SSC CHSL 11th August 2021 Shift-1

If $$3 \sin^2 A + 4 \cos^2 A - 3 = 0$$, then the value of $$\cot A$$ (where $$0 \leq A \leq 90^\circ$$) is:

A bus covered 360 km in 6 hours. If it travels at one-fourth of its usual speed, then how much more time will it take to cover the same distance?

Mohan's income is 40% more than Shyam's income. Shyam's income is what percentage less than Mohan's income?

From a point P, which is at a distance of 13 cm from the centre O of a circle, a pair of tangents PQ and PR of length 12 cm are drawn to the circle. The area of the quadrilateral PQOR (in cm$$^2$$) is:

X can complete half of the work in 20 days and Y can do one-fifth of the same work in 10 days. X started the work and left after 8 days. Then Y took over to complete the remaining work. The total number of days taken by them to complete the work is:

If $$3x + 5y = 14$$ and $$xy = 6$$, then what is the value of $$9 x^2 + 25 y^2$$?

A batsman in his $$13^{th}$$ inning makes a score of 97 runs, there by increasing his average score by 5. What is his average score after the $$13^{th}$$ inning?

Two numbers are in the ratio of 7 : 4. If each number is increased by 12, then the ratio becomes 3 : 2. The sum of the numbers is:

The marked price of an article is ₹660. A shopkeeper allows a discount of 20% and still gets a profit of 10%. If he sells it for ₹470, his profit or loss per cent, correct to two decimal places will be:

If $$\triangle ABC \sim \triangle QPR, \frac{ar(\triangle ABC)}{ar(\triangle PQR)} = \frac{4}{9}$$, AC = 18 cm and BC = 10 cm, then PR (in cm) is equal to: