Day 36: CDS Maths

5 questions (7 parts). Try each one first, then open its answer.

Question 1
Statistics. This type asked 3 times: CDS 2 2018, CDS 2 2019, CDS 2 2025. This one: CDS 2 2025 See all 3 of this type
96 $Which one of the following is a positional average?$
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Question 2
Trigonometric Ratios and Identities. This type asked 3 times: CDS 1 2020, CDS 2 2022, CDS 2 2025. This one: CDS 2 2025 See all 3 of this type
34 $(\sec\theta - \tan\theta) - \sqrt{\dfrac{1 - \sin\theta}{1 + \sin\theta}}$
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Question 3 (case study, 2 parts)
Circles. This type asked 3 times: CDS 2 2017, CDS 1 2018, CDS 1 2025. This one: CDS 1 2025 See all 3 of this type
Consider the following for the next two (02) items that follow : A circle M of radius 8 cm touches externally with another circle N of radius 16 cm. Let P, Q be the points where the common tangent touches the circles M and N respectively.
55 $What is the length of the common tangent PQ ?$
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56 $If U, V are the centres of the circles M and N respectively, then what is the area of the quadrilateral formed by the points P, Q, V and U ?$
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Question 4 (case study, 2 parts)
Mensuration 3D. This type asked 3 times: CDS 2 2016, CDS 1 2022, CDS 1 2025. This one: CDS 1 2025 See all 3 of this type
The annual rainfall at a place is 40 cm. The weight of water is 1 metric tonne per cubic meter.
67 $What is the volume of rainfall in cubic meter per hectare ?$
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68 $What is the weight of water (in metric tonnes) of annual rainfall falling there on a hectare of land ?$
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Question 5
Number System. This type asked 3 times: CDS 2 2016, CDS 1 2017, CDS 1 2025. This one: CDS 1 2025 See all 3 of this type
78 $2^{101}$
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Question 1

Question 2

Question 3 (case study, 2 parts)

Question 4 (case study, 2 parts)

Question 5