Organisation : Kishore Vaigyanik Protsahan Yojana
Exam : KVPY- Kishore Vaigyanik Protsahan Yojana Exam
Document Type : KVPY-2019 question papers (SA, SB/SX)
Year: KVPY-2019
Stream: SA, SB/SX
Website : kvpy [dot] iisc [dot] ernet [dot] in
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 : KVPY Kishore Vaigyanik Protsahan Yojana STREAM SB/SX Question Paper 2017 : www.pdfquestion.in/22934.html
Stream SA
Subject Name: Stream SA
Creation Date: 2019-11-03 13:45:55
Duration: 180
Total Marks: 100
Display Marks: Yes
Download Question Paper :
Stream -SA :
https://www.pdfquestion.in/uploads/pdf2019/34343-STREAMSA.pdf
Stream -SB/SX :
https://www.pdfquestion.in/uploads/pdf2019/34343-STREAMSBSX.pdf
Part A :
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
Stream SB
Part B :
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
Part C :
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