Binomial Theorem : Sequences and Series - Important Question Paper

11th Standard

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Maths

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

    Part A

    10 x 1 = 10
  1. The HM of two positive numbers whose AM and GM are 16,8 respectively is

    (a)

    10

    (b)

    6

    (c)

    5

    (d)

    4

  2. If Sn denotes the sum of n terms of an AP whose common difference is d, the value of Sn-2Sn-1+Sn-2 is

    (a)

    0

    (b)

    2d

    (c)

    4d

    (d)

    d2

  3. The sum up to n terms of the series \(\frac { 1 }{ \sqrt { 1 } +\sqrt { 3 } } +\frac { 1 }{ \sqrt { 1 } +\sqrt { 5 } } +\frac { 1 }{ \sqrt { 5 } +\sqrt { 7 } } +\)....is 

    (a)

    \(\sqrt { 2n+1 } \)

    (b)

    \(\frac { \sqrt { 2n+1 } }{ 2 } \)

    (c)

    \(\sqrt { 2n+1 } -1\)

    (d)

    \(\frac { \sqrt { 2n+1 } -1 }{ 2 } \)

  4. The nth term of the sequence \(\frac { 1 }{ 2 } ,\frac { 3 }{ 4 } ,\frac { 7 }{ 8 } ,\frac { 15 }{ 6 } \).+.....is

    (a)

    2n-n-1

    (b)

    1-2n

    (c)

    2-n+n-1

    (d)

    2n-1

  5. The sum up to n terms of the series \(\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +\sqrt { 32 } +\).....is

    (a)

    \(\frac { n(n+1) }{ 2 } \)

    (b)

    2n(n+)

    (c)

    \(\frac { n(n+1) }{ \sqrt { 2 } } \)

    (d)

    1

  6. The value of the series\(\quad \frac { 1 }{ 2 } +\frac { 7 }{ 4 } +\frac { 13 }{ 8 } +\frac { 19 }{ 6 } +\).....is

    (a)

    14

    (b)

    7

    (c)

    4

    (d)

    6

  7. The sum of an infinite GP is 18. If the first term is 6, the common ratio is

    (a)

    \(\frac { 1 }{ 3 } \)

    (b)

    \(\frac { 2 }{ 3 } \)

    (c)

    \(\frac { 1 }{ 6 } \)

    (d)

    \(\frac { 3 }{ 4 } \)

  8. The coefficient of x5 in the series e-2x is

    (a)

    \(\frac { 2 }{ 3 } \)

    (b)

    \(\frac { 2 }{ 3 } \)

    (c)

    \(\frac { -4 }{ 15 } \)

    (d)

    \(\frac { 4 }{ 15 } \)

  9. If \(\frac { { T }_{ 2 } }{ { T }_{ 3 } } \)is the expansion of (a+b)n and \(\frac { { T }_{ 3 } }{ { T }_{ 4 } } \) is the expansion of (a+b)n+3 are equal, then n=

    (a)

    3

    (b)

    4

    (c)

    5

    (d)

    6

  10. The Co-efficient of x-17 in \({ \left( { x }^{ 4 }-\frac { 1 }{ { x }^{ 3 } } \right) }^{ 15 }\)is

    (a)

    1365

    (b)

    -1365

    (c)

    3003

    (d)

    -3003

  11. Part B

    6 x 2 = 12
  12. Find the sum of first n terms of the series 12+32+52+...

  13. Find a negative value of m if the Co-efficient of x2 in the expansion of (1+x)m ,|x|<1 is 6

  14. Find the general term in the expansion of \({ \left( \frac { 4x }{ 5 } -\frac { 5 }{ 2x } \right) }^{ 9 }\)

  15. Find the middle term in \({ \left( x-\frac { 1 }{ 2y } \right) }^{ 10 }\)

  16. Find the greatest term in (1 + 2x)8 when x = 2.

  17. Find the \(\sqrt [ 3 ]{ 126 } \) approximately to two decimal places.

  18. Part C

    6 x 3 = 18
  19. If the roots of the equation (q - r) x2 + (r - p)x + p - q = 0 are equal, then show that p, q and r are in A.P.

  20. Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetic -geometric progression, harmonic progression and none of 'them \(\frac { (-1)^{ n } }{ n } \)

  21. Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetic -geometric progression, harmonic progression and none of 'them \(\frac { 2n+3 }{ 3n+4 } \)

  22. Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetic -geometric progression, harmonic progression and none of 'them 2018

  23. Write the nth term of the following sequences
    \(\frac { 1 }{ 2 } ,\frac { 2 }{ 3 } ,\frac { 3 }{ 4 } ,\frac { 4 }{ 5 } ,\frac { 5 }{ 6 } \)

  24. Expand \({\left( 2x-{1\over 2x} \right)}^{4}.\)

  25. Part D

    2 x 5 = 10
  26. In a race, 20 balls are placed in a line at intervals of 4 meters, with the first ball 24 meters away from the starting point. A contestant is required to bring the balls back to the starting place one at a time. How far would the contestant run to bring back all balls?

  27. Prove that \(\sqrt [ 3 ]{ x^3+7 } -\sqrt [ 3 ]{ x^3+4 } \) is approximately equal to \({1\over x^2}\) when x is large.

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