KVPY Kishore Vaigyanik Protsahan Yojana STREAM SB/SX 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 SX/SB
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.
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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 SB/SX
Section 1 – Mathematics
PartA :
1) Let be a fixed line segment in the plane. The locus of a point such that the triangle is isosceles, is (with finitely many possible exceptional points)
A) a line
B) a circle
C) the union of a circle and a line
D) the union of two circles and a line
2) The number of solution pairs of the simultaneous equations is
A) 0
B) 1
C) 2
D) 3
3) Let be a relation on the set of all natural numbers given by divides Which of the following properties does satisfy?
I. Reflexivity
II. Symmetry
III. Transitivity
A) I only
B) III only
C) I and III only
D) I and II only
4) The fractional part of a real number is , where is the greatest integer less than or equal to . Let and be the fractional parts of and respectively. Then lies between the numbers
A) 0 and 0.45
B) 0.45 and 0.9
C) 0.9 and 1.35
D) 1.35 and 1.8
5) The number of real solutions of the equation which lie in the interval is
A) 1
B) 2
C) 3
D) 4
7) Suppose are real numbers such that , . The maximum possible value of is
A) 0
B) 3
C) 9
D) 27
8) A shooter can hit a given target with probability . She keeps firing a bullet at the target until she hits it successfully three times and then she stops firing. The probability that she fires exactly six bullets lies in the interval
A) (0.5272 0.5274)
B) (0.2636 0.2638)
C) (0.3157 0.3139)
D) (0.0658 0.6630)
9) For how many different values of does the following system have at least two distinct solutions?
A) 0
B) 1
C) 2
D) Infinitely many
10 ) Let be real numbers such that , Then
A) The largest is and the smallest is
B) The largest is and the smallest is
C) The largest is and the smallest is
D) The largest is and the smallest is
Section 2 – Physics
Part A :
21) The magnitude of acceleration of the electron in the nth orbit of hydrogen atom is and that of singly ionized helium atom is . The ratio is
A) 1:8
B) 1:4
C) 1:2
D) dependent on n
22) A carrot looks orange in colour because of the ß carotene molecule in it. This means that the ß carotene molecule absorbs light of wavelengths
A) longer than 550 nm.
B) shorter than 550 nm.
C) longer than 700 nm.
D) shorter than 700 nm.
23) If some charge is given to a solid metallic sphere, the field inside remains zero and by Gauss’s law all the charge resides on the surface. Suppose now that Coulomb’s force between two charges varies as 1/r3. Then, for a charged solid metallic sphere
A) field inside will be zero and charge density inside will be zero.
B) field inside will not be zero and charge density inside will not be zero.
C) field inside will not be zero and charge density inside will be zero.
D) field inside will be zero and charge density inside will not be zero.
26) It was found that the refractive index of material of a certain prism varied as 1.5+0.004/?2, where ? is the wavelength of light used to measure the refractive index. The same material was then used to construct a thin prism of apex angle 10º. Angles of minimum deviation (dm) of the prism were recorded for the sources with wavelengths ?1 and ?2 respectively. Then
A) dm (?1) < dm (?2) if ?1 < ?2.
B) dm (?1) > dm (?2) if ?1 > ?2.
C) dm (?1) > dm (?2) if ?1 < ?2.
D) dm is the same in both the cases.
27) Two circularly shaped linear polarisers are placed coaxially. The transmission axis of the first polarizer is at 30º from the vertical while the second one is at 60º, both in the clockwise sense. If an unpolarised beam of light of intensity I = 20 W/m2 is incident on this pair of polarisers, then the intensities I1 and I2 transmitted by the first and the second polarisers, respectively, will be close to
A) I1 = 10.0 W/m2 and I2 = 7.5 W/m2
B) I1 = 20 W/m2 and I2 = 15 W/m2
C) I1 = 10.0 W/m2 and I2 = 8.6 W/m2
D) I1 = 15.0 W/m2 and I2 = 0.0 W/m2
29) A bird sitting on a single high tension wire does not get electrocuted because
A) the circuit is not complete.
