HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions

A box contains 10 red balls and 15 green balls. Two balls are drawn in succession without replacement. What is the probability that, the first is red and the second is green?

Find the modulus and amplitude of the following complex numbers.

7 − 5i

Find the modulus and amplitude of the following complex numbers.

`sqrt(3) + sqrt(2)"i"`

Find the modulus and amplitude of the following complex numbers.

−8 + 15i

Find the modulus and amplitude of the following complex numbers.

−3(1 − i)

Find the modulus and amplitude of the following complex number.

−4 − 4i

Find the modulus and amplitude of the following complex numbers.

`sqrt(3) - "i"`

Find the modulus and amplitude of the following complex numbers.

3

Find the modulus and amplitude of the following complex numbers.

1 + i

Find the modulus and amplitude of the following complex numbers.

`1 + "i"sqrt(3)`

Find the modulus and amplitude of the following complex numbers.

(1 + 2i)² (1 − i)

Find real values of θ for which `((4 + 3"i" sintheta)/(1 - 2"i" sin theta))` is purely real.

If z = 3 + 5i then represent the `"z", bar("z"), - "z", bar(-"z")` in Argand's diagram

Express the following complex numbers in polar form and exponential form: 

`-1 + sqrt(3)"i"`

Express the following complex numbers in polar form and exponential form:

− i

Express the following complex numbers in polar form and exponential form:

−1

Express the following complex numbers in polar form and exponential form:

`1/(1 + "i")`

Express the following complex numbers in polar form and exponential form:

`(1 + 2"i")/(1 - 3"i")`

Express the following complex numbers in polar form and exponential form:

`(1 + 7"i")/(2 - "i")^2`

Express the following numbers in the form x + iy: 

`sqrt(3)(cos  pi/6 + "i" sin  pi/6)`