Friday, November 22, 2024

MCQ Mathematics Chapter 14: PROBABILITY, HS 1st year

 

MCQ 1: Sample Space and Events

If a coin is tossed twice, what is the sample space (S) for this experiment?

  1. {HH,HT,TH,TT}\{HH, HT, TH, TT\}
  2. {H,T}\{H, T\}
  3. {H,T,HH,TT}\{H, T, HH, TT\}
  4. {HHT,TTT}\{HHT, TTT\}

Answer: 1. {HH,HT,TH,TT}

MCQ 2: Types of Events

In the experiment of rolling a die, which event is considered a simple event?

  1. Getting an odd number
  2. Rolling a prime number
  3. Rolling a 3
  4. Rolling a number greater than 2

Answer: 3. Rolling a 3

MCQ 3: Complementary Events

The complementary event of rolling an even number on a die is:

  1. Rolling an odd number
  2. Rolling a number greater than 3
  3. Rolling a prime number
  4. Rolling a multiple of 2

Answer: 1. Rolling an odd number

MCQ 4: Probability Axioms

According to the axiomatic approach to probability, the probability of the sample space (S) is:

  1. 0
  2. 0.5
  3. 1
  4. Undefined

Answer: 3. 1

MCQ 5: Mutually Exclusive Events

Two events A and B are said to be mutually exclusive if:

  1. A∩B=ϕA \cap B = \phi
  2. A∩B=SA \cap B = S
  3. A∪B=SA \cup B = S
  4. A−B=ϕA - B = \phi

Answer: 1. A∩B=ϕA \cap B = \phi

MCQ 6: Probability Calculation

A die is rolled. What is the probability of getting a prime number?

  1. 12\frac{1}{2}
  2. 23\frac{2}{3}
  3. 13\frac{1}{3}
  4. 16\frac{1}{6}

Answer: 1. 12\frac{1}{2}
(Prime numbers on a die: 2, 3, 5; Total outcomes: 6; Probability = 36=12\frac{3}{6} = \frac{1}{2}.)

MCQ 7: Exhaustive Events

In the experiment of rolling a die, the events: A: 'number less than 4', B: 'number between 3 and 5', and C: 'number greater than 4' are:

  1. Mutually exclusive but not exhaustive
  2. Mutually exclusive and exhaustive
  3. Not mutually exclusive but exhaustive
  4. Neither mutually exclusive nor exhaustive

Answer: 2. Mutually exclusive and exhaustive

MCQ 8: Impossible Events

Which of the following represents an impossible event when rolling a die?

  1. Rolling a number less than 7
  2. Rolling a number greater than 6
  3. Rolling a number equal to 4
  4. Rolling an odd number

Answer: 2. Rolling a number greater than 6

MCQ 9: Compound Events

Which of the following is a compound event in the experiment of tossing three coins?

  1. At least one head appears
  2. Exactly one head appears
  3. At most one head appears
  4. All of the above

Answer: 4. All of the above

MCQ 10: Mutually Exclusive and Exhaustive Events

In an experiment where a die is rolled, which of the following sets of events is both mutually exclusive and exhaustive?

  1. A: 'odd number appears', B: 'even number appears'
  2. A: 'number greater than 3', B: 'number less than 4'
  3. A: 'prime number appears', B: 'number less than 5'
  4. None of the above

Answer: 1. A: 'odd number appears', B: 'even number appears'

MCQ 11: Event Algebra

If AA and BB are events, the set A∪BA \cup B represents:

  1. Elements that are in AA but not in BB
  2. Elements that are in BB but not in AA
  3. Elements that are in either AA, BB, or both
  4. Elements that are in both AA and BB

Answer: 3. Elements that are in either AA, BB, or both

MCQ 12: Probability of Event 'Not A'

If P(A)=25P(A) = \frac{2}{5}, what is P(not A)P(\text{not A})?

  1. 35\frac{3}{5}
  2. 25\frac{2}{5}
  3. 52\frac{5}{2}
  4. 12\frac{1}{2}

Answer: 1. 35\frac{3}{5}
(P(not A)=1−P(A)P(\text{not A}) = 1 - P(A))

MCQ 13: Probability Calculation

A bag contains 4 red discs, 3 blue discs, and 2 yellow discs. A disc is chosen at random. What is the probability of selecting a blue disc?

  1. 19\frac{1}{9}
  2. 13\frac{1}{3}
  3. 39\frac{3}{9}
  4. 12\frac{1}{2}

Answer: 3. 39=13\frac{3}{9} = \frac{1}{3}

MCQ 14: Valid Probability Assignments

Which of the following is NOT a valid probability assignment for outcomes in a sample space SS?

