Instructions

For the following questions answer them individually

Question 1

N solid metallic spherical balls are melted and recast into a cylindrical rod whose radius is 3 times that of a spherical ball and height is 4 times the radius of a spherical ball. The value of N is:

Question 2

If x is the remainder when $$3^{61284}$$ is divided by 5 and y is the remainder when $$4^{96}$$ is divided by 6, then what is the value of (2x - y)?

Question 3

What is the area (in square units) of the triangular region enclosed by the graphs of the equations x + y = 3, 2x + 5y = 12 and the x-axis?

Question 5

If $$\sec\theta+\tan\theta=p,\left(p>1\right)$$ then $$\frac{\operatorname{cosec}\theta+1}{\operatorname{cosec}\theta-1} = ?$$

Question 6

The value $$\cosec(67^\circ + \theta) - \sec(23^\circ - \theta) + \cos 15^\circ \cos 35^\circ \cos 55^\circ \cos 60^\circ \cos 75^\circ$$ is:

Question 7

35% of goods were sold at a profit of 65%, while the remaining were sold at x% loss. If the overall loss is 12%, then what is the value of x ? (correct to one decimal place)

Question 8

In a circle with centre O, ABCD isa cyclic quadrilateral and AC is the diameter. Chords AB and CD are produced to meet at E. If $$\angle CAE = 34^\circ$$ and $$\angle E = 30^\circ$$, then $$\angle CBD$$ is equal to:

Question 10

The radius of the base of a right circular cylinder is increased by 20%. By what per cent should its height be reduced so that its volume remains the same as before?