PYQ Vault
EbooksTutor

Day 284: CDS Maths

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

  1. Question 1 (case study, 10 parts)

    Algebraic Identities and Simplification. Asked once: CDS 2 2023

    Consider the following for the next ten (10) items that follow :
    91
    Question : Is m>nm > n if m, n are real numbers ? Statement-I : m=(1−p)(p2+p+1)m = (1 - p)(p^2 + p + 1) and n=(p+1)(p2−p+1)n = (p + 1)(p^2 - p + 1) Statement-II : m=pnm = pn

    Tap an option to check your answer.

    92
    Question : What is the other root of the quadratic equation with real coefficients if one of the roots is −4−102\frac{-4 - \sqrt{10}}{2} ? Statement-I : The product of the roots is −32(3+10)-\frac{3}{2}(3 + \sqrt{10}). Statement-II : The sum of roots of quadratic equation is −1-1.

    Tap an option to check your answer.

    93
    Question : What is the 3-digit number which is divisible by 10 ? Statement-I : If the digits in hundred's place and ten's place of the number are interchanged, the resulting number is diminished by 180. Statement-II : If the digit in hundred's place is halved and digit in ten's place and unit place of the number are interchanged, the resulting number is diminished by 336.

    Tap an option to check your answer.

    94
    Question : Are x, y, z equal, where x, y, z are real numbers ? Statement-I : x2+y2+z2−xy−yz−zx=0x^2 + y^2 + z^2 - xy - yz - zx = 0 Statement-II : x3+y3+z3−3xyz=0x^3 + y^3 + z^3 - 3xyz = 0

    Tap an option to check your answer.

    95
    Question : What is the ratio x:y:zx : y : z equal to if x,y,z≠0x, y, z \neq 0 ? Statement-I : x+zy=zx\frac{x + z}{y} = \frac{z}{x} Statement-II : z−yx=xz\frac{z - y}{x} = \frac{x}{z}

    Tap an option to check your answer.

    96
    Question : What is the sum of two natural numbers ? Statement-I : LCM of the two numbers is 144. Statement-II : One of the numbers is 72.

    Tap an option to check your answer.

    97
    Question : Is average of the largest and the smallest of 4 given numbers greater than the average of the 4 numbers ? Statement-I : The difference between the largest and the second largest numbers is less than the difference between the second smallest and the smallest of the numbers. Statement-II : The difference between the largest and the smallest numbers is greater than the difference between the second largest and the second smallest of the numbers.

    Tap an option to check your answer.

    98
    Question : Is (a−b+c)>(a+b−c)(a - b + c) > (a + b - c), where a, b and c are real numbers ? Statement-I : b is negative. Statement-II : c is negative.

    Tap an option to check your answer.

    99
    Question : What is the cost of 15 pens, 21 pencils and 18 note books ? Statement-I : The cost of 7 pens, 6 pencils and 5 note books is Rs. 200. Statement-II : The cost of 3 pens, 8 pencils and 7 note books is Rs. 210.

    Tap an option to check your answer.

    100
    Question : What is the area of the triangle inscribed in a semi-circle with the diameter as the base ? Statement-I : The diameter of semi-circle is 20 cm. Statement-II : Two shorter sides of the triangle are 12 cm and 16 cm.

    Tap an option to check your answer.

  2. Question 2

    Circles. Asked once: CDS 2 2018

    88
    If a point P moves such that the sum of the squares of its distances from two fixed points A and B is a constant, then the locus of the point P is

    Tap an option to check your answer.

  3. Question 3

    Data Interpretation. Asked once: CDS 2 2017

    94
    The pie diagrams on the monthly expenditure of two families A and B are drawn with radii of two circles taken in the ratio 16:916 : 9 to compare their expenditures. Which one of the following is the appropriate data used for the above mentioned pie diagrams ?

    Tap an option to check your answer.

  4. Question 4

    Heights and Distances. Asked once: CDS 2 2017

    53
    Let AB represent a building of height hh metre with A being its top, B being its bottom. Let A′B′A'B' represent a tower of height (h+x)(h + x) metre (x>0)(x > 0) with A′A' being its top and B′B' being its bottom. Let BB′=dBB' = d metre. Let the angle of elevation of A′A' as seen from A be 45∘45^\circ. Consider the following statements : Statement I : h+x>dh + x > d Statement II : The angle of depression of B as seen from A′A' is less than 45∘45^\circ. Which one of the following is correct in respect of the above statements ?

    Tap an option to check your answer.

  5. Question 5

    Linear Equations. Asked once: CDS 2 2018

    36
    X bought 4 bottles of lemon juice and Y bought one bottle of orange juice. Orange juice per bottle costs twice the cost of lemon juice per bottle. Z bought nothing but contributed Rs. 50 for his share of the drink which they mixed together and shared the cost equally. If Z's Rs. 50 is covered from his share, then what is the cost of one bottle of orange juice ?

    Tap an option to check your answer.