Mathematics Papers II
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) For any two sets A and B prove that (A∩B)∪(A\B)=A
b) Let Z1, Z2 be Complex No’s, Show that |Z1| = Z1
|Z2| Z2
c) Simplify
a + c
b d
a – c
b d
2- a) if A = | -1 2 | B= | 1 0 | Prove that (A+B)(A+B) ≠A2+B2+2AB
| 0 1 | |-1 2 |
b) Solve using Matrix Rule
2x-6y+3z = -12
3x-2y+5z = -4
2x+5y-2z = 10
c) Without Expanding Show that
|x+1 x+2 x+3|
|x+4 x+5 x+6|
|x+7 x+8 x+9|
3- a) Solve Equation 4 . 22x+1 – 9 . 2x + 1=0
b) Find the Condition that one Root of px2+qx+r = 0 may be cube of the
other
4- a) Sum the series 1+3 – 5+7 +9-11+13+15-17 …….. 3n terms
b) Sum the Series to n terms
1+(1+x)r + (1+x+x2)r2 + (1+x+x2+x3)r3+…. n
c) Insert three G Ms between 256 and 1
Section II
5- From Chapter 6
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