Board of Intermediate Education, Andhra Pradesh

Mathematics (Algebra, Probability)

Time : 3 Hours
Max Marks : 75

Section – A

I. Very Short Answer Questions and Attempt all Questions.

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.

3. Ifⁿ P₄ = 1680 find ‘n’.

4. If²¹ 21C_2r+1=²¹C_r-4 find ‘r’.

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

6. 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

6. Sum the series log₃e – log₉e + log₂₇e – log₈₁e + ………..

7. 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.

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

9. 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.

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

11. State and prove Bayes’ Theorem.