  1. 0.3,0.3,0.40.3, 0.3, 0.4
  2. 0.1,0.1,0.2,0.60.1, 0.1, 0.2, 0.6
  3. −0.1,0.5,0.6-0.1, 0.5, 0.6
  4. 0.25,0.25,0.25,0.250.25, 0.25, 0.25, 0.25

Answer: 3. −0.1,0.5,0.6-0.1, 0.5, 0.6
(Probabilities cannot be negative.)

MCQ 15: Events 'A and B'

If P(A)=0.5P(A) = 0.5, P(B)=0.4P(B) = 0.4, and P(A∩B)=0.2P(A \cap B) = 0.2, what is P(A∪B)P(A \cup B)?

  1. 0.70.7
  2. 0.90.9
  3. 0.60.6
  4. 1.01.0

Answer: 2. 0.90.9
(P(A∪B)=P(A)+P(B)−P(A∩B)=0.5+0.4−0.2=0.9P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.5 + 0.4 - 0.2 = 0.9)

MCQ 16: Exhaustive Events

Consider an experiment of rolling a die. Which of the following events are exhaustive?

  1. A: 'number less than 4', B: 'number greater than 4'
  2. A: 'even number appears', B: 'odd number appears'
  3. A: 'prime number appears', B: 'number less than 3'
  4. None of the above

Answer: 2. A: 'even number appears', B: 'odd number appears'

MCQ 17: Probability of Drawing Cards

What is the probability of drawing a black card from a standard deck of 52 cards?

  1. 1352\frac{13}{52}
  2. 2652\frac{26}{52}
  3. 14\frac{1}{4}
  4. 34\frac{3}{4}

Answer: 2. 2652=12\frac{26}{52} = \frac{1}{2}

MCQ 18: Tossing Coins

Three coins are tossed. What is the probability of getting exactly two heads?

  1. 14\frac{1}{4}
  2. 38\frac{3}{8}
  3. 12\frac{1}{2}
  4. 18\frac{1}{8}

Answer: 2. 38\frac{3}{8}
(Possible outcomes: HHT, HTH, THH out of 8 total outcomes.)

MCQ 19: Equally Likely Outcomes

If a sample space SS contains nn equally likely outcomes, the probability of any single outcome is:

  1. n1\frac{n}{1}
  2. n2n^2
  3. 1n\frac{1}{n}
  4. n!n!

Answer: 3. 1n\frac{1}{n}

MCQ 20: Probability of ‘A or B’

If P(A)=0.4P(A) = 0.4, P(B)=0.3P(B) = 0.3, and P(A∩B)=0.1P(A \cap B) = 0.1, then P(A∪B)P(A \cup B) is:

  1. 0.60.6
  2. 0.70.7
  3. 0.50.5
  4. 0.80.8

Answer: 4. 0.80.8
(P(A∪B)=P(A)+P(B)−P(A∩B)=0.4+0.3−0.1=0.8P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.4 + 0.3 - 0.1 = 0.8.)

MCQ 21: Complementary Events

If P(A)=0.7P(A) = 0.7, what is P(not A)P(\text{not A})?

  1. 0.30.3
  2. 0.50.5
  3. 1.71.7
  4. 0.20.2

Answer: 1. 0.30.3
(P(not A)=1−P(A)=1−0.7=0.3P(\text{not A}) = 1 - P(A) = 1 - 0.7 = 0.3.)

MCQ 22: Impossible Event

Which of the following probabilities corresponds to an impossible event?

  1. 00
  2. 0.50.5
  3. 11
  4. 1.51.5

Answer: 1. 00

MCQ 23: Mutually Exclusive Events

Two events are mutually exclusive if:

  1. They always occur together
  2. They cannot occur at the same time
  3. One event is the subset of the other
  4. They have at least one common element

Answer: 2. They cannot occur at the same time

MCQ 24: Tossing Three Coins

Three coins are tossed. What is the probability of getting at least one tail?

  1. 18\frac{1}{8}
  2. 34\frac{3}{4}
  3. 78\frac{7}{8}
  4. 58\frac{5}{8}

Answer: 3. 78\frac{7}{8}
(P(at least one tail)=1−P(no tails)=1−18=78P(\text{at least one tail}) = 1 - P(\text{no tails}) = 1 - \frac{1}{8} = \frac{7}{8}.)

MCQ 25: Rolling a Die

When a die is rolled, what is the probability of getting a number greater than 4?

