The value of the following is : $3\left(\sin ^{4} \theta+\cos ^{4} \theta\right)+$ $2\left(\sin ^{6} \theta+\cos ^{6} \theta\right)+12 \sin ^{2} \theta \cos ^{2} \theta$

AB and CD are two parallel chords of a circle lying on the opposite side of the centre and the distance between them is 17 cm. The length of AB and CD are 10 cm and 24 cm respectively. The radius (in cm) of the circle is :

O is the incentre of ΔPQR and ∠QPR = 50°, then O is the incentre of ΔPQR

the measure of ∠QOR is :

Two identical circles intersect so that their centres and the points at which they intersect form a square of side 2 cm. What is the area (in cm²) of the portion that is common to the two circles ?

If $x^{2}+x=5$ then the value of $(x+3)^{3}+\frac{1}{(x+3)^{3}}$ is

The value of $\frac{\cos \alpha+\cos \beta}{\sin \alpha+\sin \beta}$ will be

AC is transverse common tangent to two circles with centres P and Q and radius 6 cm and 3 cm at the point A and C respectively. If AC cuts PQ at the point B and AB = 8cm then the length of PQ is :

If $(x-y)=3$, then what is the value of $\left(x^{3}-y^{3}-\right.$ $9 x y)$ ?

If a + b + c = 3 and none of a, b and c is equal to 1, what is the value of

$\frac{1}{(1-a)(1-b)}+\frac{1}{(1-b)(1-c)}+\frac{1}{(1-c)(1-a)} ?$

If $x^{2}-9 x+1=0$, what is the value of $\left(x^{3}+\frac{1}{x^{3}}\right) ?$