Commerce (English Medium) इयत्ता ११ - CBSE Question Bank Solutions

Prove the following by using the principle of mathematical induction for all n ∈ N: `1+2+ 3+...+n<1/8(2n +1)^2`

Prove the following by using the principle of mathematical induction for all n ∈ N: n (n + 1) (n + 5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all n ∈ N: 10^{2n – 1} + 1 is divisible by 11

Prove the following by using the principle of mathematical induction for all n ∈ N: x²ⁿ – y²ⁿ is divisible by x + y.

Prove the following by using the principle of mathematical induction for all n ∈ N: 3^{2n + 2} – 8n– 9 is divisible by 8.

Prove the following by using the principle of mathematical induction for all n ∈ N: 41ⁿ – 14ⁿ is a multiple of 27.

Prove the following by using the principle of mathematical induction for all n ∈ N (2n +7) < (n + 3)²

Find the multiplicative inverse of the complex number.

–i 

Express the following expression in the form of a + ib.

`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`

Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.

If `x – iy = sqrt((a-ib)/(c - id))` prove that `(x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)`

If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`