Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

Using binomial theorem, evaluate the following:

(99)⁵

Using Binomial Theorem, indicate which number is larger (1.1)¹⁰⁰⁰⁰ or 1000.

Find (a + b)⁴ – (a – b)⁴. Hence, evaluate `(sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4`

Find (x + 1)⁶ + (x – 1)⁶. Hence or otherwise evaluate `(sqrt2 + 1)^6 + (sqrt2 -1)^6`

Show that 9ⁿ⁺¹ – 8n – 9 is divisible by 64, whenever n is a positive integer.

Prove that `sum_(r-0)^n 3^r  ""^nC_r = 4^n`

Find a, b and n in the expansion of (a + b)ⁿ if the first three terms of the expansion are 729, 7290 and 30375, respectively.

Find the coefficient of x⁵ in the product (1 + 2x)⁶ (1 – x)⁷ using binomial theorem.

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 expand]

Evaluate `(sqrt3 + sqrt2)^6 - (sqrt3 - sqrt2)^6`

Find the value of `(a^2 + sqrt(a^2 - 1))^4 + (a^2 - sqrt(a^2 -1))^4`

Find an approximation of (0.99)⁵ using the first three terms of its expansion.

Expand using Binomial Theorem `(1+ x/2 - 2/x)^4, x != 0`

Find the expansion of (3x² – 2ax + 3a²)³ using binomial theorem.

Find the equation of the line which satisfy the given condition:

Passing through the point (–4, 3) with slope `1/2`.

Find the equation of the line which satisfy the given condition:

Passing though `(2, 2sqrt3)` and is inclined with the x-axis at an angle of 75°.

Find the equation of the line which satisfy the given condition:

Intersects the x-axis at a distance of 3 units to the left of origin with slope –2.