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IPMAT Rohtak Mathematics — practice by topic

Browse 175 questions across 41 Mathematics topics. Choose what you want to revise, then open a question to check its answer and worked solution.

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Mathematics topics

Binomial Theorem (88)Sequences and Series (71)Geometry (63)Probability & Statistics (63)Sequences (63)Permutations and Combinations (54)Sequences and Series Gp (52)Correlation and Regression (46)Linear Programming (46)Mean (46)Median (46)Permcomb (46)Vectors & 3D Geometry (43)Algebra (37)Logarithms (37)Number Theory (37)Quadratic Equations (37)Class11 Sets Basics (35)Sets Basics (35)Probability (26)Probability Density Function (26)Probability Distribution (26)Application of Integrals (20)Calculus (20)Class11 Sets Operations (20)Class12 Functions Basics (20)Class12 Relations Basics (20)Conic Sections (20)Even/Odd Functions (20)Integral Calculus (20)Limits and Continuity (20)Matrices and Determinants (20)Mensuration (20)Relations and Functions (20)Sets, Relations and Functions (20)Statistics (20)Trigonometry (20)Cartesian Product Relations (16)Straight Lines (14)Surface Areas and Volumes (12)Three Dimensional Geometry (12)

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The set A = {x : x is a natural number, 1 < x < 2} isRead the answer and worked solution →Which of the following sets is INFINITE?Read the answer and worked solution →Writing the set {x : x is an integer and −3 ≤ x < 7} in roster form givesRead the answer and worked solution →The number of distinct elements of the set A formed by the letters of the word 'LOYAL' isRead the answer and worked solution →

Worked practice questions

The set A = {x : x is a natural number, 1 < x < 2} is

  1. A finite set with one element
  2. An infinite set
  3. The empty set
  4. Equal to {1, 2}
Show answer and solution

Correct answer: C. The empty set

There is no natural number strictly between 1 and 2, so A is empty (denoted φ or { }).

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Which of the following sets is INFINITE?

  1. The set of months of a year
  2. {1, 2, 3, …, 99, 100}
  3. The set of positive integers greater than 100
  4. The set of prime numbers less than 99
Show answer and solution

Correct answer: C. The set of positive integers greater than 100

There is no upper bound on the positive integers greater than 100, so it is infinite. The other three each contain a finite, definite count of elements.

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Writing the set {x : x is an integer and −3 ≤ x < 7} in roster form gives

  1. {−2, −1, 0, 1, 2, 3, 4, 5, 6}
  2. {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6, 7, 8}
  3. {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6}
  4. {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6, 7}
Show answer and solution

Correct answer: C. {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6}

The inequality includes −3 (≤) and excludes 7 (strict <), giving the integers −3, −2, −1, 0, 1, 2, 3, 4, 5, 6.

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