Instructions

For the following questions answer them individually

Question 2

Calculate the total numbers of prime factors in the expression $$(9)^{11} \times (5)^7 \times (7)^5 \times (3)^2 \times (17)^2$$

Question 4

The two equations are 4x + 4ky-6=0 and x+6y-12=0. Find the value of k for the pair of two linear equations represents the parallel lines.

Question 5

The two circles with radii 6 cm and 3 cm centered at the point P and Q respectively. A transverse common tangent AC to the both circles cuts line joining P and Q at the point B such that AB = 8 cm. Calculate the length (in cm) of PQ.

Question 6

The circle of radius 4 cm and centre O has a tangent PR. If $$\angle POR=90^\circ$$ and OR = 7 cm and OP = 24 cm. Calculate the length (in cm) of PR.

Question 7

In an election between two candidates, the winning candidate got 70% of the valid votes and won by a majority of 9000 votes. If out of total votes polled 90% votes are valid, then what is the total number of votes polled?

Question 9

7 litres mixture of milk and water contains 30% water. 3.5 litres of milk is added to this mixture. What is the percentage of water in the new mixture?