  1. 23\frac{2}{3}
  2. 13\frac{1}{3}
  3. 16\frac{1}{6}
  4. 12\frac{1}{2}

Answer: 2. 13\frac{1}{3}
(Numbers greater than 4: 5, 6; Total outcomes: 6; Probability = 26=13\frac{2}{6} = \frac{1}{3}.)

MCQ 26: Probability of Compound Events

In an experiment of rolling two dice, what is the probability of getting a sum of 7?

  1. 16\frac{1}{6}
  2. 136\frac{1}{36}
  3. 536\frac{5}{36}
  4. 636\frac{6}{36}

Answer: 4. 636=16\frac{6}{36} = \frac{1}{6}
(Sum of 7 can occur as (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)(1,6), (2,5), (3,4), (4,3), (5,2), (6,1): 6 outcomes out of 36.)

MCQ 27: Deck of Cards

What is the probability of drawing an ace from a standard deck of 52 cards?

  1. 113\frac{1}{13}
  2. 14\frac{1}{4}
  3. 152\frac{1}{52}
  4. 413\frac{4}{13}

Answer: 1. 113\frac{1}{13}

MCQ 28: Red and Blue Discs

A bag contains 6 red discs and 4 blue discs. If one disc is drawn at random, what is the probability that it is blue?

  1. 14\frac{1}{4}
  2. 25\frac{2}{5}
  3. 35\frac{3}{5}
  4. 46\frac{4}{6}

Answer: 2. 25\frac{2}{5}
(Probability = number of blue discstotal discs=410=25\frac{\text{number of blue discs}}{\text{total discs}} = \frac{4}{10} = \frac{2}{5}.)

MCQ 29: Probability of A and B

If P(A)=0.6P(A) = 0.6, P(B)=0.5P(B) = 0.5, and P(A∪B)=0.8P(A \cup B) = 0.8, then P(A∩B)P(A \cap B) is:

  1. 0.30.3
  2. 0.10.1
  3. 0.50.5
  4. 0.80.8

Answer: 2. 0.10.1
(P(A∩B)=P(A)+P(B)−P(A∪B)=0.6+0.5−0.8=0.1P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.6 + 0.5 - 0.8 = 0.1.)

MCQ 30: Drawing Cards

What is the probability of drawing a red king from a standard deck of 52 cards?

  1. 152\frac{1}{52}
  2. 126\frac{1}{26}
  3. 113\frac{1}{13}
  4. 252\frac{2}{52}

Answer: 2. 126\frac{1}{26}
(There are 2 red kings in a deck of 52 cards; Probability = 252=126\frac{2}{52} = \frac{1}{26}.)

MCQ 31: Event ‘A or B’

If P(A)=0.5P(A) = 0.5, P(B)=0.6P(B) = 0.6, and P(A∩B)=0.2P(A \cap B) = 0.2, what is P(A∪B)P(A \cup B)?

  1. 0.80.8
  2. 0.90.9
  3. 1.01.0
  4. 0.70.7

Answer: 2. 0.90.9
(P(A∪B)=P(A)+P(B)−P(A∩B)=0.5+0.6−0.2=0.9P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.5 + 0.6 - 0.2 = 0.9.)

MCQ 32: Probability of 'At Least One'

Two dice are rolled. What is the probability that at least one die shows a 6?

  1. 136\frac{1}{36}
  2. 1136\frac{11}{36}
  3. 16\frac{1}{6}
  4. 1136\frac{11}{36}

Answer: 4. 1136\frac{11}{36}
(The probability of at least one 6 = 1−P(no 6s)=1−2536=11361 - P(\text{no 6s}) = 1 - \frac{25}{36} = \frac{11}{36}.)

MCQ 33: Exhaustive Events

In the experiment of flipping three coins, which of the following sets of events is exhaustive?

  1. A: 'two heads appear', B: 'no tails appear'
  2. A: 'at least one tail appears', B: 'no heads appear'
  3. A: 'at least one head appears', B: 'at most two tails appear'
  4. A: 'no heads appear', B: 'at least two heads appear', C: 'exactly one head appears'

Answer: 4. A: 'no heads appear', B: 'at least two heads appear', C: 'exactly one head appears'

MCQ 34: Coin Toss

A fair coin is tossed three times. What is the probability of getting no heads?

  1. 12\frac{1}{2}
  2. 18\frac{1}{8}
  3. 38\frac{3}{8}
  4. 14\frac{1}{4}

Answer: 2. 18\frac{1}{8}
(Only one outcome, TTTTTT, has no heads; P=18P = \frac{1}{8}.)

