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11th Standard English Medium Maths Subject Binomial Theorem, Sequences and Series Book Back 5 Mark Questions with Solution Part - II

11th Standard

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Maths

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

    5 Marks

    10 x 5 = 50
  1. if the binomial co-efficients of three consecutive terms in the expansion of ( a + xn) are in the radio 1:7:42 then find n

  2. In the binomial coefficient of (1+x)n  the Coefficients of the 5th, 6th and 7th terms are in A.P find all values of n

  3. If p - q is small compared to either p or q, then show that \(n\sqrt { \frac { p }{ q } } =\frac { \left( n+1 \right) p+\left( n-1 \right) q }{ \left( n-1 \right) p+\left( n+1 \right) q } \)
    Hence find \(8\sqrt { \frac { 15 }{ 16 } } \)

  4. Find the coefficient of x4 in the expansion of \(\frac { 3-4x+{ x }^{ 2 } }{ { e }^{ 2x } } \)

  5. The 2nd, 3rd and 4th terms in the binomial expansion of (x + a)n are 240, 720 and 1080 for a suitable value of x. Find x, a and n.

  6. Using Binomial theorem, prove that 6n - 5n always leaves remainder 1 when divided by 25 for all positive integer n.

  7. Find the last two digits of the number 7400.

  8. Find the sum of the first n terms of the series \({1\over 1+\sqrt{2}}+{1\over\sqrt{2}+\sqrt{3}}+{1\over\sqrt{3}+\sqrt{4}}+...\)

  9. Find \(\sqrt [ 3 ]{ 65} .\)

  10. 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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