Day 330: CDS Maths

5 questions (6 parts). Try each one first, then open its answer.

Question 1
Mensuration 3D. Asked once: CDS 1 2018
74 $There are as many square centimetres in the surface area of a sphere as there are cubic centimetres in its volume. What is the radius of the sphere ?$
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Question 2
Number System. Asked once: CDS 1 2020
41 $The number of three digit numbers (all digits are different) which are divisible by 7 and also divisible by 7 on reversing the order of the digits, is$
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Question 3 (case study, 2 parts)
Triangles. Asked once: CDS 2 2019
Consider the following for the next two (02) items : An equilateral triangle ABC is inscribed in a circle of radius $20\sqrt{3}$ cm.
97 $What is the length of the side of the triangle ?$
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98 $The centroid of the triangle ABC is at a distance d from the vertex A. What is d equal to ?$
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Question 4
Trigonometric Ratios and Identities. Asked once: CDS 2 2019
57 $3 \tan \theta = \cot \theta$
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Question 5
Algebraic Identities and Simplification. Asked once: CDS 1 2018
2 $a + b = 2c$
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Question 1