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Day 327: CDS Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Trigonometric Ratios and Identities. Asked once: CDS 2 2020

    48
    ABC is a triangle inscribed in a semicircle of diameter AB. What is cos⁡(A+B)+sin⁡(A+B)\cos(A + B) + \sin(A + B) equal to ?

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  2. Question 2

    Algebraic Identities and Simplification. Asked once: CDS 1 2019

    11
    Let aa and bb be two positive real numbers such that aa+bb=32a\sqrt{a} + b\sqrt{b} = 32 and ab+ba=31a\sqrt{b} + b\sqrt{a} = 31. What is the value of 5(a+b)7\dfrac{5(a+b)}{7} ?

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  3. Question 3

    Mensuration 2D. Asked once: CDS 1 2020

    98
    In the given figure, there are three semi circles ABCABC, AEFAEF and CDFCDF. The distance between AA and CC is 28 units and FF is the mid-point of ACAC. What is the total area of the three semi circles?

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  4. Question 4

    Mensuration 3D. Asked once: CDS 1 2018

    72
    What is the volume of a cone of maximum volume cut out from a cube of edge 2a such that their bases are on the same plane ?

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  5. Question 5

    Number System. Asked once: CDS 2 2020

    2
    The number of (a,b,c)(a, b, c), where aa, bb, cc are positive integers such that abc=30abc = 30, is

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