SSC CGL Tier l 26th July 2023 Shift-2

The ratio of the number of boys in a school to the total number of boys and girls in that school is 7 : 17. If the number of boys in that school is 1099, then how many girls are there in that school?

For congruent triangles $$\triangle ABC$$ and $$\triangle DEF$$, which of the following statements is correct?

Ram and Shyam are racing along a circular track. The speed of Ram is thrice the speed of Shyam. The length of the circular track is 1440 m. After the start of the race from the same point simultaneously, Ram meets Shyam for the first time at the end of the 8th minute. If Ram and Shyam start the race again from the same starting point simultaneously, then the time taken by Shyam to finish the race is: (given that the length of the race is same as the length of the track)

Pipe A and pipe B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill it, then the time in which A and B will fill that cistern separately will be, respectively, _____________.

If $$\left(a^{3} + b^{3}+ c^{3}- 3abc\right)= 405$$, and $$(a - b)^{2} + (b - c)^{2} + (c - a)^{2} = 54$$, find the value of (a + b + c).

What is the surface area (in $$cm^{2}$$) of a spherical sculpture whose radius is 35 cm?
[Use $$\pi = \frac{22}{7}$$]

Pipe A can fill 50% of the tank in 6 hours and pipe B can completely fill the same tank in 18 hours. If both the pipes are opened at the same time, in how much time (in minutes) will the empty tank be completely filled?

A 9-digit number 846523X7Y is divisible by 9, and Y - X = 6.
Find the value of $$\sqrt{2X + 4Y}$$.

$$\triangle$$ ABC is a right triangle. If $$\angle B = 90^{\circ}$$ and $$\tan A \frac{1}{\sqrt{3}}$$, then the value of $$\sin A \cos A + \cos A \sin C$$ is:

A policeman spots a thief at a distance of 360 m. Both the policeman and the thief simultaneously start running, with the former chasing the latter. While the thief runs at the speed of 8 km/h, the policeman runs at 9.2 km/h. How many metres will the policeman have to run before he catches up with the thief?