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Day 299: CDS Maths

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

  1. Question 1

    Surds, Indices and Simplification. Asked once: CDS 2 2019

    26
    For any two real numbers a and b, (a−b)2+(b−a)2\sqrt{(a - b)^2} + \sqrt{(b - a)^2} is

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  2. Question 2 (case study, 3 parts)

    Triangles. Asked once: CDS 1 2024

    Consider the following for the next three (03) items that follow : ABC is a right-angled triangle with ∠ABC=90∘\angle ABC = 90^\circ. The centre of the incircle of the given triangle is at O, whose radius is 2 cm. Two more circles with centres at O1O_1 and O2O_2 touch this circle and the two sides as shown in the figure given below. Further, MA : MC = 2 : 3.
    88
    What is AB + BC equal to ?

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    89
    What is the radius of the circle with centre at O1O_1 ?

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    90
    What is the radius of the circle with centre at O2O_2 ?

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  3. Question 3

    Trigonometric Ratios and Identities. Asked once: CDS 1 2024

    9
    If t=cos⁡79∘t = \cos 79^\circ, then what is cosec⁡79∘(1−cos⁡79∘)\operatorname{cosec} 79^\circ (1 - \cos 79^\circ) equal to ?

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  4. Question 4

    Algebraic Identities and Simplification. Asked once: CDS 1 2023

    45
    If x=a+b+(a−b)24a+4bx = a + b + \frac{(a - b)^2}{4a + 4b} and y=a+b4+aba+by = \frac{a + b}{4} + \frac{ab}{a + b}, then what is the value of (x−a)2−(y−b)2(x - a)^2 - (y - b)^2 ?

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  5. Question 5

    Circles. Asked once: CDS 1 2018

    96
    In the figure given below, XA and XB are two tangents to a circle. If ∠AXB=50∘\angle AXB = 50^\circ and AC is parallel to XB, then what is ∠ACB\angle ACB equal to ?

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