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

Find the value of x³ - x² + x + 46, if x = 2+3i. 

Find the value of x³ - x² + x + 46, if x = 2 + 3i.

Examine the consistency of the following equation:

2x − y + 3 = 0, 3x + y − 2 = 0, 11x + 2y − 3 = 0

Examine the consistency of the following equation:

2x + 3y − 4 = 0, x + 2y = 3, 3x + 4y + 5 = 0

Examine the consistency of the following equation:

x + 2y −3 = 0, 7x + 4y − 11 = 0, 2x + 4y − 6 = 0

Find k if the following equations are consistent:

2x + 3y - 2 = 0, 2x + 4y − k = 0, x − 2y + 3k =0

Find k if the following equations are consistent:

kx + 3y + 1 = 0, x + 2y + 1 = 0, x + y = 0

Answer the following question:

Find the value of k, if the following equations are consistent:

(k + 1)x + (k – 1)y + (k – 1) = 0
(k – 1)x + (k + 1)y + (k – 1) = 0
(k – 1)x + (k – 1)y + (k + 1) = 0

Answer the following question:

Find the value of k, if the following equations are consistent:

3x + y − 2 = 0 kx + 2y − 3 = 0 and 2x − y = 3

Answer the following question:

Find the value of k if the following equation are consistent:

(k − 2)x + (k − 1)y = 17 , (k − 1)x + (k − 2)y = 18 and x + y = 5

Answer the following question:

Find the area of triangle whose vertices are L(1, 1), M(−2, 2), N(5, 4)

Answer the following question:

Show that the lines x − y = 6, 4x − 3y = 20 and 6x + 5y + 8 = 0 are concurrent. Also find the point of concurrence

For two events A and B of a sample space S, if P(A) =` 3/8`, P(B) = `1/2` and P(A ∪ B) = `5/8`. Find the value of the following: P(A ∩ B)

For two events A and B of a sample space S, if P(A) = `3/8` , P(B) = `1/2` and P(A ∪ B) = `5/8` . Find the value of the following: P(A' ∩ B')

For two events A and B of a sample space S, if P(A) =` 3/8`, P(B) = `1/2` and P(A ∪ B) = `5/8`. Find the value of the following: P(A' ∪ B')

For two events A and B of a sample space S, if P(A ∪ B) = `5/6`, P(A ∩ B) = `1/3` and P(B') = `1/3`, then find P(A).

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