SSC CGL Tier-2 13th September 2019 Maths

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 4

The value of $$\sqrt{28+10\sqrt{3}}-\sqrt{7-4\sqrt{3}}$$ is closest to:

Question 5

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

Question 6

The value $$\cosec(67^\circ + \theta) - \sec(23^\circ - \theta) + \cos 15^\circĀ \cos 35^\circĀ \cos 55^\circĀ \cos 60^\circĀ \cos 75^\circ$$ 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 9

$$ab(a - b) + bc(b - c) + ca(c - a)$$ 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?

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