluid. It is a combination of g, the acceleration due to gravity, ρ, the density of the surrounding fluid, σ and a characterstic length scale Lwhich could be the radius of the bubble. A possible expression for E_{0} is

Question 13 of 32
13. Question
Category: ChemistryThe entropy change in the isothermal reversible expansion of 2moles of an ideal gas from 10 to 100 L at 300 K is

Question 14 of 32
14. Question
Category: ChemistryDGlucose upon treatment with brominewater gives

Question 15 of 32
15. Question
Category: ChemistryIn the structure of borax, the numbers of boron atoms and BOB units, respectively, are

Question 16 of 32
16. Question
Category: ChemistryThe number of peptide bonds in the compound

Question 17 of 32
17. Question
Category: ChemistryFor the isothermal reversible expansion of an ideal gas

Question 18 of 32
18. Question
Category: ChemistryIf the angle of incidence of Xray of wavelength 3Å which produces a second order diffracted beam from the (100) planes in a simple cubic lattice with interlayer spacing a = 6 Å is 30°, the angle of incidence that produ ces a firstorder diffracted beam from the (200) planes is

Question 19 of 32
19. Question
Category: BiologyChlorofluorocarbons (CFCs) are belived to be associated with cancers because,

Question 20 of 32
20. Question
Category: BiologyMorphogeneticmovements take place predominantly during the following embryonic stage

Question 21 of 32
21. Question
Category: BiologyThe only organ which is capable of producing Fructose in humans is

Question 22 of 32
22. Question
Category: BiologyStroke could be prevented/treated with

Question 23 of 32
23. Question
Category: BiologyIn orange and lemon, the edible part of the fruit is

Question 24 of 32
24. Question
Category: BiologyWhich one of the following statements about nitrogenase is correct?

Question 25 of 32
25. Question
Category: Maths IILet f(x) = 1+ (x/1!) + (x^{2}/2!) + (x^{3}/3!) + (x^{4}/4!) . The number of real roots of f(x) = 0 is

Question 26 of 32
26. Question
Category: Maths IISuppose that the earth is a sphere of radius 6400 kilometers. The height from the earths surface from where exactly a fourth of the earths surface is visible, is

Question 27 of 32
27. Question
Category: Physics IIA ball is rolling without slipping in a spherical shallow bowl (radius R) as shown in the figure and is executing simple harmonic motion. If the radius of the ball is doubled, the period of oscillation

Question 28 of 32
28. Question
Category: Physics IIA solid sphere rolls without slipping, first horizontal and then up to a point X at height h on an inclined plane before rolling down, as shown.

Question 29 of 32
29. Question
Category: Chemistry IIConsider the equilibria (1) and (2) with equilibrium constants K_{1} and K_{2}, respectively
K_{1} and K_{2} are related as

Question 30 of 32
30. Question
Category: Chemistry IIAqueous solution of metallic nitrate X reacts with NH_{4}OH to form Y which dissolves in excess NH_{4}OH. The resulting complex is reduced by acetaldehyde to deposit the metal. X and Y, respectively, are

Question 31 of 32
31. Question
Category: Biology IIThe figure below demonstrates the growth curves of two organismsAand B growing in the same area.What kind of relation exists between A and B?

Question 32 of 32
32. Question
Category: Biology IIA scientist has cloned an 8 Kb fragment of a mouse gene into the Eco RI site of a vector of 6 Kb size. The cloned DNA has no other Eco RI site within. Digestions of the cloned DNA is shown below.
Which one of the following sets of DNA fragments generated by digestion with both Eco RI and Bam HI as shown in (iii) is from the gene?