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Posted Date: 05 Apr 2009 Posted By: shilpa kumari jain Member Level: Gold
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2007 Andhra Pradesh State MATHEMATICS MODEL QUESTION PAPER 3 Question paper
MODEL QUESTION PAPER
MATHEMATICS – Paper II A
(Algebra, Probability)
Time : 3 Hours Max Marks : 75
Section – A
I. Very Short Answer Questions
Attempt all Questions. Each Question carries 2 marks.
10 x 2 = 20 Marks
1. If a and b are the roots of the equation 2x2 + 3y2 + 6 = 0 find the
quadratic equation whose roots are a3 and b3.
2. If the roots of the equation x3 – 3x2 – 6x + 8 = 0 are in A.P. find them.
2 4 0 0
3. If A = and A2 = find the value of k.
- 1 k 0 0
1 w w2
4. Find the value of the determinant of w w2 1 where w3 = 1.
w2 1 w
5. If nP4 = 1680 find ‘n’.
6. If 21C2r+1 = 21Cr-4 find ‘r’.
1 8
7. Find 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. Find the sum of the infinite series
1 1 1
1 + + + +………..
2! 4! 6!
10. In a Binominal distribution if the sum of the mean and the variance is
1.8 find the distribution when n = 5.
Section – B
II. Short Answer Questions
Attempt any five questions. Each question carries 4 marks
5 x 4 = 20 Marks
11. If x is real show that the values of the expression
x2 – 34x – 71 do not lie between 5 and 9.
x2 + 2x – 7
12. For 1 < 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. Find the partial fractions of
(2x –1 ) (x +2) (x – 3)
15. Sum the series log3e – log9e + log27e – log81e + ………..
1 2 2
16. If A = 2 1 2 then show that A2 – 4A – 5I = O.
2 2 1
17. If two numbers are selected randomly from 20 consecutive natural
numbers find the probability that the sum of the two numbers is
(i) an even number (ii) an odd number.
Section – C
II. Long Answer Questions 5 x 7 = 35 Marks
Attempt any five questions. Each question carries 7 marks
18. Solve x3 – 18x – 35 = 0 by using Cardan’s method.
19. Find the number of ways of selecting 11 members for a
cricket team from 7 batsmen, 5 bowlers and 3 wicket
keepers having atleast 3 bowlers and 2 wicket keepers.
1.3 1.3.5 1.3.5.7
20. Find 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 find C and also the
2k
mean of X.
* * *
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