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Day 311: CDS Maths

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

  1. Question 1

    Trigonometric Ratios and Identities. Asked once: CDS 1 2023

    46
    Consider the following : 1. cos⁡4θ−sin⁡4θ=2tan⁡θ1−tan⁡2θ\cos^4\theta - \sin^4\theta = \frac{2\tan\theta}{1 - \tan^2\theta}, 0<θ<π20 < \theta < \frac{\pi}{2} 2. cosec⁡ θ+cot⁡θ=1cosec⁡ θ−cot⁡θ\operatorname{cosec}\,\theta + \cot\theta = \frac{1}{\operatorname{cosec}\,\theta - \cot\theta}, 0<θ<π20 < \theta < \frac{\pi}{2} 3. cos⁡2θ−sin⁡2θ=1−tan⁡2θ1+tan⁡2θ\cos^2\theta - \sin^2\theta = \frac{1 - \tan^2\theta}{1 + \tan^2\theta}, 0<θ<π20 < \theta < \frac{\pi}{2} Which of the above equations are identities ?

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  2. Question 2

    Algebraic Identities and Simplification. Asked once: CDS 1 2022

    15
    If x2=17x+yx^2 = 17x + y and y2=x+17yy^2 = x + 17y, x≠yx \ne y, then what is the value of x2+y2+1\sqrt{x^2 + y^2 + 1} ?

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  3. Question 3

    Mensuration 2D. Asked once: CDS 2 2022

    92
    X, Y and Z are three equilateral triangles. The sum of the areas of X and Y is equal to the area of Z. If the side lengths of X and Y are 6 cm and 8 cm respectively, then what is the side length of Z ?

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  4. Question 4

    Mensuration 3D. Asked once: CDS 1 2020

    88
    A right circular cylinder just encloses a sphere. If pp is the surface area of the sphere and qq is the curved surface area of the cylinder, then which one of the following is correct ?

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  5. Question 5

    Number System. Asked once: CDS 1 2024

    24
    If HCF of 768 and x6y2x^6 y^2 is 32xy for natural numbers x≥2,y≥2x \ge 2, y \ge 2, then what is the value of (x+y)(x + y) ?

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