PYQ Vault

Day 10: CDS Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Trigonometric Ratios and Identities. This type asked 5 times: CDS 2 2016, CDS 1 2018, CDS 2 2018, CDS 1 2019, CDS 2 2026. This one: CDS 2 2026 See all 5 of this type

    38
    If cos⁡2x+cos⁡4x=1\cos^2 x + \cos^4 x = 1, where 0<x<π20 < x < \frac{\pi}{2}, then what is (sin⁡2x+sin⁡3x)+(sin⁡3x+sin⁡4x)(\sin^2 x + \sin^3 x) + (\sin^3 x + \sin^4 x) equal to ?

    Tap an option to check your answer.

  2. Question 2

    Trigonometric Ratios and Identities. This type asked 5 times: CDS 2 2020, CDS 1 2021, CDS 1 2023, CDS 1 2024, CDS 2 2026. This one: CDS 2 2026 See all 5 of this type

    47
    What is the ratio of the greatest value of sin⁡2x+2\sin^2 x + 2 (where 0≤x≤π20 \le x \le \frac{\pi}{2}) to its least value ?

    Tap an option to check your answer.

  3. Question 3 (case study, 2 parts)

    Algebraic Identities and Simplification. This type asked 5 times: CDS 1 2018, CDS 1 2020, CDS 1 2021, CDS 2 2025, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    For the next two (02) items that follow : 16(x4+1x4)−257=016\left(x^4 + \frac{1}{x^4}\right) - 257 = 0
    83
    What is (x2+1x2)\left(x^2 + \frac{1}{x^2}\right) equal to ?

    Tap an option to check your answer.

    84
    What is (x3+1x3)\left(x^3 + \frac{1}{x^3}\right) equal to ?

    Tap an option to check your answer.

  4. Question 4

    Circles. This type asked 5 times: CDS 2 2016, CDS 1 2020, CDS 2 2021, CDS 2 2022, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    75
    A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : Two circles with radii p, q (p>q)(p > q) in cm touch externally, where p, q are natural numbers and each greater than 1. What is the value of (p−q)(p - q) ? Statement-I : The sum of their areas is 130π130\pi cm2\text{cm}^2 Statement-II : The distance between the centres of the two circles is 14 cm Which one of the following is correct in respect of the above Question and the Statements ?

    Tap an option to check your answer.

  5. Question 5

    Circles. This type asked 5 times: CDS 1 2017, CDS 2 2017, CDS 2 2019, CDS 2 2023, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    65
    Let O be the centre of a circle. Let the chords AB = 10 cm and CD = 24 cm be two parallel chords of the circle. The two chords are on opposite side of the centre and the distance between them is 17 cm. Let P be the midpoint of AB and Q be the midpoint of CD. Further, the points O and A, the points O and C, the points A and C are joined. Which of the statements given below is/are correct ? I. Area of triangle OAP is equal to area of triangle OCQ. II. Area of triangle OAC is equal to 102102 cm2\text{cm}^2. Select the answer using the code given below :

    Tap an option to check your answer.