HSC Arts Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Write the first 6 terms of the exponential series
`"e"^(-2x)`

Write the first 6 terms of the exponential series
`"e"^(1/2x)`

Write the first 4 terms of the logarithmic series
log(1 + 4x) Find the intervals on which the expansions are valid.

Write the first 4 terms of the logarithmic series
log(1 – 2x) Find the intervals on which the expansions are valid.

Write the first 4 terms of the logarithmic series
`log((1 + 3x)/(1 -3x))` Find the intervals on which the expansions are valid.

Write the first 4 terms of the logarithmic series
`log((1 - 2x)/(1 + 2x))` Find the intervals on which the expansions are valid.

If y = `x + x^2/2 + x^3/3 + x^4/4  ...`, then show that x = `y - y^2/(2!) + y^3/(3!) - y^4/(4) + ...`

If p − q is small compared to either p or q, then show `root("n")("p"/"q")` ∼ `(("n" + 1)"p" + ("n" - 1)"q")/(("n"- 1)"p" +("n" + 1)"q")`. Hence find `root(8)(15/16)`

Find the coefficient of x⁴ in the expansion `(3 - 4x + x^2)/"e"^(2x)`

Find the value of `sum_("n" = 1)^oo 1/(2"n" - 1) (1/(9^("n" - 1)) + 1/(9^(2"n"- 1)))`

Choose the correct alternative:
The coefficient of x⁶ in (2 + 2x)¹⁰ is

Choose the correct alternative:
The coefficient of x⁸y¹² in the expansion of (2x + 3y)²⁰ is

Choose the correct alternative:
If a is the arithmetic mean and g is the geometric mean of two numbers, then

Choose the correct alternative:
If (1 + x²)² (1 + x)ⁿ = a₀ + a₁x + a₂x² + …. + x^{n + 4} and if a₀, a₁, a₂ are in AP, then n is

Choose the correct alternative:
If S_n denotes the sum of n terms of an AP whose common difference is d, the value of S_n − 2S_n−1 + S_n−2 is

Choose the correct alternative:
The sum up to n terms of the series `1/(sqrt(1)  +sqrt(3)) + 1/(sqrt(3) + sqrt(5)) + 1/(sqrt(5) + sqrt(7)) + ...` is 

Choose the correct alternative:
The value of the series `1/2 + 7/4 + 13/8 + 19/16 + ...` is

Choose the correct alternative:
The sum of an infinite GP is 18. If the first term is 6, the common ratio is

Choose the correct alternative:
The coefficient of x⁵ in the series e^-2x is

Choose the correct alternative:
The value of `1/(2!) + 1/(4!) + 1/(6!) + ...` is