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Day 276: CDS Maths

5 questions (11 parts). Try each one first, then open its answer.

  1. Question 1

    Triangles. Asked once: CDS 2 2025

    84
    A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question : In a triangle ABCABC, ∠A=∠B−∠C\angle A = \angle B - \angle C. Is angle AA acute? Statement-I : ABCABC is not an obtuse-angled triangle. Statement-II : Angle CC is acute. Which one of the following is correct in respect of the above Question and the Statements?

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  2. Question 2 (case study, 3 parts)

    Trigonometric Ratios and Identities. Asked once: CDS 2 2024

    Consider the following for the next three (03) items that follow : Let ABCABC be a triangle right-angled at BB. Let PP be the point on BCBC such that BP=PCBP = PC. If AB=10AB = 10 cm, ∠BAP=45∘\angle BAP = 45^\circ and ∠CAP=θ\angle CAP = \theta (use tan⁡(α+β)=tan⁡α+tan⁡β1−tan⁡αtan⁡β\tan(\alpha + \beta) = \dfrac{\tan\alpha + \tan\beta}{1 - \tan\alpha \tan\beta})
    51
    What is tan⁡θ\tan\theta equal to ?

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    52
    If ∠ACP=γ\angle ACP = \gamma, then what is tan⁡γ\tan\gamma equal to ?

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    53
    Consider the following statements : I. The line segment APAP divides the area of the triangle ABCABC into two equal parts II. The perimeter of the triangle APCAPC is more than 46 cm III. The area of the triangle APCAPC is 50 square cm Which of the statements given above are correct ?

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  3. Question 3

    Algebraic Identities and Simplification. Asked once: CDS 1 2024

    21
    If p=(a+a2+b3)3+(a−a2+b3)3p = \sqrt[3]{\left(a + \sqrt{a^2 + b^3}\right)} + \sqrt[3]{\left(a - \sqrt{a^2 + b^3}\right)}, then what is p3+3bpp^3 + 3bp equal to ?

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  4. Question 4

    Circles. Asked once: CDS 2 2020

    81
    A circle is inscribed in a triangle ABC. It touches the sides AB and AC at M and N respectively. If O is the centre of the circle and ∠A=70∘\angle A = 70^\circ, then what is ∠MON\angle MON equal to ?

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  5. Question 5 (case study, 5 parts)

    Data Interpretation. Asked once: CDS 2 2017

    For the next five (05) items that follow : In a University there are 1200 students studying four different subjects, Mathematics, Statistics, Physics and Chemistry. 20% of the total number of students are studying Mathematics, one-fourth of the total number of students are studying Physics, 320 students are studying Statistics and remaining students are studying Chemistry. Three-fifth of the total number of students studying Chemistry are girls. 150 boys are studying Mathematics. 60% of students studying Physics are boys. 250 girls are studying Statistics.
    86
    What is the total number of boys studying Statistics and Physics ?

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    87
    The number of girls studying Statistics is what percent (approximate) of the total number of students studying Chemistry ?

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    88
    In which subjects is the difference between the number of boys and girls equal ?

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    89
    What is the difference between the number of boys studying Mathematics and the number of girls studying Physics ?

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    90
    What is the ratio of the total number of boys to the total number of girls ?

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