PYQ Vault

Day 136: CDS Maths

5 questions (14 parts). Try each one first, then open its answer.

  1. Question 1

    Time and Work. Asked once: CDS 2 2023 (same type asked 2 times) See all 2 of this type

    4
    If A and B can finish a work in 10 days, B and C can finish the same work in 12 days, C and A can finish the same work in 15 days; then in how many days can A, B and C together finish half of the work ?

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  2. Question 2

    Triangles. Asked once: CDS 1 2023 (same type asked 2 times) See all 2 of this type

    29
    If a, b and c are the sides of a triangle ABC, then a+b−c\sqrt{a} + \sqrt{b} - \sqrt{c} is always :

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  3. Question 3

    Mensuration 3D. Asked once: CDS 1 2017 (same type asked 2 times) See all 2 of this type

    82
    If the radius of a right circular cone is increased by p% without increasing its height, then what is the percentage increase in the volume of the cone ?

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  4. Question 4 (case study, 10 parts)

    Number System. Asked once: CDS 1 2023 (same type asked 2 times) See all 2 of this type

    For the next ten (10) items that follow : Each item contains a Question followed by two Statements. Answer each item using the following instructions :
    71
    A number 277XY5 (where X, Y are digits) is divisible by 25. Question : What is the value of X ? Statement I : The given number is divisible by 9. Statement II : X>5X > 5.

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    72
    Question : What are the unique values of a, b and c if 2 is a root of the equation ax2+bx+c=0ax^2 + bx + c = 0 ? Statement I : Ratio of c to a is 1. Statement II : Ratio of b to a is (−52)\left(-\frac{5}{2}\right).

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    73
    Question : Is m>nm > n, where m, n are non-zero numbers ? Statement I : mn>1\frac{m}{n} > 1. Statement II : m>2nm > 2n.

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    74
    Question : Can a circle be drawn through the points A, B and C ? Statement I : AB = 5 cm, BC = 5 cm, CA = 6 cm. Statement II : AB = 3 cm, BC = 4 cm, CA = 7 cm.

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    75
    x and y are consecutive odd integers. Question : Can the value of (x+y)(x + y) be determined uniquely ? Statement I : (x+y)4=256(x + y)^4 = 256. Statement II : (x+y)3<16(x + y)^3 < 16.

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    76
    Question : Is p2+q2+qp^2 + q^2 + q odd, where p, q are positive integers ? Statement I : 2p+q2p + q is odd. Statement II : q−2pq - 2p is odd.

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    77
    Question : What is the area of the circle C ? Statement I : An arc of length 7 cm subtends an angle 30∘30^\circ at the centre of C. Statement II : A chord of length 10 cm subtends an angle 90∘90^\circ at the centre of C.

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    78
    Question : Is triangle △\triangle right angled ? Statement I : The length of the line segment joining the mid-points of two sides of △\triangle is half of the third side of △\triangle. Statement II : The angles of △\triangle are in the ratio 1 : 2 : 3.

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    79
    The lengths of two longer sides of the triangle △\triangle are 25 cm and 24 cm. Question : What is the length of the shortest side ? Statement I : The angles of △\triangle are in the ratio 1 : 2 : 3. Statement II : The length of the perpendicular drawn on the longest side of △\triangle from its opposite vertex is 6.72 cm.

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    80
    A chord PQ of the circle C divides it into two segments such that 3 times the area of the major segment is 4 times the area of the minor segment. Question : What is the radius of C ? Statement I : Area of the minor segment is 66 square cm. Statement II : Area of the major segment is 88 square cm.

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  5. Question 5

    Polynomials. Asked once: CDS 2 2018 (same type asked 2 times) See all 2 of this type

    50
    If α\alpha, β\beta and γ\gamma are the zeros of the polynomial f(x)=ax3+bx2+cx+df(x) = ax^3 + bx^2 + cx + d, then α2+β2+γ2\alpha^2 + \beta^2 + \gamma^2 is equal to

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