SSC CGL 17th August 2021 Shift-2

Points P, Q, R, S and lie in this order on a circle with centre O. If chord TS is parallel to diameter PR and $$\angle RQT = 58^\circ$$ then find the measure (in degrees) of $$\angle RTS$$.

If $$\sin A = \frac{1}{2}, A$$ is an acute angle, then find the value of $$\frac{\tan A - \cot A}{\sqrt{3}(1 + \cosec A)}$$

In $$\triangle ABC, AD$$ is the bisector of $$\angle A$$ meeting BC at D. If AC = 21 cm, BC = 11 cm and the length of BD is 3 cm less than DC, then the length(in cm) of side AB is:

In $$\triangle ABC, AD \perp BC$$ at D and AE is the bisector of $$\angle A$$. If $$\angle B = 62^\circ$$ and $$\angle C = 36^\circ$$, then what is the measure of $$\angle DAE ?$$

For $$0^\circ < \theta < 90^\circ, \frac{1}{\cos \theta} + \frac{1}{\tan \theta - \sec \theta}$$ is equal to:

What is the volume(in cm$$^3$$a) ofa spherical shell whose inner and outerradii are respectively 2 cm and 3 cm ?

Table shows District-wise data of the number of primary school teachers posted in schools of a city. Study the table and answer the question:

What is the average number of female teachers in the five districts?

Find the smallest value of a so that 42a48b (a > b)is divisible by 11.

Pie-chart shows the distribution of percentage of students in various courses. Total number of students is 1400

What is the ratio of number of girls in B.Sc. Maths to number of boys in B.Sc. C. Sci.?

In a class the ratio of rural to urban students is 4 : 7. In an examination the average percentage marks of the rural and the urban studentsare respectively 65 and 63. Whatis the overall average percentage marks of the class (correct to two decimal places)?