MCQ 35: Mutually Exclusive and Exhaustive

In an experiment of rolling a die, which of the following represents mutually exclusive and exhaustive events?

  1. A: 'even number appears', B: 'prime number appears'
  2. A: 'even number appears', B: 'odd number appears'
  3. A: 'number less than 4', B: 'number greater than 4'
  4. None of these

Answer: 2. A: 'even number appears', B: 'odd number appears'

MCQ 36: Drawing Cards

What is the probability of drawing a face card from a deck of 52 cards?

  1. 313\frac{3}{13}
  2. 14\frac{1}{4}
  3. 413\frac{4}{13}
  4. 913\frac{9}{13}

Answer: 1. 313\frac{3}{13}
(12 face cards in total; Probability = 1252=313\frac{12}{52} = \frac{3}{13}.)

MCQ 37: Mutually Exclusive Events

If events A and B are mutually exclusive, then:

  1. P(A∩B)=0P(A \cap B) = 0
  2. P(A∪B)=1P(A \cup B) = 1
  3. P(A)+P(B)=1P(A) + P(B) = 1
  4. P(A)×P(B)=0P(A) \times P(B) = 0

Answer: 1. P(A∩B)=0P(A \cap B) = 0

MCQ 38: Probability of Compound Events

Two dice are rolled. What is the probability of getting a sum of 8?

  1. 536\frac{5}{36}
  2. 16\frac{1}{6}
  3. 736\frac{7}{36}
  4. 13\frac{1}{3}

Answer: 1. 536\frac{5}{36}
(Sum of 8: (2,6),(3,5),(4,4),(5,3),(6,2)(2,6), (3,5), (4,4), (5,3), (6,2).)

MCQ 39: Random Events

In the experiment of rolling a die twice, what is the probability of getting at least one 4?

  1. 1136\frac{11}{36}
  2. 12\frac{1}{2}
  3. 16\frac{1}{6}
  4. 1336\frac{13}{36}

Answer: 1. 1136\frac{11}{36}
(1−P(no 4s)=1−2536=11361 - P(\text{no 4s}) = 1 - \frac{25}{36} = \frac{11}{36}.)

MCQ 40: Deck of Cards

What is the probability of drawing a queen of hearts from a standard deck of 52 cards?

  1. 113\frac{1}{13}
  2. 152\frac{1}{52}
  3. 452\frac{4}{52}
  4. 213\frac{2}{13}

Answer: 2. 152\frac{1}{52}

MCQ 41: Drawing Marbles

A bag contains 5 red marbles, 7 blue marbles, and 3 green marbles. What is the probability of drawing a green marble?

  1. 15\frac{1}{5}
  2. 315\frac{3}{15}
  3. 13\frac{1}{3}
  4. 14\frac{1}{4}

Answer: 2. 315=15\frac{3}{15} = \frac{1}{5}

MCQ 42: Dice Experiment

If two dice are thrown, what is the probability of getting doubles (both dice showing the same number)?

  1. 112\frac{1}{12}
  2. 16\frac{1}{6}
  3. 13\frac{1}{3}
  4. 536\frac{5}{36}

Answer: 2. 16\frac{1}{6}
(Doubles: (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)(1,1), (2,2), (3,3), (4,4), (5,5), (6,6); Total = 6/36 = 1/6.)

MCQ 43: Complementary Events

If P(A)=0.35P(A) = 0.35, what is P(not A)P(\text{not A})?

  1. 0.550.55
  2. 0.750.75
  3. 0.650.65
  4. 0.850.85

Answer: 3. 0.650.65
(P(not A)=1−P(A)=1−0.35=0.65P(\text{not A}) = 1 - P(A) = 1 - 0.35 = 0.65.)

MCQ 44: Axioms of Probability

Which of the following statements violates the axioms of probability?

  1. P(A)=0.3P(A) = 0.3
  2. P(A)=−0.5P(A) = -0.5
  3. P(A)=1P(A) = 1
  4. P(A)=0P(A) = 0

Answer: 2. P(A)=−0.5P(A) = -0.5

MCQ 45: Rolling Dice

What is the probability of rolling a number less than 3 on a standard die?

  1. 12\frac{1}{2}
  2. 13\frac{1}{3}
  3. 16\frac{1}{6}
  4. 23\frac{2}{3}

Answer: 2. 13\frac{1}{3}
(Numbers less than 3: 1,21, 2; Probability = 26=13\frac{2}{6} = \frac{1}{3}.)


