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Day 133: CDS Maths

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

  1. Question 1

    Algebraic Identities and Simplification. Asked once: CDS 2 2023 (same type asked 2 times) See all 2 of this type

    80
    If 2s=a+b+c2s = a + b + c, then what is s2+(s−a)(s−b)+(s−b)(s−c)+(s−c)(s−a)s^2 + (s - a)(s - b) + (s - b)(s - c) + (s - c)(s - a) equal to ?

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  2. Question 2

    Algebraic Identities and Simplification. Asked once: CDS 2 2023 (same type asked 2 times) See all 2 of this type

    1
    If a2−bc=αa^2 - bc = \alpha, b2−ac=βb^2 - ac = \beta, c2−ab=γc^2 - ab = \gamma, then what is aα+bβ+cγ(a+b+c)(α+β+γ)\dfrac{a\alpha + b\beta + c\gamma}{(a + b + c)(\alpha + \beta + \gamma)} equal to ?

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  3. Question 3

    Mensuration 2D. Asked once: CDS 1 2021 (same type asked 2 times) See all 2 of this type

    87
    If the perimeter of a right-angled triangle is 30 cm and the hypotenuse is 13 cm, then what is the area of the triangle?

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  4. Question 4

    Mensuration 3D. Asked once: CDS 2 2022 (same type asked 2 times) See all 2 of this type

    91
    A closed box is built of wood of uniform thickness. Its external dimensions are 12 cm, 10 cm and 8 cm. If the inner surface area is 376 square cm, then what is the thickness of the wood ?

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  5. Question 5

    Number System. Asked once: CDS 2 2022 (same type asked 2 times) See all 2 of this type

    19
    There are two natural numbers x and y, where x>yx > y. When x is divided by 6, it leaves the remainder 2 and; when y is divided by 6, it leaves the remainder 3. What is the remainder when (x−y)(x - y) is divided by 6 ?

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