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Day 340: CDS Maths

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

  1. Question 1

    Trigonometric Ratios and Identities. Asked once: CDS 2 2017

    52
    Consider the following statements : 1. If 45∘<θ<60∘45^\circ < \theta < 60^\circ, then sec⁡2θ+cosec⁡2θ=α2\sec^2 \theta + \operatorname{cosec}^2 \theta = \alpha^2 for some real number α>1\alpha > 1. 2. If 0∘<θ<45∘0^\circ < \theta < 45^\circ, then 1+cos⁡θ1−cos⁡θ=x2\frac{1 + \cos \theta}{1 - \cos \theta} = x^2 for some real number x>2x > 2. 3. If 0∘<θ<45∘0^\circ < \theta < 45^\circ, then cos⁡θ1−tan⁡θ+sin⁡θ1−cot⁡θ≥2\frac{\cos \theta}{1 - \tan \theta} + \frac{\sin \theta}{1 - \cot \theta} \ge 2. What is the number of true statements ?

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  2. Question 2

    Mensuration 2D. Asked once: CDS 2 2018

    91
    In the figure given below, ABC is a right-angled triangle where ∠A=90∘\angle A = 90^\circ, AB = p cm and AC = q cm. On the three sides as diameters semicircles are drawn as shown in the figure. The area of the shaded portion, in square cm, is

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  3. Question 3

    Number System. Asked once: CDS 1 2019

    14
    Consider the following statements : 1. Unit digit in 1717417^{174} is 7. 2. Difference of the squares of any two odd numbers is always divisible by 8. 3. Adding 1 to the product of two consecutive odd numbers makes it a perfect square. Which of the above statements are correct ?

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  4. Question 4

    Triangles. Asked once: CDS 2 2017

    78
    In a triangle PQR, X is a point on PR and Y is a point on QR such that PR = 10 cm, RX = 4 cm, YR = 2 cm, QR = 5 cm. Which one of the following is correct ?

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  5. Question 5

    Trigonometric Ratios and Identities. Asked once: CDS 1 2017

    63
    What is the value of θ\theta which satisfies the equation cos⁡θ+tan⁡θ=1\cos \theta + \tan \theta = 1 ?

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