#### Algebra Two Marks Question

11th Standard

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Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. Verify that 8C4+8C3=9C4

2. Evaluate the following expression.$\frac { 7! }{ 6! }$

3. If four dice are rolled, find the number of possible outcomes in which atleast one die shows 2.

4. ResoIve into partial fractions :$\frac { 12x-17 }{ (x-2)(x-1) }$

5. Show that 10P3 = 9 P3 + 3. 9P2

6. Find the number of permutations of English vowels A, E, I, 0, U taking two at a time?

7. Find n if 25 Cn+5 = 25 C2n-1.

8. Find the number of diagonals that can be drawn by joining the angular points of octagon ?

9. If P(n) is the statement "23n -1 is a multiple of 7" then show that P (5) is true.

10. Evaluate: 8P

11. Using 9 digits from 1,2,3,……9, taking 3 digits at a time, how many 3 digits numbers can be formed when repetition is allowed?

12. In how many ways 8 students can be arranged along a circle

13. If nC4 = nC6 , find 12Cn

14. From a class of 32 students, 4 students are to be chosen for competition. In how many ways can this be done?

15. If (n + 2)Cn = 45, find n