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KVPY Mock Test – SA (Full Length)
KVPY Mock Test – Full Length
Number of questions  80 
Type of questions  Multiple Choice Question with single answer correct 
Time limit (duration of exam)  180 minutes (3 hours) 
Mock Test for  KVPY SA Stream 
Marks for correct answer in Part I  +1 
Marks for correct answer in Part II  +2 
Maximum Marks  100 
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 Answered
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Question 1 of 80
1. Question
Category: MathsLet x, y, z be three nonnegative integers such that x + y + z = 10. The maximum possible value of xyz + xy + yz + zx is

Question 2 of 80
2. Question
Category: MathsIf a, b are natural numbers such that 2013 + a^{2} = b^{2}, then the minimum possible value of ab is

Question 3 of 80
3. Question
Category: MathsThe number of values of b for which there is an isosceles triangle with sides of length b + 5, 3b – 2 and 6 – b is

Question 4 of 80
4. Question
Category: MathsLet a, b be nonzero real numbers. Which of the following statements about the quadratic equation ax^{2} + (a + b)x + b = 0 is neccesarily true ?
(I) It has at least one negative root
(II) It has at least one positive root.
(III) Both its roots are real. 
Question 5 of 80
5. Question
Category: MathsLet x, y, z be nonzero real numbers such that x/y + y/z + z/x = 7 and y/x + z/y + x/z = 9, then x^{3}/y^{3} + y^{3}/z^{3} + z^{3}/x^{3} is equal to

Question 6 of 80
6. Question
Category: MathsIn a triangle ABC with ∠A < ∠B < ∠C, points D,E,F are on the interior of segments BC, CA, AB, respectively. Which of the folloing triangles cannot be similar to ABC?

Question 7 of 80
7. Question
Category: MathsTangents to a circle at points P and Q on the circle intersect at a point R. If PQ = 6 and PR = 5 then the radius of the circle is

Question 8 of 80
8. Question
Category: MathsIn an acuteangled triangle ABC, the altitudes from A, B, C when extended intersect the circumcircle again at points A_{1}, B_{1}, C_{1}, respectively. If ∠ABC = 45° then ∠A_{1}B_{1}C_{1} equals

Question 9 of 80
9. Question
Category: MathsIn a rectangle ABCD, points X and Y are the midpoints of AD and DC, respectively. Lines BX and CD when extended intersect at E, lines BY and AD when extended intersect at F. If the area of ABCD is 60 then the area of BEF is

Question 10 of 80
10. Question
Category: MathsIn the figure given below, ABCDEF is a regular hexagon of side length 1, AFPS and ABQR are squares. Then the ratio Area (APQ)/ Area (SRP) equals

Question 11 of 80
11. Question
Category: MathsA person X is running around a circular track completing one round every 40 seconds. Another person Y running in the opposite direction meets X every 15 second. The time, expressed in seconds, taken by Y to complete one round is

Question 12 of 80
12. Question
Category: MathsThe least positive integer n for which √(n+1) – √(n1) < 0.2 is

Question 13 of 80
13. Question
Category: MathsHow many natural numbers n are there such that n!+10 is a perfect square?

Question 14 of 80
14. Question
Category: MathsTen points lie in a plane so that no three of them are collinear. The number of lines passing through exactly two of these points and dividing the plane into two regions each containing four of the remaining points is

Question 15 of 80
15. Question
Category: MathsIn a city, the total income of all people with salary below Rs. 10000 per annum is less than the total income of all people with salary above Rs. 10000 per annum. If the salaries of people in the first group increases by 5% and the salaries of people in the second group decreases by 5% then the average income of all people

Question 16 of 80
16. Question
Category: PhysicsA man inside a freely falling box throws a heavy ball towards a side wall. The ball keeps on bouncing between the opposite walls of the box. We neglect air resistance and friciton. Which of the following figures depicts the motion of the centre of mass of the entire system (man, the ball and the box)?

