Algebra Book Back Questions

11th Standard

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Business Maths

Time : 00:45:00 Hrs
Total Marks : 30
    5 x 1 = 5
  1. The value of n, when nP2 = 20 is

    (a)

    3

    (b)

    6

    (c)

    5

    (d)

    4

  2. The number of diagonals in a polygon of n seates is equal to

    (a)

    nC2

    (b)

    nC2 - 2

    (c)

    nC2 - n

    (d)

    nC2 - 1

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

    (a)

    2n

    (b)

    2n- 1

    (c)

    n2

    (d)

    n2 - 1

  5. 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

  6. 3 x 2 = 6
  7. Evaluate the following using binomial theorem:(999)5

  8. How many triangles can be formed by joining the vertices of a hexagon?

  9. How many distinct words can be formed using all the letters of the following words.
    MISSISSIPPI

  10. 3 x 3 = 9
  11. Find the middle terms in the expansion of \({ \left( x+\frac { 1 }{ x } \right) }^{ 11 }\)

  12. Find x if \(\frac { 1 }{ 6! } +\frac { 1 }{ 7! } =\frac { x }{ 8! } \).

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

  14. 2 x 5 = 10
  15. Prove that the term independent of x in the expansion of \({ \left( x+\frac { 1 }{ x } \right) }^{ 2n }is\quad \frac { 1.3.5.....,(2n-1){ 2 }^{ n } }{ n! } \)

  16. By the principle of mathematical induction, prove the following.
    13+23+33+.......+n3=\(\frac { { n }^{ 2 }(n+1)^{ 2 } }{ 4 } \) for all \(n\in N\).

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