HSC Science (Computer Science) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Select the correct option from the given alternatives :

If sin θ = n sin (θ + 2α), then tan (θ + α) is equal to

Select the correct option from the given alternatives :

Let 0 < A, B < `pi/2` satisfying the equation 3 sin²A + 2 sin²B = 1 and 3 sin 2A − 2 sin 2B = 0 then A + 2B is equal to ______

Prove the following:

tan 20° tan 80° cot 50° = `sqrt(3)`

Prove the following:

cosec 48° + cosec 96° + cosec 192° + cosec 384° = 0

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)|`

Answer the following :

Find the lengths of the intercepts made on the co-ordinate axes, by the circle:

x² + y² – 8x + y – 20 = 0

Answer the following :

Find the lengths of the intercepts made on the co-ordinate axes, by the circle:

x² + y² – 5x + 13y – 14 = 0