SSC CHSL 6th August 2021 Shift-1

Simplify the following expression.
$$\frac{3}{5} + 2\frac{2}{5} \div \left[\left(\frac{7}{8} - \frac{3}{4}\right) \times 4 - 6 \frac{2}{3} \div \frac{4}{3}\right]\times \frac{1}{3}$$

PA and PB are tangents drawn to a circle with centre O from an external point P. If A and B are points on the circle and $$\angle OBA = 42^\circ$$, then $$\angle APB$$ is:

Simplify the following expression.
$$(2a - b - 3c)(4a^2 + b^2 + 9c^2 + 2ab + 6ac - 3bc)$$

A soft drink company prepares drinks of three different flavors - A, B and C. The production of the three flavors over a period of five years from 2010 to 2014 has been expressed in the given bar graph.
Study the graph and answer the question that follows.
Production of three different flavors A, B and C (in lakh bottles) by a company over five years.

The difference between the average production of flavor A in 2012, 2013 and 2014 and the average production of flavor C in 2012, 2013 and 2014 is:

If $$x - y = 4$$ and $$xy = 3$$, then what is the value of $$x^3 - y^3$$ ?

In a rectangi1lar park having dimensions 60 m $$\times$$ 40 m, two circular flower beds with radius 7 m are developed. What is the area of the remaining portion of the park?(Use $$\pi = \frac{22}{7}$$)

Joseph bought two woollen jackets for ₹2,100 and ₹3,150, respectively. By selling the first at a gain of k% and the second at a loss of k%, he found that the selling price of both is the same. What is the value of k?

If the number 34k56k is divisible by 6, then what will be the largest value of k?

Evaluate the following expression.
$$\frac{\tan^2 60^\circ + \cosec^2 30^\circ \sin 90^\circ + 3\sec^2 30^\circ}{4\sin^2 45^\circ + \sec^2 60^\circ - \cot^2 30^\circ - 5\cos^2 90^\circ}$$

Two chords PQ and RS of a circle meet at A when produced. AT is a tangent to the circle meeting it at T. The ratio PA : SA is equal to which of the following?