KVPY Kishore Vaigyanik Protsahan Yojana Stream SA Question Paper 2017

Name of the Organisation : Kishore Vaigyanik Protsahan Yojana
Name of the Paper : Kishore Vaigyanik Protsahan Yojana KVPY 2017
Year : 2017
Subject : Stream SA
Website : http://www.kvpy.iisc.ernet.in/main/index.htm
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Kishore Vaigyanik Protsahan Yojana Paper

** The Kishore Vaigyanik Protsahan Yojana (KVPY) is an on-going National Program of Fellowship in Basic Sciences, initiated and funded by the Department of Science and Technology, Government of India, to attract exceptionally highly motivated students for pursuing basic science courses and research career in science.

Related : IARCS Indian National Olympiad in Informatics INOI Question Paper 2017 : www.pdfquestion.in/22923.html

KVPY 2017 Question Paper

Aptitude Test :
** Selection of the students is made from those studying in XI standard to 1st year of any undergraduate Program in Basic Sciences namely B.Sc./B.S./B.Stat./B.Math./Int. M.Sc./M.S. in Mathematics, Physics, Chemistry and Biology having aptitude for scientific research.

STREAM SA

Section 1 – Mathematics

PartA :
1) A quadrilateral has distinct integer side lengths. If the second-largest side has length ,
then the maximum possible length of the largest side is
A) 25
B) 26
C) 27
D) 28

2) The largest power of that divides is
A) 98
B) 99
C) 100
D) 101

3) Let be the set of all ordered pairs of positive integers satisfying the condition Then
A) is an infinite set
B) is the empty set
C) has exactly one element
D) is a finite set and has at least two elements

5) Let be a nine-sided regular polygon with side length 2 units. The difference between the lengths of the diagonals and equals
A) 2
B) 2 /3
C) 6
D) 2

6) Let be nonzero real numbers, of which are positive and remaining are negative. The number of ordered pairs , for which is positive, is 55. Similarly, the number of ordered pairs , for which is negative, is 50. Then the value of is
A) 629
B) 325
C) 125
D) 221

7) Let be the remainder when the polynomial is divided by . Then
A) is the zero polynomial
B) is a nonzero constant
C) degree of is one
D) degree of is two

8) It is given that the number can be written as a product of two distinct prime numbers . Further, assume that there are 42900 numbers which are less than and are co-prime to it. Then, is
A) 462
B) 464
C) 400
D) 402

9) In the figure, is a unit square. A circle is drawn with centre on the extended line and passing through . If the diagonal is tangent to the circle, then the area of the shaded region is
A)9/6
B)8/6
C)7/4
D)6/4

10) The sum of all non-integer roots of the equation is x5-6×4+11x
A) 6
B) –11
C) –5
D) 3

Section 2 – Physics

PartA :
16) Consider the following statements (X and Y stand for two different elements)
(I) 32X65 and 33Y65 are isotopes.
(II) 42X86 and 42Y85 are isotopes.
(III) 85X174 and 88Y177 have the same number of neutrons.
(IV) 92X235 and 94Y235 are isobars
The correct statements are:
A) II and IV only.
B) I, II and IV only.
C) II, III and IV only.
D) I, II, III and IV.

17) A student performs an experiment to determine the acceleration due to gravity g. The student throws a steel ball up with initial velocity u and measures the height h travelled by it at different times t. The graph the student should plot on a graph paper to readily obtain the value of g is
A) h versus t.
B) h versus t2.
C) h versus vt.
D) h/t versus t

18) A person goes from point P to point Q covering 1/3 of the distance with speed 10 km/hr, the next 1/3 of the distance at 20 km/hr and the last 1/3 of the distance at 60 km/hr. The average speed of the person is
A) 30 km/hr
B) 24 km/hr
C) 18 km/hr
D) 12 km/hr

19) A person looks at the image of two parallel finite length lines PQ and RS in a convex mirror (see figure). Which of the following represents schematically the image correctly? (Note: Letters P, Q, R and S are used only to denote the endpoints of the lines.)
A) A
B) B
C) C
D) D

20) In Guericke’s experiment to show the effect of atmospheric pressure, two copper
hemispheres were tightly fitted to each other to form a hollow sphere and the air from the
sphere was pumped out to create vacuum inside. If the radius of each hemisphere is R and the
atmospheric pressure is P, then the minimum force required (when the two hemispheres are
pulled apart by the same force) to separate the hemispheres is
A) 2/2 r
B) 4/r
C) r2
D) r2/p2