Question 17 of 80
17. Question
Category: PhysicsA ball is thrown horizontally from a height with a certain initial velocity at time t = 0. The ball bounces repeatedly from the ground with the coefficient of restitution less than 1 as shown.
Neglect air resistance and taking the upward direction as positive, which figure qualitatively depicts the vertical component of the ballís velocity (V_{y}) as a function of time (t)? 
Question 18 of 80
18. Question
Category: PhysicsA tall tank filled with water has an irregular shape as shown. The wall CD makes an angle of 45° with the horizontal; the wall AB is normal to the base BC. The lengths AB and CD are much smaller than the height h of water (figure not to scale).
Let P_{1}, P_{2} and P_{3}
be the pressures exerted by the water on the wall AB, base BC and the wall CD respectively. Density of water is and g is acceleration due to gravity. Then, approximately 
Question 19 of 80
19. Question
Category: PhysicsThe accompanying graph of position x versus time t represents the motion of a particle. If p and q are both positive constants, the expression that best describes the acceleration α of the particle is

Question 20 of 80
20. Question
Category: PhysicsTwo stones of mass m_{1} and m_{2} (such that m_{1} > m_{2}) are dropped Δt time apart from the same height towards the ground. At a later time t the difference in their speed is ΔV and their mutual separation is ΔS. While both stones are in flight

Question 21 of 80
21. Question
Category: PhysicsThe refractive index of a prism measured using three lines of a mercury vapour lamp. If μ_{1}, μ_{2}, μ_{3} are the measured refractive indices for these green, blue and yellow lines respectively, then

Question 22 of 80
22. Question
Category: PhysicsA horizontal parallel beam of light passes through a vertical convex lens of focal length 20 cm and is then reflected by a tilted plane mirror so that it converges to a point I. The distance PI is 10 cm.
M is a point at which the axis of the lens intersects the mirror. The distance PM is 10 cm. The angle which the mirror makes with the horizontal is 
Question 23 of 80
23. Question
Category: PhysicsIn a car a rear view mirror having a radius of curvature 1.50 m forms a virtual image of a bus located 10.0 m from the mirror. The factor by which the mirror magnifies the size of the bus is close to

Question 24 of 80
24. Question
Category: PhysicsConsider the circuit shown in the figure below :
All the resistors are identical. The ratio I/I’ is 
Question 25 of 80
25. Question
Category: PhysicsThe figure shows a bar magnet and a metallic coil. Consider four situations.
(I) Moving the magnet away from the coil.
(II) Moving the coil towards the magnet.
(III) Rotating the coil about the vertical diameter.
(IV) Rotating the coil about its axis
An emf in the coil will be generated for the following situations 
Question 26 of 80
26. Question
Category: PhysicsA current of 0.1 A flows through a 25 Ω resistor represented by the circuit diagram. The current in the 80 Ω resistor is

Question 27 of 80
27. Question
Category: PhysicsSolar energy is incident normally on the earthís surface at the rate of about 1.4 kW m^{2} . The distance between the earth and the sun is 1.5 × 10^{11} m. Energy (E) and mass (m) are related by Einstein equation
E=mc^{2} where c (3 × 10^{8} m/s) is the speed of light in free space. The decrease in the mass of the sun is 
Question 28 of 80
28. Question
Category: PhysicsIf the current through a resistor in a circuit increases by 3%, the power dissipated by the resistor

Question 29 of 80
29. Question
Category: PhysicsAn ideal gas filled in a cylinder occupies volume V. The gas is compressed isothermally to the volume V/3. Now the cylinder valve is opened and the gas is allowed to leak keeping temperature same. What percentage
of the number of molecules escape to bring the pressure in the cylinder back to its original valuye. 
Question 30 of 80
30. Question
Category: PhysicsAn electron enters a chamber in which a uniform magnetic field is present as shown
An electric field of appropriate magnitude is also applied so that the electron travels undeviated without any change in its speed thorugh the chamber. We are ignoring gravity. Then, the direction of the electric field is 
Question 31 of 80
31. Question
Category: ChemistryThe moelcule having a formly group is

Question 32 of 80
32. Question
Category: ChemistryThe structure of cis3hexene is

Question 33 of 80
33. Question
Category: ChemistryThe number of sp
hybridized carbon atoms in

Question 34 of 80
34. Question
Category: ChemistryThe number of valence electrons in an atom with electronic configuration 1s^{2}^{ 2s}^{2}^{ 2p}^{6}^{ 3s}^{2}^{ 3p}^{3}^{}

Question 35 of 80
35. Question
Category: ChemistryThe pair of atoms having the same number of neutrons is

Question 36 of 80
36. Question
Category: ChemistryWhich of the following molecules has no dipole moment ?

