Commerce (English Medium) Class 11 - CBSE Question Bank Solutions

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 that satisfies 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.

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

Intersects the y-axis at a distance of 2 units above the origin and making an angle of 30° with the positive direction of the x-axis.

Find the equation of the line which is at a perpendicular distance of 5 units from the origin and the angle made by the perpendicular with the positive x-axis is 30°

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

The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.

The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.