#### Algebra Important Questions

11th Standard

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Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. If nC3 = nC2, then the value of nC4 is

(a)

2

(b)

3

(c)

4

(d)

5

2. The middle term in the expansion of ${ \left( x+\frac { 1 }{ x } \right) }^{ 10 }$

(a)

10C4$\left( \frac { 1 }{ x } \right)$

(b)

10C5

(c)

10C6

(d)

10C7x4

3. There are 10 true or false questions in an examination. Then these questions can be answered in

(a)

240 ways

(b)

120 ways

(c)

1024 ways

(d)

100 ways

4. The value of (5Co + 5C1) + (5C1 + 5C2) + (5C2 + 5C3) + (5C3 + 5C4) + (5C4 + 5C5 ) is

(a)

26-2

(b)

25-1

(c)

28

(d)

27

5. Number of words with or without meaning that can be formed using letters of the word "EQUATION" , with no repetition of letters is

(a)

7!

(b)

3!

(c)

8!

(d)

5!

6. 5 x 2 = 10
7. Evaluate the following using binomial theorem:(101)4

8. Evaluate the following using binomial theorem:(999)5

9. Evaluate the following expression.$\frac { 8! }{ 5! }$

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

11. If 15C3r = 15Cr+3 , find r

12. 5 x 3 = 15
13. Find the 5th term in the expansion of (x - 2y)13.

14. Find the middle terms in the expansion of ${ \left( 3x+\frac { { x }^{ 2 } }{ 2 } \right) }^{ 8 }$

15. Find the number of arrangements that can be made out of the letters of the word "ASSASSINATION".

16. Find the Co-efficient of x11 in the expansion of ${ \left( x+\frac { 2 }{ { x }^{ 2 } } \right) }^{ 17 }$

17. In how many ways can 12 things be equally divided among 4 persons?

18. 4 x 5 = 20
19. In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?

20. In how many ways can the following prizes be given away to a class of 30 students, first and second in mathematics, first and second in physics, first in chemistry and first in English?

21. If m parallel lines in a plane are intersected by a family of n parallel lines. Find the number of parallelogram formed?

22. Resolve into partial fractions:$\frac{2x+1}{(x-1)(x^2+1)}$