MCQs for NEET, JEE, IIT, NIT, CUET, CTET, and SSC Entrance Exams: Your Ultimate Preparation Guide

Are you preparing for competitive exams like NEET, JEE, IIT, NIT, CUET, CTET, or SSC? Multiple Choice Questions (MCQs) are a proven way to enhance your preparation strategy. These MCQs are designed to strengthen your concepts, boost problem-solving skills, and improve time management—key elements to ace any entrance exam.

Why MCQs Are Essential for Competitive Exams?

  1. Concept Clarity: MCQs cover important topics, ensuring a deep understanding of fundamental concepts.
  2. Time Management: Practicing MCQs improves speed and accuracy, essential for high-stakes exams.
  3. Exam Pattern Familiarity: MCQs simulate the real exam pattern, helping you feel confident on the big day.

Benefits of Using These MCQs for NEET, JEE, IIT, and More

  • Targeted Preparation: Specially curated MCQs focus on the specific syllabus of exams like NEET, JEE, and CUET, making your study focused and efficient.
  • Wide Subject Coverage: Includes questions from Physics, Chemistry, Mathematics, Biology, and more.
  • Boosts Competitive Edge: High-quality MCQs ensure you're ready to tackle even the trickiest questions.

Exams These MCQs Help With:

  • NEET: For aspiring medical students.
  • JEE & IIT: For engineering and technical aspirants.
  • NIT Admissions: A stepping stone to prestigious National Institutes of Technology.
  • CUET: Common University Entrance Test for undergraduate programs.
  • CTET: A mandatory test for teachers.
  • SSC: Government job aspirants preparing for SSC exams.

Pro Tips to Use MCQs Effectively:

  1. Regular Practice: Dedicate time daily to solve topic-wise MCQs.
  2. Review and Revise: Go through solutions and explanations to understand your mistakes.
  3. Mock Tests: Attempt full-length MCQ tests to build exam stamina.

Get Started Now!

Our extensive MCQ collections are tailored to help you succeed in NEET, JEE, IIT, NIT, CUET, CTET, and SSC. Start practicing today and take a step closer to your dream career. Bookmark this page and share it with fellow aspirants.

Tags:

MCQs for NEET, JEE MCQs, IIT preparation, CUET questions, CTET practice, SSC MCQs, competitive exam tips, entrance exam success.

Make your preparation smarter, not harder. Let these MCQs guide your way to success!

at No comments:

MCQ Mathematics Chapter 13: STATISTICS, HS 1st year

 

  1. MCQs on Statistics:

    1. Who defined statistics as "the science of averages and their estimates"?
      a) Karl Pearson
      b) Sir Ronald A. Fisher
      c) A.L. Bowley & A.L. Boddington
      d) Francis Galton
      Answer: c) A.L. Bowley & A.L. Boddington

    2. Which measure of central tendency is NOT commonly used to calculate the mean deviation?
      a) Mean
      b) Median
      c) Mode
      d) Range
      Answer: d) Range

    3. What is the range of scores for Batsman A in the example given in the content?
      a) 117
      b) 14
      c) 0
      d) 53
      Answer: a) 117

    4. Which of the following is NOT a measure of dispersion mentioned in the chapter?
      a) Range
      b) Quartile Deviation
      c) Mean Deviation
      d) Mean
      Answer: d) Mean

    5. For a data set, the deviation from a central tendency (mean or median) is measured using which of the following?
      a) Range
      b) Standard deviation
      c) Mode
      d) Quartile deviation
      Answer: b) Standard deviation

    6. What is the formula to calculate the mean of deviations about a central value ‘a’?
      a) M.D.(a)=Sum of deviationsNumber of observationsM.D.(a) = \frac{\text{Sum of deviations}}{\text{Number of observations}}
      b) M.D.(a)=Sum of absolute values of deviations from aNumber of observationsM.D.(a) = \frac{\text{Sum of absolute values of deviations from } a}{\text{Number of observations}}
      c) M.D.(a)=Sum of maximum and minimum values2M.D.(a) = \frac{\text{Sum of maximum and minimum values}}{2}
      d) M.D.(a)=Sum of squares of deviationsNumber of observationsM.D.(a) = \frac{\text{Sum of squares of deviations}}{\text{Number of observations}}
      Answer: b) M.D.(a)=Sum of absolute values of deviations from aNumber of observationsM.D.(a) = \frac{\text{Sum of absolute values of deviations from } a}{\text{Number of observations}}

    7. What is the median for the data set: 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21?
      a) 9
      b) 10
      c) 12
      d) 7
      Answer: a) 9

