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Day 79: CDS Maths

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

  1. Question 1

    Quadrilaterals. This type asked 2 times: CDS 2 2017, CDS 1 2021. This one: CDS 1 2021 See all 2 of this type

    89
    ABCDABCD is a trapezium in which ABAB is parallel to DCDC and 2AB=3DC2AB = 3DC. The diagonals ACAC and BDBD intersect at OO. What is the ratio of the area of △AOB\triangle AOB to that of △DOC\triangle DOC?

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  2. Question 2

    Triangles. This type asked 2 times: CDS 1 2019, CDS 1 2021. This one: CDS 1 2021 See all 2 of this type

    77
    △ABC\triangle ABC is similar to △DEF\triangle DEF. The perimeters of △ABC\triangle ABC and △DEF\triangle DEF are 40 cm and 30 cm respectively. What is the ratio of (BC+CA)(BC + CA) to (EF+FD)(EF + FD) equal to?

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  3. Question 3

    Trigonometric Ratios and Identities. This type asked 2 times: CDS 1 2017, CDS 1 2021. This one: CDS 1 2021 See all 2 of this type

    55
    Let cos⁡α+cos⁡β=2\cos\alpha + \cos\beta = 2 and sin⁡α+sin⁡β=0\sin\alpha + \sin\beta = 0, where 0≤α≤90∘0 \le \alpha \le 90^\circ, 0≤β≤90∘0 \le \beta \le 90^\circ. What is the value of cos⁡2α−cos⁡2β\cos 2\alpha - \cos 2\beta?

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  4. Question 4

    Algebraic Identities and Simplification. This type asked 2 times: CDS 1 2018, CDS 2 2020. This one: CDS 2 2020 See all 2 of this type

    30
    If ab+xy−xb=0ab + xy - xb = 0 and bc+yz−cy=0bc + yz - cy = 0, then what is xa+cz\frac{x}{a} + \frac{c}{z} equal to ?

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  5. Question 5

    Linear Equations. This type asked 2 times: CDS 1 2020, CDS 2 2020. This one: CDS 2 2020 See all 2 of this type

    17
    A 60-page book has nn lines per page. If the number of lines were reduced by 3 in each page, the number of pages would have to be increased by 10 to give the same writing space. What is the value of nn ?

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