SSC CGL Tier l 25th July 2023 Shift-4

Simplify the expression $$\frac{s^{2} + t^{2} + 2st - u^{2}}{s^{2} - t^{2} - 2tu - u^{2}}$$, provided $$\left(s + t + u\right) \neq 0$$.

Find $$\left(1  / \sin \theta \right) - \sin \theta$$.

A shopkeeper purchased 1600 mangos at the rate of ₹120 per dozen. Out of these, he sold 900 mangoes at ₹15 per mango and the remaining mangoes at ₹14 per mango. His gain percentage is:

A thief steals an item and escapes, running at a speed of 15 km/h. A policeman arrives at the spot of the crime after 4 minutes and immediately starts chasing the thief. 16 minutes after the policeman started to chase the thief; there is still a gap of 200 m between the two. At what distance from the spot of the crime will the policeman catch up the thief and what is the speed (in km/h) of the policeman?

In the following figure, the circles with centres B and D have radii 4 cm and x cm, respectively. AC is a tangent to both the circles. Find the value of x.

In the figure given below. PQ is the diameter of the circle with centre O. If $$\anle QOR = 100^{\circ}$$ then the measure of $$\angle PSR$$ is·

If (a + b - c) = 20, and $$a^{2} + b^{2} + c^{2} = 152$$, find the value of $$a^{3} + b^{3} - c^{3} + 3abc$$.

A 40-litre mixture contains 25% alcohol and 75% water. If 10 litres of water are added to the mixture, the percentage of alcohol in the new mixture is:

The following bar chart shows the vends of foreign direct investment (FDI) into India from all over the world.

What was the average of India's FDI over the years 1992 - 1997?

The marked price of a microwave oven is ₹15,990 and it is sold for ₹12,792. What is the rate of discount offered?