PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions

cos 40° + cos 80° + cos 160° + cos 240° =

sin 163° cos 347° + sin 73° sin 167° =

If sin 2 θ + sin 2 ϕ = \[\frac{1}{2}\] and cos 2 θ + cos 2 ϕ = \[\frac{3}{2}\], then cos² (θ − ϕ) =

The value of cos 52° + cos 68° + cos 172° is

The value of sin 78° − sin 66° − sin 42° + sin 60° is ______.

If sin α + sin β = a and cos α − cos β = b, then tan \[\frac{\alpha - \beta}{2}\]=

cos 35° + cos 85° + cos 155° =

The value of sin 50° − sin 70° + sin 10° is equal to

sin 47° + sin 61° − sin 11° − sin 25° is equal to

If cos A = m cos B, then \[\cot\frac{A + B}{2} \cot\frac{B - A}{2}\]=

If A, B, C are in A.P., then \[\frac{\sin A - \sin C}{\cos C - \cos A}\]=

If sin (B + C − A), sin (C + A − B), sin (A + B − C) are in A.P., then cot A, cot B and cot Care in

If sin x + sin y = \[\sqrt{3}\] (cos y − cos x), then sin 3x + sin 3y =

If \[\tan\alpha = \frac{x}{x + 1}\] and 

State whether the following pairs of sets are disjoint.

{1, 2, 3, 4} and {x : x is a natural number and 4 ≤ x ≤ 6}

State whether the following pairs of sets are disjoint.

{a, e, i, o, u} and {c, d, e, f}

State whether the following pairs of sets are disjoint.

{x : x is an even integer} and {x : x is an odd integer}

State whether the following statement is true or false. Justify your answer.

{2, 3, 4, 5} and {3, 6} are disjoint sets.

State whether the following statement is true or false. Justify your answer.

{a, e, i, o, u } and {a, b, c, d} are disjoint sets.

State whether the following statement is true or false. Justify your answer.

{2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.