SSC CGL 17th August 2021 Shift-2

Instructions

For the following questions answer them individually

Question 51

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 $$\angle RTS$$.

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Question 52

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

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Question 53

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:

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Question 54

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 $$\angle DAE ?$$

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Question 55

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

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Question 56

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

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Question 57

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?

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Question 58

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

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Question 59

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.?

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Question 60

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)?

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