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

Prove the following:

sin 20° sin 40° sin 80° = `sqrt(3)/8`

Prove the following:

sin 18° = `(sqrt(5) - 1)/4`

Prove the following:

cos 36° = `(sqrt(5) + 1)/4`

Prove the following:

sin 36° = `(sqrt(10 - 2sqrt(5)))/4`

Prove the following:

`tan  pi/8 = sqrt(2) - 1`

Prove the following:

tan6° tan42° tan66° tan78° = 1

Prove the following:

sin47° + sin61° − sin11° − sin25° = cos7°

Find the minor and cofactor of element of the determinant

D = `|(2, -1, 3),(1, 2, -1),(5, 7, 2)|`

Evaluate A = `|(2, -3,5),(6, 0, 4),(1, 5, -7)|` Also find minor and cofactor of elements in the 2^nd row of determinant and verify − a₂₁.M₂₁ + a₂₂.M₂₂ − a₂₃.M₂₃ = value of A

where M₂₁, M₂₂ , M₂₃ are minor of a₂₁ , a₂₂, a₂₃ and C₂₁, C₂₂, C₂₃ are cofactor of a₂₁, a₂₂, a₂₃

Evaluate A = `|(2, -3,5),(6, 0, 4),(1, 5, -7)|` Also find minor and cofactor of elements in the 2^nd row of determinant and verify a₂₁ C₂₁ + a₂₂ C₂₂ + a₂₃ C₂₃ = value of A

where M₂₁, M₂₂, M₂₃ are minors of a₂₁, a₂₂, a₂₃ and

C₂₁, C₂₂, C₂₃ are cofactors of a₂₁, a₂₂, a₂₃.

Find the value of determinant expanding along third column

`|(-1, 1, 2),(-2, 3, -4),(-3, 4, 0)|`

Answer the following question:

Evaluate determinant along second column

`|(1, -1, 2),(3, 2, -2),(0, 1, -2)|`

Answer the following question:

Find minor and cofactor of elements of the determinant:

`|(-1, 0, 4),(-2, 1, 3),(0, -4, 2)|`

Answer the following question:

Find minor and cofactor of elements of the determinant:

`|(1, -1, 2),(3, 0, -2),(1, 0, 3)|`

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

An urn contains 4 black, 5 white and 6 red balls. Two balls are drawn one after the other without replacement. What is the probability that at least one of them is black?

Solve the following:

There are 6 positive and 8 negative numbers. Four numbers are chosen at random, without replacement, and multiplied. Find the probability that the product is a positive number.

Simplify : `sqrt(-16) + 3sqrt(-25) + sqrt(-36) - sqrt(-625)`

Simplify : `4sqrt(-4) + 5sqrt(-9) - 3sqrt(-16)`

Find a and b if a + 2b + 2ai = 4 + 6i