B) the bird feet has an insulating covering.
C) capacitance of the bird is too small and the line frequency is too small.
D) resistance of the bird is too high.
30) A transverse wave of frequency 500 Hz and speed 100 m/s is travelling in the positive x direction on a long string. At time t = 0 s the displacements at x = 0.0 m and at x = 0.25 m are 0.0 m and 0.02 m, respectively. The displacement at x = 0.2 m at t = 5 × 10-4 s is
A) -0.04 m
B) -0.02 m
C) 0.04 m
D) 0.02 m
31) Two satellites S1 and S2 are revolving around a planet in the opposite sense in coplanar circular concentric orbits. At time t = 0, the satellites are farthest apart. The periods of revolution of S1 and S2 are 3 h and 24 h respectively. The radius of the orbit of S1 is 3×104 km.
Then the orbital speed of S2 as observed from
A) the planet is km h-1 when S2 is closest from S1.
B) the planet is km h-1 when S2 is farthest from S1.
C) S1 is km h-1 when S2 is closest from S1.
D) S1 is km h-1 when S2 is closest to S1.
Section 3 – Chemistry
Part A :
42) Among the a-amino acids – threonine, tyrosine, methionine, arginine and tryptophan, those which contain an aromatic group in their side chain are
A) threonine and arginine
B) tyrosine and tryptophan
C) methionine and tyrosine
D) arginine and tryptophan
43) The number of stereoisomers possible for the following compound is CH3-CH=CH-CH(OH)-CH3
A) 1
B) 2
C) 3
D) 4
44) In electrophilic aromatic substitution reactions of chlorobenzene, the ortho/para-directing ability of chlorine is due to its
A) positive inductive effect (+I)
B) negative inductive effect (–I)
C) positive resonance effect (+R)
D) negative resonance effect (–R)
46) Upon reaction with CH3MgBr followed by protonation, the compound that produces ethanol is
A) CH3CHO
B) HCOOH
C) HCHO
D) (CHO)2
47) Which of the following is NOT an oxidation-reduction reaction?
A) H2 + Br2 ? 2 HBr
B) NaCl + AgNO3 ? NaNO3 + AgCl
C) 2 Na2S2O3 + I2 ? Na2S4O6 + 2 NaI
D) Cl2 + H2O ? HCl + HOCl
48) The thermal stability of alkaline earth metal carbonates ? MgCO3, CaCO3, SrCO3 and BaCO3, follows the order
A) BaCO3 > SrCO3 > CaCO3 > MgCO3
B) CaCO3 > SrCO3 > BaCO3 > MgCO3
C) MgCO3 > CaCO3 > SrCO3 > BaCO3
D) SrCO3 > CaCO3 > MgCO3 > BaCO3
49) When a mixture of diborane and ammonia is heated, the final product is
A) BH3
B) NH4BH4
C) NH2NH2
D) B3N3H6
50) Among the following metals, the strongest reducing agent is
A) Ni
B) Cu
C) Zn
D) Fe
51) The molecule which is NOT hydrolysed by water at 25 ºC is
A) AlCl3
B) SiCl4
C) BF3
D) SF6
51) The molecule which is NOT hydrolysed by water at 25 ºC is
A) AlCl3
B) SiCl4
C) BF3
D) SF6
53) Chlorine has two naturally occurring isotopes, 35Cl and 37Cl. If the atomic mass of Cl is 35.45, the ratio of natural abundance of 35Cl and 37Cl is closest to
A) 3.5:1
B) 3:1
C) 2.5:1
D) 4:1
54) The reaction C2H6 (g) ? C2H4 (g) + H2 (g) is at equilibrium in a closed vessel at 1000 K. The enthalpy change (?H) for the reaction is 137.0 kJ mol–1. Which one of the following actions would shift the equilibrium to the right?
A) Decreasing the volume of the closed reaction vessel
B) Decreasing the temperature at which the reaction is performed
C) Adding an inert gas to the closed reaction vessel
D) Increasing the volume of the closed reaction vessel