FIIT JEE KVPY Class XI Mathematics Model Question Paper 2015
Name of the Organisation :FIIT JEE Ltd
Name of the Paper : KVPY Mathematics Model Question Paper 2015
Year : 2015
Name of the Subject : Mathematics
Class : XI STD
Website : http://www.fiitjee.co/DownLoads/KVPY-Question-Papers-and-Solutions/16
Download Sample Question Paper Class XI 2015 : https://www.pdfquestion.in/uploads/8191Maths.pdf
Download Sample Question Paper Class XI 2012 SA Stream- Stage I : https://www.pdfquestion.in/uploads/8191mathsI.pdf
Download Sample Question Paper Class XI 2012 SA Stream- Stage II : https://www.pdfquestion.in/uploads/8191MathsII.pdf
KVPY Mathematics Model Question Paper :
1. Two distinct polynomials f (x) and g(x) are defined as follows f(x)= x + ax+=2 = g(x) = x+2x+a If the equation f(x)= 0 & g(x)=0 and have a common root then the sum of the roots of the equation g(x)+f(x)= 0
Related : FIIT JEE KVPY Class XII Mathematics Model Question Paper 2015 : www.pdfquestion.in/8187.html
(A) -1/2 (B) 1/2 (C) 0 (D) 0
2. If n is the smallest natural number such that n + 2n + 3n +……. + 99n is a perfect square, then the number of digits in n2 is
(A) 1 (B) 2 (C) 3 (D) more than 3
3. Let x, y, z be positive reals. Which of the following implies x = y = z?
(I) x3 +Y3 +Z3 = 3xyz
(II) x3+y2+2xy+z + 3 yz = 3xyz
(III) x3 + x2x + y2z + z2x = 3xyz
(IV) (x+y+z)3 = 27xyz
(A) I, IV only
(B) I, II, IV only
(C) I, II and III only
(D) All of them
4. In the figure given below, a rectangle of perimeter 76 units is divided into 7 congruent rectangles. What is the perimeter of each of the smaller rectangles?
(A) 38 (B) 32 (C) 28 (D) 19
5. The largest non – negative integer k such that 24k divides 13! Is
(A) 2 (B) 3 (C) 4 (D) 5
6. In a triangle ABC, points X and Y are on AB and AC, respectively, such the XY is parallel to
BC. Which of the two following equalities always hold? (Here [PQR] denotes the area of triangle PQR)
(I) [BCX] = [BCY]
(II) [ACX].[ABY] = [AXY??ABC]
(A) Neither (I) nor (II)
(B) (I) only
(C) (II) only
(D) Both (I) and (II)
7. Let P be an interior point of triangle ABC. Let Q and R be the reflections of P in AB and AC, respectively. If Q, A, R are collinear then A equals
(A) 30 (B)60 (C) 90 (D)120
8. Let ABCD be a square of side length 1, and there be a circle passing through B and C, and touching AD. The radius of the circle is
(A) 3/8 (B)1/2 (C) 5/8 (D)1/20
9. A man standing on a railway platform noticed that a train took 21 seconds to cross the platform (this means the time elapsed from the moment the engine enters the platform till the last compartment leaves the platform) which is 88 metres long, and that it took 9 seconds to pass him. Assuming that the train was moving with uniform speed, what is the length of the train in metres?
(A) 55 (B) 60 (C) 66 (D) 72
What is the KVPY?
** The “Kishore Vaigyanik Protsahan Yojana” (KVPY) is a program started in 1999 by the Department of Science and Technology (DST), Government of India to encourage students who are studying Basic Sciences to take up research career in Science.
** The aim of the program is to identify and encourage talented and motivated students to pursue career in research.
** This program aims to assist the students to realize their potential and to ensure that the best scientific talent is groomed for research and development in the country. Generous fellowship and contingency grant are provided to the selected KVPY Fellows up to the pre Ph.D. level or 5 years whichever is earlier. In addition, summer camps for the KVPY Fellows are organized in prestigious research and educational institutions in the country.
The Department of Science and Technology, the nodal agency of the Government has entrusted the overall responsibility for organizing and running the KVPY Program to the Indian Institute of Science, Bangalore and set up a Management Committee and a National Advisory Committee (NAC) for overseeing its implementation. A core committee looks after both the day-to-day and academic aspects of the KVPY Program.
Eligibility :
Stream SA: Students enrolled in the XI Standard (Science Subjects) and having secured a minimum of 80% (70% for SC/ST/PWD) marks in aggregate in Mathematics and Science in the X Standard Board Examination.
Stream SX: Students enrolled in XII Standard/ (+2) (Science subjects) and aspiring to join undergraduate program in Basic Sciences namely Physics/Chemistry/Mathematics & Biology leading to B.Sc./B.S./B.Stat./B.Math./Int. M.Sc./M.S. provided they have secured a minimum of 80% (70% for SC/ST/PWD) marks in aggregate in MATHEMATICS and SCIENCE subjects (Physics/Chemistry/Biology) in the X Standard Board Examination and a minimum of 60% (50% for SC/ST/PWD) marks in aggregate in SCIENCE subjects (Physics/Chemistry/Biology) in the XII standard Board Examination.
Stream SB: Students enrolled in the 1st year of undergraduate program in Basic Sciences namely Physics/Chemistry/Mathematics & Biology leading to B.Sc./B.S./B.Stat./B.Math./Int. M.Sc./M.S. and having secured a minimum of 60% (50% for SC/ST/PWD) marks in aggregate in SCIENCE subjects (Physics/Chemistry/Biology/Mathematics) in the XII Standard Board Examination. In the 1st year final examination of B.Sc./B.S./B.Math./B.Stat./Int. M.Sc./M.S. they must secure 60% (50% for SC/ST/PWD) marks before taking up the fellowship, if awarded.