    8. What does the range of a data set indicate?
      a) Measure of central tendency
      b) Measure of variability between maximum and minimum values
      c) Measure of the mean deviation
      d) Measure of dispersion around the mean
      Answer: b) Measure of variability between maximum and minimum values

    9. In grouped data, the median is found using which key component?
      a) Mid-point of the median class
      b) Frequency of the median class
      c) Lower boundary of the median class
      d) All of the above
      Answer: d) All of the above

    10. Who is known as the Father of Modern Statistics?
      a) Karl Pearson
      b) Sir Ronald A. Fisher
      c) Francis Galton
      d) Captain John Graunt
      Answer: b) Sir Ronald A. Fisher

  2.   What does a measure of central tendency represent in a data set?
    a) The spread of the data
    b) The central value where data points cluster
    c) The maximum value of the data set
    d) The lowest value of the data set
    Answer: b) The central value where data points cluster

  3. Which measure of central tendency is most affected by extreme values?
    a) Mean
    b) Median
    c) Mode
    d) Range
    Answer: a) Mean

  4. In the calculation of mean deviation, why are absolute deviations used?
    a) To simplify the calculation
    b) To avoid negative values canceling positive ones
    c) To emphasize larger deviations
    d) None of the above
    Answer: b) To avoid negative values canceling positive ones

  5. If the number of observations is odd, how is the median calculated?
    a) Mean of the two middle observations
    b) The value of the middle observation after arranging in order
    c) The mode of the dataset
    d) The average of all observations
    Answer: b) The value of the middle observation after arranging in order

  6. Which of the following measures is used to describe the spread of data points?
    a) Mean
    b) Median
    c) Mode
    d) Dispersion
    Answer: d) Dispersion

Range and Variability

  1. What is the formula to calculate the range of a dataset?
    a) Maximum value + Minimum value
    b) Maximum value - Minimum value
    c) Sum of values ÷ Total observations
    d) Maximum value × Minimum value
    Answer: b) Maximum value - Minimum value

  2. If the range of a dataset is small, it indicates that the data is:
    a) More dispersed
    b) Clustered closely
    c) Normally distributed
    d) Symmetrical
    Answer: b) Clustered closely

  3. The range of the scores of Batsman B (46 to 60) is:
    a) 14
    b) 60
    c) 46
    d) 53
    Answer: a) 14

  4. What additional factor is needed to fully interpret the variability of data beyond central tendency?
    a) Mode
    b) Dispersion
    c) Median
    d) Sum of observations
    Answer: b) Dispersion

  5. What is the limitation of using range as a measure of dispersion?
    a) It ignores variability within the dataset
    b) It is hard to calculate
    c) It only considers central values
    d) It does not work for grouped data
    Answer: a) It ignores variability within the dataset

Mean Deviation

  1. What is the mean deviation of a dataset where the absolute deviations from the mean total 30 and there are 6 observations?
    a) 30
    b) 6
    c) 5
    d) 3
    Answer: c) 5

  2. Which measure of dispersion depends on the deviations of data from a central value?
    a) Range
    b) Mean deviation
    c) Mode
    d) Quartile deviation
    Answer: b) Mean deviation

  3. For grouped data, the mean deviation about the mean is calculated using:
    a) Class midpoints and frequencies
    b) Individual data points
    c) Sum of squared deviations
    d) Upper and lower boundaries of each class
    Answer: a) Class midpoints and frequencies

  4. The sum of deviations from the mean in a dataset is always:
    a) Equal to the range
    b) Zero
    c) Positive
    d) Negative
    Answer: b) Zero

  5. The absolute mean deviation from the median of a dataset indicates:
    a) Central tendency
    b) Variability around the median
    c) Highest and lowest values
    d) Mean value of deviations
    Answer: b) Variability around the median

Standard Deviation

  1. What is the standard deviation?
    a) The square root of the variance
    b) The mean of the dataset
    c) The absolute deviation from the mean
    d) The range divided by the total observations
    Answer: a) The square root of the variance

  2. What does a high standard deviation indicate?
    a) The data points are closely clustered around the mean
    b) The data points are more spread out from the mean
    c) There is no variability in the data
    d) The range is small
    Answer: b) The data points are more spread out from the mean

  3. If the standard deviation of a dataset is 5, what is the variance?
    a) 25
    b) 5
    c) 10
    d) 15
    Answer: a) 25

  4. How is the variance of a dataset calculated?
    a) Mean of deviations from the median
    b) Sum of squared deviations from the mean divided by the number of observations
    c) Absolute deviations divided by the range
    d) Sum of deviations from the maximum value
    Answer: b) Sum of squared deviations from the mean divided by the number of observations

