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Day 302: CDS Maths

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

  1. Question 1

    Algebraic Identities and Simplification. Asked once: CDS 2 2022

    11
    Consider the following statements : 1. x4(y−z)+y4(z−x)+z4(x−y)x^4(y - z) + y^4(z - x) + z^4(x - y) is positive if x>y>zx > y > z. 2. x4(y−z)+y4(z−x)+z4(x−y)x^4(y - z) + y^4(z - x) + z^4(x - y) is negative if x<y<zx < y < z. Which of the above statements is/are correct ?

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  2. Question 2

    Circles. Asked once: CDS 2 2016

    59
    If two tangents inclined at an angle 60∘60^\circ are drawn to a circle of radius 3 cm, then what is the length of each tangent ?

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  3. Question 3

    Linear Equations. Asked once: CDS 2 2016

    7
    In an examination, a student was asked to divide a certain number by 8. By mistake he multiplied it by 8 and got the answer 2016 more than the correct answer. What was the number ?

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  4. Question 4

    Mensuration 2D. Asked once: CDS 2 2023

    73
    An isosceles triangle has its base length 2a and its height is h. On each side of the triangle a square is drawn external to the triangle. What is the area of the figure thus formed ?

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  5. Question 5

    Mensuration 3D. Asked once: CDS 1 2021

    64
    The difference between the outside and the inside surface area of a cylindrical pipe 14 cm long is 44 cm2^2. The pipe is made of 99 cm3^3 of metal. If RR is the outer radius and rr is the inner radius of the pipe, then what is (R+r)(R + r) equal to? (Take π=227\pi = \frac{22}{7})

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