Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions

Find the square root of the following complex number:

1 − i

Find the square root of the following complex number:

 −8 − 6i

Find the square root of the following complex number:

8 −15i

Find the square root of the following complex number:

\[- 11 - 60\sqrt{- 1}\]

Find the square root of the following complex number:

 \[1 + 4\sqrt{- 3}\]

Find the square root of the following complex number:

 4i

Find the square root of the following complex number:

−i

Write the values of the square root of −i.

If x + iy =\[\sqrt{\frac{a + ib}{c + id}}\] then write the value of (x² + y²)².

If\[\sqrt{a + ib} = x + iy,\] then possible value of \[\sqrt{a - ib}\] is

If a = 1 + i, then a² equals

For all positive integers n, show that ²ⁿC_n + ²ⁿC_{n − 1} = `1/2` ^{2n + 2}C_n+1 

Evaluate

Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
n · _^n − 1C_{r − 1} = (n − r + 1) ⁿC_{r − 1}

Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

 ⁿC_r + 2 · ⁿC_{r − 1} + ⁿC_{r − 2} = ^n + 2C_r.