SSC CGL 19th April 2022 Shift-1

In the following figure, MN is a tangent to a circle with centre O at point A. If BC is a diameter and $$\angle ABC = 42^{\circ}$$, then find the measure of $$\angle$$ MAB.

Of the three numbers, second is one-third of first and is also three-fourth of the third number. If the average of three numbers is 112, then what is the smallest number?

If each of the two numbers $$5^{16}$$ and $$5^{25}$$ are divided by 6, the remainders are $$R_{1}$$ and $$R_{2}$$, respectively. What is the value of $$\frac{R_{1}+R_{2}}{R_{2}}$$?

If $$A = 60^{\circ}$$, ·what is the value of:
$$\frac{10\sin \frac{A}{2}+8\cos A}{7\sin \frac{3A}{2}-12\cos A}$$?

If $$x + y + z = 7, xy + yz + zx = 8$$, then what is the value of $$x^{3} + y^{3} + z^{3} - 3xyz$$?

The value of $$\frac{\left[\frac{3}{8}-\left\{\frac{3}{8}-\left(\frac{5}{8}-\frac{3}{8}\right)\right\}\right] of 4.8-0.9}{4\frac{1}{6}\div2.5\times0.2\div\frac{1}{5} of 50+\left(\frac{3}{4}-\frac{1}{8}\right)}$$ is:

Let $$\triangle ABC - \triangle$$ QPR and (Area of $$\triangle$$ ABC) : (Area of $$\triangle$$ PQR) = 121 : 64. If QP = 14.4 cm, PR = 12 cm and AC = 18 cm, then what is the length of AB?

In a $$\triangle$$ ABC, D, E and Fare the mid-points of side BC, CA and AB respectively. If BC = 14.4 cm, CA = 15.2 cm and AB= 12.4 cm, what is the perimeter (in cm) of the $$\triangle$$ DEF?

A vegetable vendor supplies vegetables to a housing complex of 50 families. On a particular day, the break-up sale of vegetables is represented in the form of a pie chart as shown.
Study the pie chart carefully and answer the question that follows.

What is the ratio of the central angle corresponding to the sale of potatoes, tomatoes and beans together to the central angle corresponding to the combined sale of onions and others?

PQ and RS are two parallel chords of a circle of length 14 cm and 48 cm. respectively, and lie on the same side of the centre O. If the distance between the chords is 17 cm, what is the radius (i.n cm) of the circle?