Osmania University (OU) 2009 P.U.C Physics, Chemistry, Maths & Biology Maths II Model of Intermedate to be conducted by Board of intermediate - Question Paper

MODEL ques. PAPER
MATHEMATICS – Paper II A
(Algebra, Probability)
Time : three Hours Max Marks : 75
part – A
I. Very Short ans ques.
Attempt all ques.. every ques. carries two marks.
10 x two = 20 Marks

1. If a and b are the roots of the formula 2x2 + 3y2 + six = 0 obtain the
quadratic formula whose roots are a3 and b3.

2. If the roots of the formula x3 – 3x2 – 6x + eight = 0 are in A.P. obtain them.
2 four 0 0

3. If A = and A2 = obtain the value of k.
- one k 0 0
1 w w2

4. obtain the value of the determinant of w w2 one where w3 = 1.
w2 one w

5. If nP4 = 1680 obtain ‘n’.

6. If 21C2r+1 = 21Cr-4 obtain ‘r’.
1 8

7. obtain the term independent of ‘x’ in x5 –
x3

8. If a card is drawn at random from a pack of cards, what is the
probability that it is an ace or a diamond.

9. obtain the sum of the infinite series
1 one 1
1 + + + +………..
2! 4! 6!

10. In a Binominal distribution if the sum of the mean and the variance is
1.8 obtain the distribution when n = 5.
part – B

II. Short ans ques.
Attempt any 5 ques.. every ques. carries four marks
5 x four = 20 Marks

11. If x is real show that the values of the expression
x2 – 34x – 71 do not lie ranging from five and 9.
x2 + 2x – 7

12. For one < r < n prove, with usual notation, that
nCr-1 + nCr = (n+1)Cr-1find ‘r’.
(2n)!

13. Prove that C0Cr + C1Cr+1 + C2Cr+2+ ……… + Cn-rCn =
(n – r)! (n + r)!
x3

14. obtain the partial fractions of
(2x –1 ) (x +2) (x – 3)

15. Sum the series log3e – log9e + log27e – log81e + ………..
1 two 2

16. If A = two one two then show that A2 – 4A – 5I = O.
2 two 1

17. If 2 numbers are opted randomly from 20 consecutive natural
numbers obtain the probability that the sum of the 2 numbers is
(i) an even number (ii) an odd number.
part – C
II. Long ans ques. five x seven = 35 Marks
Attempt any 5 ques.. every ques. carries seven marks

18. Solve x3 – 18x – 35 = 0 by using Cardan’s method.

19. obtain the number of ways of selecting 11 members for a
cricket team from seven batsmen, five bowlers and three wicket
keepers having atleast three bowlers and two wicket keepers.
1.3 1.3.5 1.3.5.7

20. obtain the sum of the series + + + ……….
3.6 3.6.9 3.6.9.12

21. Solve by Gauss-Jordan method, the system of equations :
x + y + z = 6
2x + 3y – z = 3
3x + 5y + 2z = 19

22. Show that
a – b - c 2a 2a
2b b – c – a 2b = (a + b +c)3
2c 2c c – a – b

23. State and prove Bayes’ Theorem.

24. If X is a random variable with the probability distribution
(k + 1)C
P(X = k) = (k = 0,1,2,…..) then obtain C and also the
2k
mean of X.
* * *

Earning:   Approval pending.