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Day 149: CDS Maths

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

  1. Question 1

    Algebraic Identities and Simplification. Asked once: CDS 2 2017 (same type asked 2 times) See all 2 of this type

    32
    If ab+bc+ca=0ab + bc + ca = 0, then what is the value of a2a2−bc+b2b2−ca+c2c2−ab\frac{a^2}{a^2 - bc} + \frac{b^2}{b^2 - ca} + \frac{c^2}{c^2 - ab} ?

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  2. Question 2

    Mensuration 2D. Asked once: CDS 1 2018 (same type asked 2 times) See all 2 of this type

    95
    What is the area of the region bounded internally by a square of side of length 'a' and externally by a circle passing through the four corners of the square ?

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  3. Question 3

    Circles. Asked once: CDS 2 2016 (same type asked 2 times) See all 2 of this type

    70
    ABCDAABCDA is a con-cyclic quadrilateral of a circle ABCDABCD with radius rr and centre at OO. If ABAB is the diameter and CDCD is parallel and half of ABAB and if the circle completes one rotation about the centre OO, then the locus of the middle point of CDCD is a circle of radius

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  4. Question 4

    Polynomials. Asked once: CDS 2 2017 (same type asked 2 times) See all 2 of this type

    6
    Let f(x)f(x) and g(x)g(x) be two polynomials (with real coefficients) having degrees 3 and 4 respectively. What is the degree of f(x)g(x)f(x)g(x) ?

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  5. Question 5

    Triangles. Asked once: CDS 1 2017 (same type asked 2 times) See all 2 of this type

    98
    In the figure given below, M is the mid-point of AB and ∠DAB=∠CBA\angle DAB = \angle CBA and ∠AMC=∠BMD\angle AMC = \angle BMD. Then the triangle ADM is congruent to the triangle BCM by

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