HSC Arts (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Answer the following:

Solve the following equations for x, y ∈ R:

(x + iy) (5 + 6i) = 2 + 3i

Solve the following equation for x, y ∈ R:

2x + i⁹y (2 + i) = xi⁷ + 10i¹⁶

Answer the following:

Evaluate: (1 − i + i²)⁻¹⁵ 

Answer the following:

Evaluate: i¹³¹ + i⁴⁹ 

Answer the following:

Find the value of x³ + 2x² − 3x + 21, if x = 1 + 2i

Answer the following:

Find the value of x⁴ + 9x³ + 35x² − x + 164, if x = −5 + 4i

Answer the following:

Find the real numbers x and y such that `x/(1 + 2"i") + y/(3 + 2"i") = (5 + 6"i")/(-1 + 8"i")`

Show that `(1/sqrt(2) + "i"/sqrt(2))^10 + (1/sqrt(2) - "i"/sqrt(2))^10` = 0

Answer the following:

show that `((1 + "i")/sqrt(2))^8 + ((1 - "i")/sqrt(2))^8` = 2

Answer the following:

If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x² + y² = 1

Answer the following:

Show that z = `((-1 + sqrt(-3))/2)^3` is a rational number

Answer the following:

Show that `(1 - 2"i")/(3 - 4"i") + (1 + 2"i")/(3 + 4"i")` is real

Answer the following:

Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`

Answer the following:

Simplify: `("i"^65 + 1/"i"^145)`

Answer the following:

Simplify: `("i"^238 + "i"^236 + "i"^234 + "i"^232 + "i"^230)/("i"^228 + "i"^226 + "i"^224 + "i"^222 + "i"^220)`

Answer the following:

Simplify `[1/(1 - 2"i") + 3/(1 + "i")] [(3 + 4"i")/(2 - 4"i")]`

Check whether the following sequence is G.P. If so, write t_n.

2, 6, 18, 54, …

Check whether the following sequence is G.P. If so, write t_n.

1, –5, 25, –125 …

Check whether the following sequence is G.P. If so, write t_n.

`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5))`, ...

Check whether the following sequence is G.P. If so, write t_n.

3, 4, 5, 6, …