Question 37 of 80
37. Question
Category: ChemistryThe decay profiles of three radioactive species A, B and C are given below :
These profiles imply that the decay constants k_{A}, k_{B} and k_{C} follow the order 
Question 38 of 80
38. Question
Category: ChemistryA specific volume of H_{2} requires 24 s to diffuse out of a container. The time required by an equal volume of O_{2} to diffuse out under identical conditions, is

Question 39 of 80
39. Question
Category: ChemistryAcetic acid reacts with sodium metal at room temperature to produce

Question 40 of 80
40. Question
Category: ChemistryThe equilibrium constant, K_{C} for
is 4L^{2}mol^{2}. If the equilibrium concentration of benzene is 0.5 mol L^{1}, that of accetyle in mol L^{1} must be 
Question 41 of 80
41. Question
Category: ChemistryThe weight percent of sucrose (formula weight = 342 g mol^{1}) in an aqueous solution is 3.42. The density of the solution is 1gmL^{1}, the concentration of sucrose in the solution in molL^{1} is

Question 42 of 80
42. Question
Category: ChemistryThe order of reactivity of K, Mg, Au and Zn with water is

Question 43 of 80
43. Question
Category: ChemistryWhich of the following is an anhydride ?

Question 44 of 80
44. Question
Category: ChemistryWhich of the following metals will precipitate copper from copper sulfate solution?

Question 45 of 80
45. Question
Category: ChemistryThe radii of the first Bohr orbit of

Question 46 of 80
46. Question
Category: BiologyThe Bowmanís capsule, a part of the kidney is the site of

Question 47 of 80
47. Question
Category: BiologyIn human brain the sensation of touch, pain and temperature is controlled by the

Question 48 of 80
48. Question
Category: BiologyA pathogan which can not be cultured in an artificial medium is

Question 49 of 80
49. Question
Category: BiologyMeiosis I and Meiosis II are characterised by the separation of,

Question 50 of 80
50. Question
Category: BiologyPeople suffering from albinism cannot synthesize

Question 51 of 80
51. Question
Category: BiologyShort sightedness in humans can be corrected by using

Question 52 of 80
52. Question
Category: BiologyA person with blood group “A” can (a) donate blood to, and (b) receive blood from

Question 53 of 80
53. Question
Category: BiologyAnimal cells after removal of nuclei still contained DNA. The source of this DNA is

Question 54 of 80
54. Question
Category: BiologyWhich one of the following combinations is found in DNA?

Question 55 of 80
55. Question
Category: BiologyWhich one of the following is NOT a mode of asexual reproduction?

Question 56 of 80
56. Question
Category: BiologyWhich one of the following class of animals consitutes the largest biomass on earth?

Question 57 of 80
57. Question
Category: BiologyIn the digestive system, the pH of the stomach and the intestine, respectively are

Question 58 of 80
58. Question
Category: BiologyThe major nitrogenous excretory product in mammals is

Question 59 of 80
59. Question
Category: BiologyWhich of the following plant traits (characters) is NOT an adaptatioin to dry (Xeric) habitats?

Question 60 of 80
60. Question
Category: BiologyBiological diversity increases with the productivity of an ecosystem. In which of the following habitats do we see the greatest diversity of species?

Question 61 of 80
61. Question
Category: Maths IILet a, b, c, d, e be natural numbers in an arithmetic progression such that a + b + c + d + e is the cube of an integer and b + c + d is square of an integer. The least possible value of the number of digits of c is

Question 62 of 80
62. Question
Category: Maths IIOn each face of a cuboid, the sum of its perimeter and its area is written. Among the six numbers so written, there are three distinct numbers and they are 16, 24 and 31. The volume of the cuboid lies between

Question 63 of 80
63. Question
Category: Maths IILet ABCD be a square and let P be point on segment CD such that DP : PC = 1 : 2. Let Q be a point on segment AP such that ∠BQP = 90°. Then the ratio of the area of quadrilateral PQBC to the area of the square ABCD is

Question 64 of 80
64. Question
Category: Maths IISuppose the height of a pyramid with a square base is decreased by p% and the lengths of the sides of its square base are increased by p% (where p > 0). If the volume remains the same, then

