HSC Science कक्षा ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

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The number of 5 digit numbers all digits of which are odd i

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The number of five digit telephone numbers having at least one of their digits repeated i

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There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is

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The number of 10 digit number that can be written by using the digits 2 and 3 is

Expand `(2x^2 - 3/x)^3`

Expand `(2x^2 -3sqrt(1 - x^2))^4 + (2x^2 + 3sqrt(1 - x^2))^4`

Compute 102⁴ 

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