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Binomial Theorem, Sequences and Series Model Question Paper

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. The sequence\(\frac { 1 }{ \sqrt { 3 } } ,\frac { 1 }{ \sqrt { 3 } +\sqrt { 2 } } \frac { 1 }{ \sqrt { 3 } +2\sqrt { 2 } } \)...form an 

    (a)

    AP

    (b)

    GP

    (c)

    HP

    (d)

    AGP

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

    (a)

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

    (b)

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

    (c)

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

    (d)

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

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

    (a)

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

    (b)

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

    (c)

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

    (d)

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

  4. The term without x in \({ \left( 2x-\frac { 1 }{ 2{ x }^{ 2 } } \right) }^{ 12 }\) is 

    (a)

    495

    (b)

    -495

    (c)

    -7920

    (d)

    7920

  5. The value of \({ 9 }^{ \frac { 1 }{ 3 } }\) ,\({ 9 }^{ \frac { 1 }{ 9 } }\)\({ 9 }^{ \frac { 1 }{ 27 } }\) ,\(\infty \)is

    (a)

    1

    (b)

    3

    (c)

    9

    (d)

    none of these

  6. 5 x 2 = 10
  7. 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 \(\frac { 2n+3 }{ 3n+4 } \)

  8. 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

  9. If \(x=a+\frac { a }{ r } +\frac { a }{ { r }^{ 2 } } +...+\infty ,y=b-\frac { b }{ r } +\frac { b }{ { r }^{ 2 } } +.....+\infty \quad z=c+\frac { c }{ { r }^{ 2 } } +\frac { c }{ { r }^{ 4 } } +...+\infty\) then show that \(\frac{xy}{z}=\frac{ab}{c}\)

  10. If H be the H. M. between a and b, then show that (H - 2a) (H - 2b) = H2

  11. Find a positive value of m for which the coefficient of x2 in the expansion of (1+x)m is 6.

  12. 5 x 3 = 15
  13. Compute 97

  14. Write the first 4 terms of the logarithmic series of log (1 - 2x)

  15. The sum of two members is\(\frac { 13 }{ 6 } \) .An even number A.M.S are being inserted between them and their sum exceeds their number by 1.Find the number of A.M.S inserted.

  16. Find \(\sum_{1}^{\infty}{\frac{1}{(k+1)(k+2)}}\).

  17. Sum the series: (1 + x) + (1 + x + x2) + (1 + x + x2 +x3) + ... up to n terms

  18. 4 x 5 = 20
  19. Compute the sum of first n terms of 1 + (1 + 4) + (1 + 4 + 42) + (1 + 4 + 42 + 43) + ...

  20. Find the value of n if the sum to n terms of the series \(\sqrt { 3 } +\sqrt { 75 } +\sqrt { 243 } +....is\quad 435\sqrt { 3 } .\)

  21. Find the sum of the series \(1+\frac { 2 }{ 5 } +\frac { 3 }{ { 5 }^{ 2 } } +\frac { 5 }{ { 5 }^{ 3 } } +\)

  22. Find the fourth root of 623 correct to seven places of decimal.

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