  5. If all data values are the same in a dataset, the standard deviation will be:
    a) 1
    b) 0
    c) Equal to the mean
    d) Undefined
    Answer: b) 0

Grouped Data

  1. In a frequency distribution, the midpoint of a class is calculated as:
    a) The difference between the upper and lower boundaries
    b) The average of the upper and lower boundaries
    c) The product of frequency and range
    d) None of the above
    Answer: b) The average of the upper and lower boundaries

  2. What is the formula for mean deviation about the mean for grouped data?
    a) M.D.=Σf⋅∣x−xˉ∣N\text{M.D.} = \frac{\Sigma f \cdot |x - \bar{x}|}{N}
    b) M.D.=Σ∣x−xˉ∣N\text{M.D.} = \frac{\Sigma |x - \bar{x}|}{N}
    c) M.D.=Σf⋅∣x−median∣N\text{M.D.} = \frac{\Sigma f \cdot |x - \text{median}|}{N}
    d) M.D.=Σ∣x−mean∣N\text{M.D.} = \frac{\Sigma |x - \text{mean}|}{N}
    Answer: a) M.D.=Σf⋅∣x−xˉ∣N\text{M.D.} = \frac{\Sigma f \cdot |x - \bar{x}|}{N}

  3. For continuous frequency distribution, the standard deviation is calculated using:
    a) Class limits
    b) Cumulative frequencies
    c) Class midpoints and frequencies
    d) Range
    Answer: c) Class midpoints and frequencies

  4. If each observation in a dataset is multiplied by a constant kk, the variance is:
    a) k×original variancek \times \text{original variance}
    b) k2×original variancek^2 \times \text{original variance}
    c) The same as the original variance
    d) original variancek\frac{\text{original variance}}{k}
    Answer: b) k2×original variancek^2 \times \text{original variance}

  5. In the shortcut method, deviations are taken from:
    a) Class midpoints
    b) Assumed mean
    c) Mean deviation
    d) Range
    Answer: b) Assumed mean

Historical Development of Statistics

  1. Who is considered the "Father of Modern Statistics"?
    a) Karl Pearson
    b) Sir Ronald A. Fisher
    c) Jacob Bernoulli
    d) Francis Galton
    Answer: b) Sir Ronald A. Fisher

  2. The first known census was conducted in which country?
    a) India
    b) Egypt
    c) England
    d) China
    Answer: b) Egypt

  3. Kautilya’s Arthashastra mentions a system for collecting which type of data?
    a) Weather statistics
    b) Birth and death statistics
    c) Agricultural statistics
    d) Trade statistics
    Answer: b) Birth and death statistics

  4. The theory of probability began development in which century?
    a) 16th century
    b) 17th century
    c) 18th century
    d) 19th century
    Answer: b) 17th century

  5. Who introduced the Chi-square test?
    a) Karl Pearson
    b) Francis Galton
    c) Ronald A. Fisher
    d) Abul Fazl
    Answer: a) Karl Pearson

Measures of Dispersion

  1. What is the primary purpose of measuring dispersion in a dataset?
    a) To find the average value of data
    b) To analyze the spread or variability of data
    c) To identify the median
    d) To determine the maximum value
    Answer: b) To analyze the spread or variability of data

  2. Which of the following is NOT a measure of dispersion?
    a) Range
    b) Mean deviation
    c) Variance
    d) Arithmetic mean
    Answer: d) Arithmetic mean

  3. What is the range if the maximum value is 75 and the minimum value is 15?
    a) 60
    b) 90
    c) 15
    d) 75
    Answer: a) 60

  4. What is the main limitation of using the range as a measure of dispersion?
    a) It is difficult to calculate
    b) It considers only two values in the dataset
    c) It cannot be used for grouped data
    d) It depends on the mean
    Answer: b) It considers only two values in the dataset

  5. If the range of Dataset A is greater than Dataset B, it implies that Dataset A is:
    a) More consistent
    b) More scattered
    c) Less variable
    d) Symmetrical
    Answer: b) More scattered

Mean Deviation and Variance

  1. Which of the following is used to calculate the mean deviation about the mean?
    a) Absolute deviations from the mean
    b) Squared deviations from the mean
    c) Total sum of observations
    d) Difference between maximum and minimum values
    Answer: a) Absolute deviations from the mean

  2. What does the variance measure in a dataset?
    a) Central tendency
    b) Average of squared deviations from the mean
    c) Difference between mean and median
    d) Relationship between mean and mode
    Answer: b) Average of squared deviations from the mean

