HSC Commerce: Marketing and Salesmanship इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

If ω is a complex cube root of unity, then prove the following.

(ω² + ω −1)³ = −8

If ω is a complex cube-root of unity, then prove the following:

(a + b) + (aω + bω²) + (aω² + bω) = 0

If w is a complex cube root of unity, show that `((a + bω + cω^2))/(c + aω + bω^2) = ω^2`

If ω is a complex cube-root of unity, then prove the following:

(ω² + ω −1)³ = −8

If ω is a complex cube-root of unity, then prove the following :

(ω² + ω − 1)³ = − 8

Find the value of `sqrt(-3) xx sqrt(-6)`.

If w is a complex cube-root of unity, then prove the following

(w² + w - 1)³ = - 8

If ω is a complex cube-root of unity, then prove the following:

(ω² + ω − 1)³ = −8

 Find the value of `sqrt(-3)xx sqrt (-6)`

If w is a complex cube root of unity, show that `((a+bw+cw^2))/(c+aw+bw^2) = w^2`

If w is a complex cube root of unity, show that `((a + bw + cw^2))/(c + aw + bw^2) = w^2`

If w is a complex cube root of unity, show that `((a+bw+cw^2))/(c+aw+bw^2)=w^2`

If w is a complex cube-root of unity, then prove the following. 

(w² + w - 1)³ = - 8

If w is a complex cube root of unity, show that `((a + bomega + comega^2))/(c + aomega + bomega^2) = w^2`

If ω is a complex cube root of unity, show that `((a + bomega + comega^2))/(c + aomega + bomega^2)=omega^2`

If ω is a complex cube root of unity, show that `((a + b\omega + c\omega^2))/(c + a\omega + b\omega^2) = \omega^2`

If ω is a complex cube-root of unity, then prove the following.

(ω² + ω − 1)³ = −8

English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?

How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?

Find the sum `sum_("r" = 1)^"n"("r" + 1)(2"r" - 1)`.