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Day 111: CDS Maths

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

  1. Question 1

    Algebraic Identities and Simplification. Asked once: CDS 1 2021 (same type asked 3 times) See all 3 of this type

    7
    If a+b+c=0a + b + c = 0, then which of the following are correct? 1. a3+b3+c3=3abca^3 + b^3 + c^3 = 3abc 2. a2+b2+c2=−2(ab+bc+ca)a^2 + b^2 + c^2 = -2(ab + bc + ca) 3. a3+b3+c3=−3ab(a+b)a^3 + b^3 + c^3 = -3ab(a + b) Select the correct answer using the code given below.

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  2. Question 2

    Mensuration 2D. Asked once: CDS 2 2023 (same type asked 3 times) See all 3 of this type

    54
    The corners of an equilateral triangular plate were cut in such a manner that it forms a regular hexagonal plate. What is the ratio of the area of the triangular plate to the area of the hexagonal plate ?

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  3. Question 3

    Mensuration 3D. Asked once: CDS 1 2022 (same type asked 3 times) See all 3 of this type

    65
    A cylindrical pipe has inner diameter of 14 cm. Water flows through it at a rate of 154 litres per minute. What is the speed of water in km/hr? (Take π=227\pi = \dfrac{22}{7})

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  4. Question 4

    Quadrilaterals. Asked once: CDS 1 2022 (same type asked 3 times) See all 3 of this type

    52
    If AA, BB, CC, DD are the angles of a cyclic quadrilateral, then what is the value of the following? sin⁡(A+C2)+sin⁡(B+D2)\sin\left(\frac{A + C}{2}\right) + \sin\left(\frac{B + D}{2}\right)

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  5. Question 5

    Quadrilaterals. Asked once: CDS 2 2026 (same type asked 3 times) See all 3 of this type

    80
    In a quadrilateral ABCD, ∠ABC=90∘\angle ABC = 90^\circ and ∠ACD=90∘\angle ACD = 90^\circ. Let AB = p units, BC = q units, AC = r units, CD = s units, AD = t units, where p<q<r<s<t<15p < q < r < s < t < 15. If p, q, r, s and t are integers, then what is the area of the quadrilateral ?

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