Andhra Pradesh Board Class 12 Math Sample Papers 2007

SAMPLE QUESTION PAPER
MATHEMATICS 

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 2x 2 + 3y 2 + 6 = 0 find the quadratic equation whose roots are a
3 and b 3
.
2. If the roots of the equation x 3– 3x 2– 6x + 8 = 0 are in A.P. find them.2 4 0 0

3. If    A =     and A 2 =find the value of k. - 1 k 0 0 1 w w 2

4. Find the value of the determinant of  w w
2 1 where w 3 = 1. w 2 1 w

5. If n P4 = 1680 find ‘n’.

6. If 2 1 C2r+1 = 2 1 Cr-4 find ‘r’.1  

7. Find the term independent of ‘x’ in x 5   –  x 3

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
   x
2
– 34x – 71      do not lie between 5 and 9. 
     x
2
+ 2x – 7

12. For 1 < r < n prove, with usual notation, that
n
Cr-1 + 
n
Cr
=
(n+1)
Cr-1find ‘r’.    (2n)!
13. Prove that C0Cr
+ C1Cr+1 + C2Cr+2+ ……… + Cn-rCn 
=(n – r)! (n + r)!x

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

15. Sum the series log3e – log9e + log2 7e – log8 1e + ………..
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  x
3
– 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
2
k
mean of X.