For the following questions answer them individually
$$\frac{sec^{2}\theta-\cot^{2}(90^{\circ}-\theta)}{cosec^{2}67^{\circ}-\tan^{2}23^{\circ}}+sin^{2}40^{\circ}+sin^{2}50^{\circ}$$ is equal to
If P denotes the perimeter and S denotes the sum of the distances of a point within a triangle from its angular points, then
Two circles touch each other externally at a point P and a direct common tangent touches the circles at the points Q and R respectively. Then ∠QPR is
In triangle ABC, AB = 12 cm, ∠B = 60°, the perpendicular from A to BC meets it at D. The bisector of ∠ABC meets AD at E. Then E divides AD in the ratio
If the average of x and $$\frac{1}{x}$$ be 1, then the value of $$x^{10}+\frac{1}{x^{10}}$$ is
If the operation Θ is defined for all real numbers a and b by the relation $$aΘ b =a^{2}\frac{b}{{3}}$$ then $$2Θ {3Θ(Â-1)} = ?$$
O is the centre of a circle. AB is a chord of the circle but not its diameter. OC is perpendicular to AB. If OC = CB and radius of the circle be 7 cm, then the length of AB is
In ΔABC, D, E, F are midÂpoints of AB, BC, CA respectively and ∠B = 90°, AB = 6 cm, BC = 8 cm. Then area of A DEF (in sq. cm) is
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