HSC Arts इयत्ता ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Prove that using the Mathematical induction
`sin(alpha) + sin (alpha + pi/6) + sin(alpha + (2pi)/6) + ... + sin(alpha + (("n" - 1)pi)/6) = (sin(alpha + (("n" - 1)pi)/12) xx sin(("n"pi)/12))/(sin (pi/12)`

Choose the correct alternative:
In 3 fingers, the number of ways four rings can be worn is · · · · · · · · · ways

Choose the correct alternative:
If `""^("a"^2 - "a")"C"_2 = ""^("a"^2 - "a")"C"_4` then the value of a is

Choose the correct alternative:
Everybody in a room shakes hands with everybody else. The total number of shake hands is 66. The number of persons in the room is ______

Choose the correct alternative:
1 + 3 + 5 + 7 + · · · + 17 is equal to

Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid

`1/(5 + x)`

Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid

`2/(3 + 4x)^2`

Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid

`(5 + x^2)^(2/3)`

Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid

`(x + 2) - 2/3`

Find `root(3)(10001)` approximately (two decimal places

Prove that `root(3)(x^3 + 6) - root(3)(x^3 + 3)` is approximately equal to `1/x^2` when x is sufficiently large

Prove that `sqrt((1 - x)/(1 + x))` is approximately euqal to `1 - x + x^2/2` when x is very small

Write the first 6 terms of the exponential series
e^5x 

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) + ...`