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 INCORRECTLY spelt word.
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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