PYQ Vault

Day 72: CDS Maths

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

  1. Question 1

    Mensuration 3D. This type asked 2 times: CDS 1 2017, CDS 1 2024. This one: CDS 1 2024 See all 2 of this type

    56
    The length, breadth and height of a cuboid are increased by 10%, 20% and 50% respectively. What is the percentage increase in volume of the cuboid ?

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  2. Question 2 (case study, 10 parts)

    Number System. This type asked 2 times: CDS 1 2023, CDS 1 2024. This one: CDS 1 2024 See all 2 of this type

    Consider the following for the next ten (10) items that follow : Each item contains a Question followed by two Statements. Answer each item using the following instructions :
    61
    Let a, b, c and d be positive integers. Question : Which one of a, b, c, d is closest to the product abcd ? Statement-I : a > b > c Statement-II : c is not the smallest.

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    62
    Let mn = k, where m and n are prime numbers and k is an even number. Question : What is the value of mn−n+1mn - n + 1 ? Statement-I : m > n Statement-II : One of the numbers is 2.

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    63
    Question : If p is a positive integer, then what is the remainder when pnp^n is divided by p + 1 ? Statement-I : n is even. Statement-II : p is even.

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    64
    Question : Is xy positive ? Statement-I : x=−0.196833x = \sqrt[3]{-0.19683} Statement-II : y=x3y = \sqrt[3]{x}

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    65
    Let a, b and c be the sides of a triangle ABC. Question : Is the triangle equilateral ? Statement-I : a2+b2+c2=(ab+bc+ca)a^2 + b^2 + c^2 = (ab + bc + ca) Statement-II : 3a2+3b2+4c2=2ab+4bc+4ca3a^2 + 3b^2 + 4c^2 = 2ab + 4bc + 4ca

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    66
    Area of a rectangle with length x and breadth y is P and area of a parallelogram (which is strictly not a rectangle) with adjacent sides of length x and y is Q. Question : Is P > Q ? Statement-I : x : y = 2 : 1 Statement-II : The angle between the two adjacent sides of the parallelogram is 60∘60^\circ.

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    67
    A circle touches all the four sides AB, BC, CD, DA of a quadrilateral ABCD. Question : What is the perimeter of the quadrilateral ? Statement-I : AB + DC = 10 cm Statement-II : AD + BC = 10 cm

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    68
    Question : What is the ratio of the lengths of diagonals of a rhombus ? Statement-I : One diagonal of the rhombus is equal to its side. Statement-II : The longer diagonal of the rhombus is equal to 3\sqrt{3} times its side.

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    69
    The chord of a circle of radius R touches at a point on the circumference of a concentric circle of radius r. The length of the chord is 24 units. Question : What are the values of r and R ? Statement-I : r is an integer. Statement-II : R is an integer.

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    70
    P, Q, R, S are the mid-points of sides AB, BC, CD, DA respectively of a quadrilateral ABCD. Question : What is the difference in the area of the quadrilateral ABCD and the area of the quadrilateral PQRS ? Statement-I : Area of the quadrilateral ABCD is 100 square unit. Statement-II : Area of the quadrilateral PQRS is 50 square unit.

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  3. Question 3

    Polynomials. This type asked 2 times: CDS 2 2018, CDS 1 2024. This one: CDS 1 2024 See all 2 of this type

    8
    If 2 is a zero of the polynomial p(x)=x3+3x2−6x−ap(x) = x^3 + 3x^2 - 6x - a, then what is the sum of the squares of the other zeros of the polynomial ?

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  4. Question 4

    Quadratic Equations. This type asked 2 times: CDS 1 2022, CDS 1 2024. This one: CDS 1 2024 See all 2 of this type

    7
    If the sum and product of the roots of a quadratic equation are 2 and −100-100 respectively, then which one of the following is correct ?

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  5. Question 5

    Surds, Indices and Simplification. This type asked 2 times: CDS 2 2016, CDS 1 2024. This one: CDS 1 2024 See all 2 of this type

    30
    If x=12+34+56+78+910x = \cfrac{1}{2 + \cfrac{3}{4 + \cfrac{5}{6 + \cfrac{7}{8 + \cfrac{9}{10}}}}}, then which one of the following is correct ?

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