Important 5 mark questions chapter 4,5

11th Standard

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Maths

Use blue pen Only

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

    Part A

    Answer all the questions

    10 x 5 = 50
  1. Prove that 2nCn =  \(\frac { { 2 }^{ n }\times 1\times3\times ...(2n-1) }{ n! } \)

  2. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly three aces in each combination.

  3. Prove 1.3+2.32+3.33+...+n-3n=\(\frac{(2n-1)3^{n+1}+3}{4}\) for all n ∈ N

  4. Prove that the sum of the first n non-zero even numbers is n2 + n,

  5. n2 - n is divisible by 6, for each natural number n \(\ge\) 2.

  6. 1 + 5 + 9 + ... + (4n - 3) = n(2n -1), \(\forall\)n \(\in\)N.

  7. Find the sum of the series \(\frac { { 1 }^{ 3 } }{ 1 } +\frac { { 1 }^{ 3 }+{ 2 }^{ 3 } }{ 1+3 } +\frac { { 1 }^{ 3 }+{ 2 }^{ 3 }+3^{ 3 }+.... }{ 1+3+5 } to\quad n\quad terms\)

  8. Find the coefficient of x in the expansion of \(log(\frac{1}{1-5x+6x^2})\).

  9. Expand \({1\over(1+3x)^2} \) in powers of x. Find a condition on x for which the expansion is valid.

  10. Find the value of \((a^{2}+\sqrt{a^{2}-1})^{4}+(a^{2}-\sqrt{a^{2}-1})^{4}\)

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