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Day 324: CDS Maths

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

  1. Question 1

    Number System. Asked once: CDS 1 2021

    1
    If the number 413283P759387 is divisible by 13, then what is the value of P ?

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  2. Question 2

    Quadratic Equations. Asked once: CDS 2 2016

    9
    The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, then what is the difference of the larger and smaller numbers ?

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  3. Question 3

    Triangles. Asked once: CDS 2 2020

    64
    ABC is an equilateral triangle. The side BC is trisected at D such that BC = 3 BD. What is the ratio of AD2AD^2 to AB2AB^2 ?

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  4. Question 4

    Trigonometric Ratios and Identities. Asked once: CDS 2 2020

    59
    If 0≤α,β≤90∘0 \le \alpha, \beta \le 90^\circ such that cos⁡(α−β)=1\cos (\alpha - \beta) = 1, then what is sin⁡α−sin⁡β+cos⁡α−cos⁡β\sin \alpha - \sin \beta + \cos \alpha - \cos \beta equal to ?

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  5. Question 5

    Algebraic Identities and Simplification. Asked once: CDS 1 2021

    5
    How many terms are there in the following product? (a1+a2+a3)(b1+b2+b3+b4)(c1+c2+c3+c4+c5)(a_1 + a_2 + a_3)(b_1 + b_2 + b_3 + b_4)(c_1 + c_2 + c_3 + c_4 + c_5)

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