For the following questions answer them individually
What is the volume of the largest sphere that can be carved out of a wooden cube of sides 21 cm?
(Take $$ \pi = \frac{22}{7}$$)
The ratio of the incomes of two employees is 7 : 4, and the ratio of their expenditures is 3 : 1. If each of them manages to save ₹4,800 per month, find the sum of their monthly incomes (in ₹).
If radius of a sphere is decreased by 48%, then by what percent does its surface area decrease?
The product of the two numbers is 1500 and their HCF is 10. The number of such possible pairs is/are:
A man buys a machine for Rs.5,000. After one year, he sells it for Rs.6000. After two years, again he buys the same machine at Rs.8,000 and sells it for Rs.10,000. Find his overall profit percentage for both the transactions.
Evaluate the following.
$$\sin 25^{\circ} \sin 65^{\circ} - \cos 25^{\circ} \cos 65^{\circ}$$.
In $$\triangle PQR,PQ=QR$$ and O is an interior point of $$\triangle PQR$$ such that $$\angle OPR= \angle ORP$$.
Consider the following statements:
(i) $$\triangle POR$$ is an isosceles triangle.
(ii) O is the centroid of $$\triangle PQR$$.
(iii) $$\triangle PQO$$ is congruent to $$\triangle RQO$$.
Which of the above statements are correct?
A man can row 10 km/h in still water. When the river is running at a speed of 4.5 km/h, then it takes him 2 h to row to a place and comes back to the initial point . How far is the place (in km) (rounded off to two decimal places)?
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