FIIT JEE KVPY Class XII Mathematics Model Question Paper 2015

Name of the Organisation : FIIT JEE Ltd.
Name of the Paper : KVPY Mathematics Question Paper
Year : 2015
Name of the Subject : Mathematics
Class : XII STD

Website : http://www.fiitjee.co/DownLoads/KVPY-Question-Papers-and-Solutions/16
Download Sample Question Paper Class XII 2015 : https://www.pdfquestion.in/uploads/8187XIIMaths.pdf
Download Sample Question Paper Class XII 2012 SA Stream- Stage I : https://www.pdfquestion.in/uploads/8187XIIMathsI.pdf
Download Sample Question Paper Class XII 2012 SA Stream- Stage II : https://www.pdfquestion.in/uploads/8187XIIMathsII.pdf

KVPY Model Question Paper :

Part – I :
Mathematics :
1. The number of ordered pairs(x, y) of real numbers that satisfy the simultaneous equations
x + y2 = x2 + y = 12
(A) 0 (B) 1 (C) 2 (D) 4

Related : FIIT JEE National Talent Search Exam MAT Paper Model Class X : www.pdfquestion.in/7556.html

2. If z is a complex number satisfying|z3 + z-3| ? 2, then the maximum possible value of |z + z–1| is
(A) 2 (B) 3 2 (C) 2 2 (D) 1

3. The largest perfect square that divides 20143 – 20133 + 20123 – 20113 + …. + 23 –13 is
(A) 12 (B) 22 (C) 10072 (D) 20142

4. Suppose OABC is a rectangle in the xy-plane where O is the origin and A, B lie on the parabola y = x2. Then C must lie on the curve
(A) y = x2 + 2
(B) y = 2×2 + 1
(C) y = –x2 + 2
(D) y = -2×2 + 1

5. Circle C1 and C2 of radii r and R respectively, touch each other as shown in figure. The line ?, which is parallel to the line joining the centres of C1 and C2 is tangent to C1 at P and intersects C2 at A, B. If R2 = 2r2, then ?AOB equals
(A) 60 (B) 45 (C)30 (D) 22

6. The shortest distance from the origin to a variable point on the sphere (x – 2)2 + (y – 3)2 + (z – 6)2 = 1 is
(A) 5 (B) 6 (C) 7 (D) 8

7. The number of real numbers ? for which the equality sin?? cos ? sinA cosA/ Sin Cos Holds for all real ? which are not integral multiples of ?/2 is
(A) 1 (B) 2 (C) 3 (D) Infinite

8. Suppose ABCDEF is a hexagon such that AB = BC = CD = 1 and DE = EF = FA = 2. If the vertices A, B, C, D, E, F are concylic the radius of the circle passing through them is
(A) 3/5 (B) 3/6 (C) 3/2 (D) 2/7

9. Among all sectors of a fixed perimeter, choose the one with maximum area. Then the angle at the centre of this sector(i.e. the angle between the bounding radii) is(A)
(A) 3/5 (B) 3/6 (C) 3/2 (D) 2/7

10. An urn contains marbles of four colours: red, white, blue and green. When four marbles are drawn without replacement, the following events are equally likely
(1) the selection of four red marbles
(2) the selection of one white and three red marbles
(3) the selection of one white, one blue and two red marbles
(4) the selection of one marble of each colour
The smallest total number of marbles satisfying the given condition is
(A) 19 (B) 21 (C) 46 (D) 69

KVPY 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.

Selection Procedure :
Aptitude Test: After scrutiny of application forms and meeting the eligibility criteria for various streams, all eligible students will be called for a written aptitude test conducted both in Hindi and English at different centers across the country. The details of the venue of the aptitude test for the eligible students and their seat number will be published in the KVPY website during the second week of October.

Admit Card:Students may download the admit card for the aptitude test from the website from the second week of October.

Interview: Based on the performance in the aptitude test, short-listed students will be asked to appear for an interview which is the final stage of the selection procedure.