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

Compute 99⁴ 

Compute 9⁷ 

Using binomial theorem, indicate which of the following two number is larger: `(1.01)^(1000000)`, 10

Find the coefficient of x¹⁵ in `(x^2 + 1/x^3)^10`

Find the coefficient of x² and the coefficient of x⁶ in `(x^2 -1/x^3)^6` 

Find the coefficient of x⁴ in the expansion `(1 + x^3)^50 (x^2 + 1/x)^5`

Find the constant term of `(2x^3 - 1/(3x^2))^5`

Find the last two digits of the number 3⁶⁰⁰ 

If n is a positive integer, using Binomial theorem, show that, 9ⁿ⁺¹ − 8n − 9 is always divisible by 64

If n is an odd positive integer, prove that the coefficients of the middle terms in the expansion of (x + y)ⁿ are equal

If n is a positive integer and r is a non-negative integer, prove that the coefficients of x^r and x^n−r in the expansion of (1 + x)ⁿ are equal

If a and b are distinct integers, prove that a − b is a factor of aⁿ − bⁿ, whenever n is a positive integer. [Hint: write aⁿ = (a − b + b)ⁿ and expaand]

In the binomial expansion of (a + b)ⁿ, if the coefficients of the 4^th and 13^th terms are equal then, find n

If the binomial coefficients of three consecutive terms in the expansion of (a + x)ⁿ are in the ratio 1 : 7 : 42, then find n

In the binomial expansion of (1 + x)ⁿ, the coefficients of the 5^th, 6^th and 7^th terms are in AP. Find all values of n

Prove that `"C"_0^2 + "C"_1^2 + "C"_2^2 + ... + "C"_"n"^2 = (2"n"!)/("n"!)^2`

Choose the correct alternative:
The value of 2 + 4 + 6 + … + 2n is

Choose the correct alternative:
The remainder when 38¹⁵ is divided by 13 is

In problems 1 – 6, using the table estimate the value of the limit.

`lim_(x -> 2) (x - 2)/(x^2 - x - 2)`

In problems 1 – 6, using the table estimate the value of the limit
`lim_(x -> 2) (x - 2)/(x^2 - 4)`