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Day 342: CDS Maths

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

  1. Question 1

    Number System. Asked once: CDS 1 2019

    80
    Consider the following statements : 1. 75\sqrt{75} is a rational number. 2. There exists at least a positive integer xx such that −4x5<−78-\frac{4x}{5} < -\frac{7}{8}. 3. x−2x<1\frac{x-2}{x} < 1 for all real values of xx. 4. 4.232323......4.232323...... can be expressed in the form pq\frac{p}{q} where pp and qq are integers. Which of the above statements are correct ?

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  2. Question 2

    Triangles. Asked once: CDS 2 2017

    67
    If PL, QM and RN are the altitudes of triangle PQR whose orthocentre is O, then Q is the orthocentre of the triangle

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  3. Question 3

    Mensuration 2D. Asked once: CDS 1 2018

    82
    If the length of a side of a square is increased by 8 cm, its area increases by 120 square cm. What is the length of a side of the square ?

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  4. Question 4

    Number System. Asked once: CDS 1 2019

    72
    Consider the following statements : 1. If pp is relatively prime to each of qq and rr, then pp is relatively prime to the product qrqr. 2. If pp divides the product qrqr and if pp divides qq, then pp must divide rr. Which of the above statements is/are correct ?

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  5. Question 5

    Triangles. Asked once: CDS 1 2017

    97
    In the figure given below, ABC is a triangle with AB = BC and D is an interior point of the triangle ABC such that ∠DAC=∠DCA\angle DAC = \angle DCA. Consider the following statements : 1. Triangle ADC is an isosceles triangle. 2. D is the centroid of the triangle ABC. 3. Triangle ABD is congruent to the triangle CBD. Which of the above statements are correct ?

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