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

Answer the following:

State the signs of cosec 520°

Answer the following:

State the signs of cot 1899°

Answer the following:

State the signs of sin 986°

Answer the following:

State the quadrant in which θ lies if tan θ < 0 and sec θ > 0

Answer the following:

State the quadrant in which θ lies if sin θ < 0 and cos θ < 0

Answer the following:

State the quadrant in which θ lies if sin θ > 0 and tan θ < 0

Answer the following:

Which is greater sin(1856°) or sin(2006°)?

Answer the following:

Which of the following is positive? sin(−310°) or sin(310°)

Answer the following:

Show that 1 − 2sinθ cosθ ≥ 0 for all θ ∈ R.

Answer the following:

Show that tan²θ + cot²θ ≥ 2 for all θ ∈ R

Answer the following:

If sec θ = `sqrt(2)` and `(3pi)/2 < theta < 2pi` then evaluate `(1 + tantheta + "cosec"theta)/(1 + cottheta - "cosec"theta)`

Without expanding evaluate the following determinant:

`|(1, "a", "b" + "c"),(1, "b", "c" + "a"),(1, "c", "a" + "b")|`

Without expanding evaluate the following determinant:

`|(2, 3, 4),(5, 6, 8),(6x, 9x, 12x)|`

Without expanding evaluate the following determinant:

`|(2, 7, 65),(3, 8, 75),(5, 9, 86)|`

Prove that `|(x + y, y + z, z + x),(z + x, x + y, y + z),(y + z, z + x, x + y)| = 2|(x, y, z),(z, x, y),(y, z, x)|`

Using properties of determinant show that

`|("a" + "b", "a", "b"),("a", "a" + "c", "c"),("b", "c", "b" + "c")|` = 4abc

Using properties of determinant show that

`|(1, log_x y, log_x z),(log_y x, 1, log_y z),(log_z x, log_z y, 1)|` = 0

Solve the following equation: 

`|(x + 2, x + 6, x - 1),(x + 6, x - 1, x + 2),(x - 1, x + 2, x + 6)|` = 0

If  `|(4 + x, 4 - x, 4 - x),(4 - x,4 + x,4 - x),(4 - x,4 - x, 4 + x)|` = 0, then find the values of x.

Without expanding determinants show that

`|(1, 3, 6),(6, 1, 4),(3, 7, 12)| + 4|(2, 3, 3),(2, 1, 2),(1, 7, 6)| = 10|(1, 2, 1),(3, 1, 7),(3, 2, 6)|`