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Day 305: CDS Maths

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

  1. Question 1

    Quadratic Equations. Asked once: CDS 1 2019

    91
    If (b−6)(b - 6) is one root of the quadratic equation x2−6x+b=0x^2 - 6x + b = 0, where bb is an integer, then what is the maximum value of b2b^2 ?

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  2. Question 2

    Quadrilaterals. Asked once: CDS 1 2017

    93
    In the figure given below, PQRS is a parallelogram. PA bisects angle P and SA bisects angle S. What is angle PAS equal to ?

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  3. Question 3

    Surds, Indices and Simplification. Asked once: CDS 1 2018

    22
    125\frac{1}{25} of the students who registered did not appear for the examination, 1120\frac{11}{20} of those who appeared passed. If the number of registered students is 2000, the number who passed is

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  4. Question 4 (case study, 3 parts)

    Triangles. Asked once: CDS 1 2023

    Consider the following for the next three (03) items that follow : In the triangle ABC, AB = 6 cm, BC = 8 cm and AC = 10 cm. The perpendicular dropped from B meets the side AC at D. A circle of radius BD (with centre B) cuts AB and BC at P and Q respectively as shown in the figure.
    91
    What is the length of QC ?

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    92
    If ∠ABD=θ\angle ABD = \theta, then what is sin⁡θ\sin \theta equal to ?

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    93
    What is the radius of the circle ?

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  5. Question 5

    Trigonometric Ratios and Identities. Asked once: CDS 1 2023

    52
    What is the value of (1+cot⁡2θ)(1+cos⁡θ)(1−cos⁡θ)−(1+tan⁡2θ)(1+sin⁡θ)(1−sin⁡θ)(1 + \cot^2\theta)(1 + \cos\theta)(1 - \cos\theta) - (1 + \tan^2\theta)(1 + \sin\theta)(1 - \sin\theta) ?

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