21) Positive point charges are placed at the vertices of a star shape as shown in the figure. Direction of the electrostatic force on a negative point charge at the centre O of the star is
A) towards right
B) vertically up
C) towards left
D) vertically down

22) A total solar eclipse is observed from the earth. At the same time an observer on the moon views the earth. She is most likely to see (E denotes the earth)
A) A
B) B
C) C
D) D

23) Ice in a freezer is at –7 ºC. 100 g of this ice is mixed with 200 g of water at 15 ºC. Take the freezing temperature of water to be 0 ºC, the specific heat of ice equal to 2.2 J/g ºC, specific heat of water equal to 4.2 J/g ºC, and the latent heat of ice equal to 335 J/g. Assuming no loss of heat to the environment, the mass of ice in the final mixture is closest to
A) 88 g
B) 67 g
C) 54 g
D) 45 g

24) A point source of light is placed at 2f from a converging lens of focal length f. A flat mirror is placed on the other side of the lens at a distance d such that rays reflected from the mirror are parallel after passing through the lens again. If f = 30 cm, then d is equal to
A) 15 cm.
B) 30 cm.
C) 45 cm.
D) 75 cm.

25) The word “KVPY” is written on a board and viewed through different lenses such that board is at a distance beyond the focal length of the lens. Ignoring magnification effects, consider the following statements.
(I) Image (i) has been viewed from the planar side of a plano-convex lens and image
(ii) from the convex side of a plano-convex lens.
(II) Image (i) has been viewed from the concave side of a plano-concave lens and image (ii) from the convex side of a plano-convex lens.
(III) Image (i) has been viewed from the concave side of a plano-concave lens and image (ii) from the planar side of a plano-convex lens.
(IV) Image (i) has been viewed from the planar side of a plano-concave lens and image (ii) from the convex side of a plano-convex lens.
Which of the above statements are correct?
A) All four.
B) Only (III).
C) Only (IV).
D) Only (II), (III) and (IV).

Section 3 – Chemistry

PartA :
32) The stability of carbanions follows the order
A) III < IV < I < II
B) I < II < IV < III
C) III < II < I < IV
D) IV < III < II < I

36) The first ionisation energy of Na, B, N and O atoms follows the order
A) B < Na < O < N
B) Na < B < O < N
C) Na < O < B < N
D) O < Na < N < B

37) Among P2O5, As2O3, Sb2O3 and Bi2O3, the most acidic oxide is
A) P2O5
B) As2O3
C) Sb2O3
D) Bi2O3

38) Among K, Mg, Au and Cu, the one which is extracted by heating its ore in air is
A) K
B) Mg
C) Au
D) Cu

39) The metal ion with total number of electrons same as S2? is
A) Na+
B) Ca2+
C) Mg2+
D) Sr2+

40) X g of Ca [atomic mass = 40] dissolves completely in concentrated HCl solution to produce 5.04 L of H2 gas at STP. The value of X is closest to
A) 4.5
B) 8.1
C) 9.0
D) 16.2

41) A 20 g object is moving with velocity 100 m s–1. The de Broglie wavelength (in m) of the object is [Planck’s constant h = 6.626 × 10–34 J s]
A) 3.313 × 10–34
B) 6.626 × 10–34
C) 3.313 × 10–31
D) 6.626 × 10–31

42) In a closed vessel at STP, 50 L of CH4 is ignited with 750 L of air (containing 20% O2). The number of moles of O2 remaining in the vessel on cooling to room temperature is closest to
A) 5.8
B) 2.2
C) 4.5
D) 6.7

43) CO2 is passed through lime water. Initially the solution turns milky and then becomes clear upon continued bubbling of CO2. The clear solution is due to the formation of
A) CaCO3
B) CaO
C) Ca(OH)2
D) Ca(HCO3)2

44) The maximum number of electrons that can be filled in the shell with the principal quantum number n = 3 is
A) 18
B) 9
C) 8
D) 2

45) The atomic radii of Li, F, Na and Si follow the order
A) Si > Li > Na > F
B) Li > F > Si > Na
C) Na > Si > F > Li
D) Na > Li > Si > F