#### Algebra - Important Question Paper

11th Standard

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Time : 01:00:00 Hrs
Total Marks : 50

Part A

10 x 1 = 10
1. The value of n, when nP2 = 20 is

(a)

3

(b)

6

(c)

5

(d)

4

2. The number of ways selecting 4 players out of 5 is

(a)

4!

(b)

20

(c)

25

(d)

5

3. The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for n $\in$ N is

(a)

2

(b)

6

(c)

20

(d)

24

4. If n is a positive integer, then the number of terms in the expansion (x + a)n is

(a)

n

(b)

n + 1

(c)

n-1

(d)

2n

5. For all n > 0, nC1 + nC2 + nC3 + ... +nCn is equal to

(a)

2n

(b)

2n- 1

(c)

n2

(d)

n2 - 1

6. The number of parallelograms that can be formed from the set of four parallel lines intersecting another set of three parallel lines is

(a)

18

(b)

12

(c)

9

(d)

6

7. 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

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

(a)

26-2

(b)

25-1

(c)

28

(d)

27

9. The number of ways to arrange the letters of the word "CHEESE" is

(a)

120

(b)

240

(c)

720

(d)

6

10. 13 guests have participated in a dinner. The number of handshakes happened in the dinner is

(a)

715

(b)

78

(c)

286

(d)

13

11. Part B

6 x 2 = 12
12. Resolve into partial fractions for the following:
$\frac { { x }^{ 2 }-3 }{ (x+2)({ x }^{ 2 }+1) }$

13. Resolve into partial fractions for the following:
$\frac { { x }^{ 2 }-6x+2 }{ { x }^{ 2 }(x+2) }$

14. Resolve into partial fractions for the following:
$\frac { x+2 }{ (x-1)(x+3)^{ 2 } }$

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

16. How many permutations can be made out of the letters of the word "TRIANGLE" beginning with T?

17. In how many ways can 10 beads of different colours form a necklace?

18. Part C

6 x 3 = 18
19. Resolve into partial factors:$\frac { x+4 }{ ({ x }^{ 2 }-4)(x+1) }$

20. Solve : $\frac { (2x+1)! }{ (x+2)! } .\frac { (x-1)! }{ (2x-1)! } =\frac { 3 }{ 5 }$

21. It the letters of the word are arranged as in dictionary, find the rank of the word "AGAIN".

22. In how many ways can n prizes be given to n boys, when a boy may receive any number of prizes?

23. If p(n) is the statement "12n + 3" is a multiple of 5, then show that P (3) is false, whereas P(6) is true.

24. Let p(n) be the statement "n2 + n is even". If P(k) is true, then show that P(k+1) is true.

25. Part D

2 x 5 = 10
26. Expand the following by using binomial theorem.$\left( x+\frac { 1 }{ y } \right) ^{ 7 }$

27. Expand the following by using binomial theorem.${ \left( x+\frac { 1 }{ { x }^{ 2 } } \right) }^{ 6 }$