PYQ Vault

Day 277: CDS Maths

5 questions (8 parts). Try each one first, then open its answer.

  1. Question 1

    Heights and Distances. Asked once: CDS 1 2018

    59
    From a height of h units, a man observes the angle of elevation as α\alpha and angle of depression as β\beta of the top and the bottom respectively of a tower of height H (> 4h). To what further height should he climb so that the values of angle of elevation and angle of depression get interchanged for the top and bottom of the tower ?

    Tap an option to check your answer.

  2. Question 2

    Linear Equations. Asked once: CDS 2 2020

    33
    If (p+2)(2q−1)=2pq−10(p + 2)(2q - 1) = 2pq - 10 and (p−2)(2q−1)=2pq−10(p - 2)(2q - 1) = 2pq - 10, then what is pqpq equal to ?

    Tap an option to check your answer.

  3. Question 3

    Logarithms. Asked once: CDS 1 2018

    36
    For 0<m<10 < m < 1, which one of the following is correct?

    Tap an option to check your answer.

  4. Question 4 (case study, 2 parts)

    Mensuration 2D. Asked once: CDS 1 2024

    Consider the following for the next two (02) items that follow : Consider a circle of area 9π9\pi square unit and an equilateral triangle ABC as shown in the figure given below.
    94
    What is the length of the side of the triangle ABC ?

    Tap an option to check your answer.

    95
    What is the area of the shaded region ?

    Tap an option to check your answer.

  5. Question 5 (case study, 3 parts)

    Mensuration 3D. Asked once: CDS 2 2022

    Consider the following for the next three (03) items that follow : A conical vessel of radius 12 cm and height 16 cm is filled with water. A sphere is lowered into water and its size is such that it touches the sides of the vessel and it is just immersed.
    71
    What is the radius of the sphere ?

    Tap an option to check your answer.

    72
    How much water will remain in the vessel after the overflow ?

    Tap an option to check your answer.

    73
    What is the ratio of lateral surface area of the vessel to the surface area of the sphere ?

    Tap an option to check your answer.