For the following questions answer them individually
If $$8a^{3} + 27b^{3} = 16$$ and 2a + 3b = 4,then find the value of $$16a^{4} + 81b^{4}$$.
If $$\frac{k - k\cot^{2}30^{\circ}}{1+\cot^{2}30^{\circ}} = \sin^{2}60^{\circ} + 4\tan^{2}45^{\circ}-\cosec^{2}60^{\circ}$$, then the value of k (correct to two decimal places) is:
Let O be the centre of a circle and P be the point outside the circle. If PAB is a secant to the circle intersecting the circle at A and B and PT is the tangent segment drawn from P, find the length of PT, if PA = 3 cm and AB = 9 cm.
Suppose $$\angle$$ ABC be a right-angled triangle where $$\angle A = 90^{\circ}$$ and $$AD \perp BC$$. If area ($$\triangle ABC) = 80 cm^{2}$$ and BC = 16 cm, then the length of AD is:
A solid copper sphere of radius 9 cm is hammered and moulded into a wire of radius 2 cm. What is the length of this wire?
A sentence has been given with a blank to be filled with an appropriate word. Choose the correct alternative.
Every person should know their own _______, what their skill set is and how unique they are. \
Select the most appropriate ANTONYM of the given word.
Humble
Select the most appropriate meaning of the given idiom.
Bear the palm
Select the sentences that contains no spelling errors.
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