Mathematics Papers I
Time Allowed: 3 Hours Maximum Marks 100
Note: Attempt Five Questions in all, selecting at least Two questions from Section-1,
One from Section-II and Two from Section-III.
Section I
1- a) Let A , B and C be Sets prove that (A\B)∩C= (A∩C) \(B∩C)
b) Show that
c) Prove that the additive inverse of a number is unique
2- a) if A = |1 -1 2 | B= | 1 2 | Prove that (A+B)(A+B) ≠A2+B2+2AB
| 2 1 0 | |2 0 |
| -1 1|
b) Solve using Cramer’s Rule
x-2y-2z = 3
2x-4y+4z= 1
3x-3y-3z = 4
c) Without Expanding Show that
|a-b b-c c-a |
|a-c c-a a-b |
|c-a a-b b-c |
3- a) Solve Equation √ x2+3x+7 - √ x2+3x+1 =3
b) Find the value of k given that one root of x2-(3k-1)x+4k=0 is 3
4- a) The sum of an infinite Geometric series is 15 and sum of squares of its
terms is 45. Find the series
b) If l, m, n be the pth qth and rth terms of an A.P. show that
l(q-r)+m(r-p)+n(p-q)=0
c) Let a, b be any positive numbers and A,G, H have usual meanings. Show
that A>G>H
Section II
5- From Chapter 6
6- a) Sum the series upto n terms
13+53+93+……
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