Question 65 of 80
65. Question
Category: Maths IIThere are three kinds of liquids X, Y, Z,. Three jars J_{1}, J_{2}, J_{3} contain 100 ml of liquids X, Y, Z, respectively. By an operation we mean three steps in the following order:
 stir the liquid in J_{1} and transfer 10 ml from J_{1} into J_{2};
 stir the liquid in J_{2} and transfer 10 ml from J_{2} into J_{3};
 stir the liquid in J_{3} and transfer 10 ml from J_{3} into J_{1} ;
After performing the operation four times, let x, y, z be the amounts of X, Y, Z, respectively, in J_{1}. Then

Question 66 of 80
66. Question
Category: Physics IITwo identical uniform rectangular blocks (with longest side L) and a solid sphere of radius R are to be balanced at the edge of a heavy table such that the centre of the sphere remains at the maximum possible horizontal distance from the vertical edge of the table without toppling as indicated in the figure.
If the mass of each block is M and of the sphere is M/2, then the maximum distance x that can be achieved is 
Question 67 of 80
67. Question
Category: Physics IITwo skaters P and Q are skating towards each other. Skater P throws a ball towards W every 5 s such that it always leaves her hand with speed 2 ms^{1} with respect to the ground. Consider two cases:
(I) P runs with speed 1 ms^{1} towards Q while Q remains stationary
(II) Q runs with speed 1 ms^{1} towards P while P remains stationary.
Note that irrespective of speed of P, ball always leaves P’s hand with speed 2 ms^{1} with respect to the ground.
Ignore gravity. Balls will be received by Q 
Question 68 of 80
68. Question
Category: Physics IIA 10.0 W electrical heater is used to heat a container filled with 0.5 kg of water. It is found that the temperature of the water and the container rise by 3 K in 15 minutes. The container is then emptied, dried, and filled with 2 kg of an oil. It is now observed that the same heater raises the temperature of the containeroil system by 2 K in 20 minutes. Assuming no other heat losses in any of the processes, the specific heat capacity of the oil is

Question 69 of 80
69. Question
Category: Physics IIA ray of light incident on a transparent sphere at an angle Π/4 and refracted at an angle r, emerges from the sphere after suffering one internal reflection. The total angle of deviation of the ray is

Question 70 of 80
70. Question
Category: Physics IIAn electron with an initial speed of 4.0 × 10^{6} ms^{1} is brought to rest by an electric field. The mass and charge of an electron are 9 × 10^{21} kg and 1.6 × 10^{19}C, respectively. Identify the correct statement

Question 71 of 80
71. Question
Category: Chemistry IIThe degree of dissociation of acetic acid (0.1 mol L^{1} in water (Ka of acetic acid is 10^{5} is

Question 72 of 80
72. Question
Category: Chemistry IICompound ‘X’ on heating with Zn dust gives compound ‘Y’ which on treatment with O_{3} followed by reaction with Zn dust gives propionaldehyde. The structure of ‘X’ is

Question 73 of 80
73. Question
Category: Chemistry IIThe amount of metallic Zn (Atomic weight = 65.4) required to react with aqueous sodium hydroxide to produce 1 g of H_{2}, is

Question 74 of 80
74. Question
Category: Chemistry IINatural abundances of ^{12}C and ^{13}C isotopes of carbon are 99% and 1%, respectively. Assuming they only contributes to the mol. wt. of C_{2}F_{4}, the percentage of C_{2}F_{4} having a molecular mass of 101 is

Question 75 of 80
75. Question
Category: Chemistry II2, 3Dimethylbut2ene when reacted with bromine forms a compound which upon heating with alcoholic KOH produce the following major product.

Question 76 of 80
76. Question
Category: Biology IISister chromatids of a chromosome have

Question 77 of 80
77. Question
Category: Biology IIA diabetic individual becomes unconscious after selfadministering insulin. What should be done immediately to revive the individual?

Question 78 of 80
78. Question
Category: Biology IIA regular check on the unborn baby of a lady towards the end of her pregnancy showed a heart rate of 80 beats per minute. What would the doctor infer about the baby’s heart condition from this?

Question 79 of 80
79. Question
Category: Biology IIThree uniformly watered plants i, ii and iii were kept in 45% relative humidity, 45% relative humidity with blowing wind and 95% relative humidity, respectively. Arrange these plants in the order (faster to slowest) in which they will dry up.

Question 80 of 80
80. Question
Category: Biology IIMany population colonising a new habitat show a logistic population growth pattern over time, as shown in the figure below.
In such a population, the POPULATION growth rate