Instructions

For the following questions answer them individually

Question 111

The average height of 30 students of a class is 165 cm. 5 new students with average height 172 cm join the class. What is the new average (in cm) of the class?

Question 113

The present value of an ATM machine is â‚¹55,000. The value of the machine depreciates at the rate of 25% every year. What will be the value of the machine after two years?

Question 114

A large container having three different vessels contains 780 , 690 and 950 litres of oil and petrol, respectively. Find the largest measure among all three vessels.

Question 115

The garph of $$f(x) = x^2 - 5x + 6$$ is translated 2 units left and 12 units down to get h$$(x)$$. Express h$$(x)$$ in the form $$h(x) = ax^2 + bx + c$$.

Question 116

What is the domain and the vertical asymptote (VA), respectively, of $$f(x) = \log_{5}(x-4)-4, x > 0$$?

Question 117

Two straight parallel lines are cut by a transversal, such that, the measures of two co-interior angles are $$\frac{3x}{4}$$ and $$\left(\frac{5x}{4} - 20 \right)$$. What are the values of the measures of the two angles (in $$^\circ$$), respectively?

Question 118

The length of the major axis is 12 cm and that of the minor axis is 2.8 cm. What is the area (in $$cm^2$$) of the ellipse?

Question 119

If $$(x^2 - x - 6)$$ is a factor of $$x^4 + ax^3 - x^2 - bx - 12 = 0$$, what are the values of constants a and b, respectively, in the above equation ?

Question 120

A train overtakes two persons walking along a railway bridge. The first one walks at 4 km/h and the other one walks at 6 km/h. The train needs 4.2 and 4.8 seconds, respectively, to overtake them. What is the speed of the train, if both the persons are walking in the same direction?