SSC CGL 12th April 2022 Shift-1

The ratio of me speeds of two trains is 2 : 7. If me first train runs 250 km in 5 hours, then the sum of the speeds (in km/h) of both the trains is:

Two common tangents AC and BD touch two equal circles equal of radius 7 cm, at points A, C, B and D, respectively, as shown in the figure . If the length of BD is 48 cm, what is the length of AC?

If $$x$$ + y + z = 11 , $$x$$y + yz + z$$x$$ = -6 , and $$x^{3} + y^{3} + z^{3} = 1604$$, then the value of $$x$$yz is:

If $$\cot B = \frac{12}{5}$$, what is the value of $$\sec$$ B

A vertical pole and a vertical tower are on the same level ground in such a way that, from the top of the pole, the angle of elevation of the top of the tower is $$60^{\circ}$$ and the angle of depression of the bottom of the tower is $$30^{\circ}$$. If the height of the pole is 24 m, then find the height of the tower (in m).

Select the INCORRECTLY spelt word.

The following sentence has been split into four segments. Identify the segment that contains a grammatical error.
My older brother,/ which you’ll / meet later,/ is a dentist.

Select the most appropriate ANTONYM of the given word.
Rely

Select the most appropriate meaning of the given idiom.
To take after

Select the option that expresses the given sentence in active voice.
Hatred can be overcome by love.