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

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.

Find the equation of the line passing through (–3, 5) and perpendicular to the line through the points (2, 5) and (–3, 6).

A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio 1:n. Find the equation of the line.

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).

Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.