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KVPY Mock Test – SA (Short)
Number of questions  40 
Type of questions  Multiple Choice Question with single answer correct 
Time limit (duration of exam)  90 minutes (1.5 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  52 
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 40
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Question 1 of 40
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 40
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 40
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 40
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 40
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 40
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 40
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 40
8. 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 9 of 40
9. 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 10 of 40
10. 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 11 of 40
11. 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 12 of 40
12. 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 13 of 40
13. 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 14 of 40
14. 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 15 of 40
15. Question
Category: ChemistryThe moelcule having a formly group is

Question 16 of 40
16. Question
Category: ChemistryThe structure of cis3hexene is

Question 17 of 40
17. Question
Category: ChemistryThe number of sp
hybridized carbon atoms in

Question 18 of 40
18. Question
Category: ChemistryThe number of valence electrons in an atom with electronic configuration 1s^{2}^{ 2s}^{2}^{ 2p}^{6}^{ 3s}^{2}^{ 3p}^{3}^{}

Question 19 of 40
19. Question
Category: ChemistryThe pair of atoms having the same number of neutrons is

Question 20 of 40
20. Question
Category: ChemistryWhich of the following molecules has no dipole moment ?

Question 21 of 40
21. 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 22 of 40
22. Question
Category: BiologyThe Bowmanís capsule, a part of the kidney is the site of

Question 23 of 40
23. Question
Category: BiologyIn human brain the sensation of touch, pain and temperature is controlled by the

Question 24 of 40
24. Question
Category: BiologyA pathogan which can not be cultured in an artificial medium is

Question 25 of 40
25. Question
Category: BiologyPeople suffering from albinism cannot synthesize

Question 26 of 40
26. Question
Category: BiologyShort sightedness in humans can be corrected by using

Question 27 of 40
27. Question
Category: BiologyA person with blood group “A” can (a) donate blood to, and (b) receive blood from

Question 28 of 40
28. Question
Category: BiologyAnimal cells after removal of nuclei still contained DNA. The source of this DNA is

Question 29 of 40
29. 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 30 of 40
30. 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 31 of 40
31. 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 32 of 40
32. 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 33 of 40
33. 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 34 of 40
34. 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 35 of 40
35. 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 36 of 40
36. 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 37 of 40
37. 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 38 of 40
38. Question
Category: Biology IISister chromatids of a chromosome have

Question 39 of 40
39. Question
Category: Biology IIA diabetic individual becomes unconscious after selfadministering insulin. What should be done immediately to revive the individual?

Question 40 of 40
40. 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?