SSC CHSL 10th August 2021 Shift-3

Two circles of radii 18 cm and 12 cm intersect each other and the length of their common chord is 16 cm. What is the distance (in cm) between their centres?

The value of $$\cot^2 46^\circ - \sec^2 44^\circ + (\sin^2 1^\circ + \sin^2 3^\circ + \sin^2 5^\circ + ... + \sin^2 89^\circ)$$ is:

If $$(1 + \cot^2 \theta) + (1 + (\cot^2 \theta)^{-1})$$ is equal to k, then $$\sqrt{k} = ?$$

The sides AB, BC and AC of $$\triangle ABC$$ are 12 cm, 8 cm and 10 cm, respectively. A circle is inscribed in the triangle touching AB, BC and AC at D, E and F, respectively. The ratio of the lengths of AD to CE is:

By selling a car for ₹6,32,500, a showroom owner makesa profit of 15%. If he sold the car at ₹8,10,000, then what would be the profit percentage (correct to one decimal place)?

If $$(x - 1.5)^3 + (x - 4)^3 + (x - 3.5)^3 = 3 (x - 1.5)(x - 4)(x - 3.5)$$, then what is the value of x ?

Study the pie chart and answer the question that follows.
The given pie chart shows the degree of cost incurred in different expenditure on the construction of a house. The total expenditure is ₹31,50,000.

What is the percentage of expenditure on cement?

A marks her goods 25% above the cost price. She sells 25% of the goods at the marked price, 60% at 25% discount and the remaining at 10% discount. What is her overall gain or loss per cent?

Working together A, B and C can complete a piece of work in 3 days. A completes the same work in 24 days and B completes it in 6 days. How many days will C alone take to complete the same work?

A man covers $$\frac{5}{12}$$ of a total journey by train, $$\frac{7}{18}$$ of the journey by bus and the remaining 7 km on foot. His total journey (in km) is: