SSC CGL Tier l 2023 Question Paper Shift 1 (July 26th)

A vessel is filled with liquid, 5 parts of which are water and 11 parts syrup. What part of the mixture must be drawn off and replaced with water so that the mixture may be syrup and water in the ratio 3 : 2?

There are two circles that touch each other externally. Radius of the first circle with centre O is 12 cm. Radius of the second circle with centre A is 8 cm. Find the length of their common tangent BC.

In $$\triangle ABC, DE || BC$$ and $$\frac{AD}{BD} = \frac{4}{5}$$. If DE = 12 cm, find the length of BC.

If $$x^{2} + 8x - 1 = 0$$ what is the value of $$x^{2} + \frac{1}{x^{2}}$$?

In the given figure, O is the centre of the circle and $$\angle AOB= 130^{\circ}$$. Find $$\angle APB$$.

A four-digits number ab ba is divisible by 4 and a < b. How many such numbers are there?

If $$\left(X^{2} + \frac{1}{x^{2}}\right) = 6$$, 0 < x < 1, what is the value of $$x^{4} - \frac{1}{x^{4}}$$?

A boat goes 20 km upstream and 44 km downstream in 8 hours. In 5 hours, it goes 15 km upstream and 22 km downstream. Determine the speed of the boat in still water.

4 men’s work is equal to 6 women’s work, and 4 women’s work is equal to 6 boys’ work. A boy can finish the work in 60 days. In how many days can the work be finished by a man and a woman together?

A policeman saw a thief at a distance of 400 m. The thief started running at a speed of 10 km/h and the policeman chased him at a speed of 12 km/h in the same direction. At what distance from the starting point will the policeman catch the thief?