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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|
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Question 1 of 40
1. QuestionCategory: Maths
Let x, y, z be three non-negative integers such that x + y + z = 10. The maximum possible value of xyz + xy + yz + zx is
Question 2 of 40
2. QuestionCategory: Maths
If a, b are natural numbers such that 2013 + a2 = b2, then the minimum possible value of ab is
Question 3 of 40
3. QuestionCategory: Maths
The 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. QuestionCategory: Maths
Let a, b be non-zero real numbers. Which of the following statements about the quadratic equation ax2 + (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. QuestionCategory: Maths
Let x, y, z be non-zero real numbers such that x/y + y/z + z/x = 7 and y/x + z/y + x/z = 9, then x3/y3 + y3/z3 + z3/x3 is equal to
Question 6 of 40
6. QuestionCategory: Maths
In 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. QuestionCategory: Maths
Tangents 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. QuestionCategory: Physics
A 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. QuestionCategory: Physics
A 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 (Vy) as a function of time (t)?
Question 10 of 40
10. QuestionCategory: Physics
A 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 P1, P2 and P3
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. QuestionCategory: Physics
The 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. QuestionCategory: Physics
Two stones of mass m1 and m2 (such that m1 > m2) 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. QuestionCategory: Physics
The refractive index of a prism measured using three lines of a mercury vapour lamp. If μ1, μ2, μ3 are the measured refractive indices for these green, blue and yellow lines respectively, then
Question 14 of 40
14. QuestionCategory: Physics
A 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. QuestionCategory: Chemistry
The moelcule having a formly group is
Question 16 of 40
16. QuestionCategory: Chemistry
The structure of cis-3-hexene is
Question 17 of 40
17. QuestionCategory: Chemistry
The number of sp
hybridized carbon atoms in
Question 18 of 40
18. QuestionCategory: Chemistry
The number of valence electrons in an atom with electronic configuration 1s2 2s2 2p6 3s2 3p3
Question 19 of 40
19. QuestionCategory: Chemistry
The pair of atoms having the same number of neutrons is
Question 20 of 40
20. QuestionCategory: Chemistry
Which of the following molecules has no dipole moment ?
Question 21 of 40
21. QuestionCategory: Chemistry
The decay profiles of three radioactive species A, B and C are given below :
These profiles imply that the decay constants kA, kB and kC follow the order
Question 22 of 40
22. QuestionCategory: Biology
The Bowmanís capsule, a part of the kidney is the site of
Question 23 of 40
23. QuestionCategory: Biology
In human brain the sensation of touch, pain and temperature is controlled by the
Question 24 of 40
24. QuestionCategory: Biology
A pathogan which can not be cultured in an artificial medium is
Question 25 of 40
25. QuestionCategory: Biology
People suffering from albinism cannot synthesize
Question 26 of 40
26. QuestionCategory: Biology
Short sightedness in humans can be corrected by using
Question 27 of 40
27. QuestionCategory: Biology
A person with blood group “A” can (a) donate blood to, and (b) receive blood from
Question 28 of 40
28. QuestionCategory: Biology
Animal cells after removal of nuclei still contained DNA. The source of this DNA is
Question 29 of 40
29. QuestionCategory: Maths II
Let 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. QuestionCategory: Maths II
On 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. QuestionCategory: Maths II
Let 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. QuestionCategory: Physics II
Two 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. QuestionCategory: Physics II
Two 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. QuestionCategory: Physics II
A 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 container-oil 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. QuestionCategory: Chemistry II
The 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. QuestionCategory: Chemistry II
Compound ‘X’ on heating with Zn dust gives compound ‘Y’ which on treatment with O3 followed by reaction with Zn dust gives propionaldehyde. The structure of ‘X’ is
Question 37 of 40
37. QuestionCategory: Chemistry II
The amount of metallic Zn (Atomic weight = 65.4) required to react with aqueous sodium hydroxide to produce 1 g of H2, is
Question 38 of 40
38. QuestionCategory: Biology II
Sister chromatids of a chromosome have
Question 39 of 40
39. QuestionCategory: Biology II
A diabetic individual becomes unconscious after self-administering insulin. What should be done immediately to revive the individual?
Question 40 of 40
40. QuestionCategory: Biology II
A 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?