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Day 247: CDS Maths

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

  1. Question 1

    Surds, Indices and Simplification. Asked once: CDS 2 2023

    77
    If x=67−67−67−67−xx = \cfrac{6}{7 - \cfrac{6}{7 - \cfrac{6}{7 - \cfrac{6}{7 - x}}}}; x>1x > 1, then what is the value of x2−3x+2x^2 - 3x + 2 equal to ?

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  2. Question 2

    Time and Work. Asked once: CDS 1 2018

    47
    A water tank has been fitted with two taps P and Q and a drain pipe R. Taps P and Q fill at the rate of 12 litres per minute and 10 litres per minute respectively. Consider the following statements S1, S2 and S3: S1 : Pipe R drains out at the rate of 6 litres per minute. S2 : If both the taps and the drain pipe are opened simultaneously, then the tank is filled in 5 hours 45 minutes. S3 : Pipe R drains out (fully) the filled tank in 15 hours 20 minutes. To know what is the capacity of the tank, which one of the following is correct?

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  3. Question 3

    Time, Speed and Distance. Asked once: CDS 2 2024

    90
    How many times does the minute hand of a clock coincide with the second hand between 2.01 pm and 4.01 pm on the same day ?

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  4. Question 4

    Triangles. Asked once: CDS 1 2026

    50
    ABC is an equilateral triangle. Let PQRS be a square inscribed in it such that P is on AB and Q is on AC. Which of the following is/are correct ? I. AP:PB=4:3AP : PB = 4 : 3 II. 3AB=(2+3)PQ\sqrt{3}AB = (2 + \sqrt{3})PQ Select the answer using the code given below :

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  5. Question 5

    Trigonometric Ratios and Identities. Asked once: CDS 2 2025

    31
    If 2+2+2+2+…=cosec⁡θ\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\ldots}}}}=\operatorname{cosec}\theta, then what is sin⁡θ\sin\theta equal to?

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