SSC CHSL 9th August 2021 Shift-3

For what value of $$\theta$$ (in degrees) is the following equation true?
$$\sin 3 \theta \cos \theta - \cos 3 \theta \sin \theta = \frac{1}{2}, 0 < \theta < \frac{\pi}{2}$$

If $$a^2 + b^2 + c^2 = 576$$ and $$(ab + bc + ca) = 50$$, then what is the value of (a + b + c), if(a + b + c) < 0 ?

A bought a thing in ₹900 and sold to B at 25% profit. B sold it to C on ₹1350 at a loss of 10%. What is the approx. profit percentage of B?

The list price of coconut oil is 15% more than its cost price. At what per cent less should it be sold for no profit and no loss?

Study the given bar graphs and answer the question that follows.
The bar graphs represent the amount invested in raw materials (in 2 crore) and the sale of the products, by a textile companyin the years 2007— 2012. The X-axis represents the years. The Y-axis represents the amount invested in raw materials (in 2 crore) in figure 1 and sale of products in figure 2, respectively.

Figure 1

Figure 2

In which two years was the difference of the amount invested and the sales of products the same?

The value of
$$28 \div [25 + 8 \div 4 - \left\{25 + (25 of 8 \div 20) - (125 \div 5 of 25)\right\}] + (25 \times 5)$$ is:

If $$\left(2x + \frac{1}{2x}\right) = 5$$, then what is the value of $$\left(8x^3 + \frac{1}{8x^3}\right)$$

Study the given graph and answer the question that follows.

What is the ratio of the total expenditure on Infrastructure and Transport to the total expenditure on Taxes and Interest on Loans?

A can complete one-sixth of a work in 5 days and B can complete one-fourth of the same work in 15 days. In how many days, will both working together complete the work?

Chords AB and CD of a circle intersect externally at P. If AB = 8.8 cm, PB = 7.2 cm, PD = 6.4 cm, then CD is equal to: