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

A bag contains 3 red marbles and 4 blue marbles. Two marbles are drawn at random without replacement. If the first marble drawn is red, what is the probability the second marble is blue?

A box contains 5 green pencils and 7 yellow pencils. Two pencils are chosen at random from the box without replacement. What is the probability that both are yellow?

In a sample of 40 vehicles, 18 are red, 6 are trucks, of which 2 are red. Suppose that a randomly selected vehicle is red. What is the probability it is a truck?

A speaks truth in 80% of the cases and B speaks truth in 60% of the cases. Find the probability that they contradict each other in narrating an incident

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