  3. If the variance of a dataset is zero, it means:
    a) All observations are the same
    b) The dataset has no central tendency
    c) The dataset is highly variable
    d) The standard deviation is infinite
    Answer: a) All observations are the same

  4. How does multiplying all observations in a dataset by a constant kk affect the variance?
    a) Variance remains unchanged
    b) Variance becomes k2k^2 times the original variance
    c) Variance is halved
    d) Variance becomes kk times the original variance
    Answer: b) Variance becomes k2k^2 times the original variance

  5. The mean of squared deviations from the mean of a dataset is called:
    a) Mean deviation
    b) Range
    c) Variance
    d) Standard deviation
    Answer: c) Variance

Standard Deviation and Grouped Data

  1. Standard deviation is always:
    a) Negative
    b) Zero or positive
    c) Greater than variance
    d) Equal to the mean deviation
    Answer: b) Zero or positive

  2. Which step is necessary to calculate the standard deviation for grouped data?
    a) Finding midpoints of classes
    b) Calculating cumulative frequencies
    c) Determining the range
    d) Summing deviations without squaring
    Answer: a) Finding midpoints of classes

  3. In a frequency distribution, the total frequency is denoted by:
    a) ff
    b) NN
    c) σ\sigma
    d) xx
    Answer: b) NN

  4. In the shortcut method for variance, deviations are taken from:
    a) Arithmetic mean
    b) Assumed mean
    c) Median
    d) Mode
    Answer: b) Assumed mean

  5. In a continuous frequency distribution, the median class is identified using:
    a) The midpoint of each class
    b) The cumulative frequency table
    c) The total sum of observations
    d) The range of the dataset
    Answer: b) The cumulative frequency table

Historical Context of Statistics

  1. Which book by Jacob Bernoulli discussed the Law of Large Numbers?
    a) Arthashastra
    b) Ars Conjectandi
    c) Ain-i-Akbari
    d) Chi-Square Theory
    Answer: b) Ars Conjectandi

  2. Francis Galton is known for pioneering statistical methods in which field?
    a) Genetics
    b) Biometry
    c) Astronomy
    d) Agriculture
    Answer: b) Biometry

  3. Captain John Graunt is recognized for his contributions to:
    a) Biometry
    b) Vital statistics
    c) Agricultural surveys
    d) Probability theory
    Answer: b) Vital statistics

  4. During Akbar’s reign, surveys on administration were documented in:
    a) Ars Conjectandi
    b) Arthashastra
    c) Ain-i-Akbari
    d) Chi-Square Laboratory
    Answer: c) Ain-i-Akbari

  5. Who introduced the Chi-Square test in statistics?
    a) Karl Pearson
    b) Sir Ronald Fisher
    c) Jacob Bernoulli
    d) Francis Galton
    Answer: a) Karl Pearson

Applications of Statistics

  1. In statistics, the term "dispersion" refers to:
    a) Central tendency of data
    b) Spread or variability of data points
    c) The most frequently occurring value
    d) The arithmetic mean of the dataset
    Answer: b) Spread or variability of data points

  2. When is the range an ideal measure of dispersion?
    a) When comparing two datasets
    b) When the data is symmetric
    c) For small datasets with no extreme values
    d) Always
    Answer: c) For small datasets with no extreme values

  3. Mean deviation can be calculated from which measures of central tendency?
    a) Mean and median
    b) Mean and range
    c) Median and mode
    d) Mode and range
    Answer: a) Mean and median

  4. If the cumulative frequency is 30, the median class lies at:
    a) N/4N/4
    b) N/2N/2
    c) N−1N-1
    d) 3N/43N/4
    Answer: b) N/2N/2

  5. Which measure of dispersion is commonly used in modern statistical applications?
    a) Range
    b) Quartile deviation
    c) Standard deviation
    d) Mode
    Answer: c) Standard deviation

Problem Solving in Statistics

  1. The median of the dataset: 4, 8, 10, 15, 20, 22, 30 is:
    a) 15
    b) 10
    c) 20
    d) 18
    Answer: a) 15

  2. What happens to the mean if 5 is added to every observation in a dataset?
    a) Mean increases by 5
    b) Mean decreases by 5
    c) Mean doubles
    d) Mean remains unchanged
    Answer: a) Mean increases by 5

  3. If the standard deviation of a dataset is σ\sigma, the variance is given by:
    a) σ/2\sigma/2
    b) σ2\sigma^2
    c) 2σ2\sigma
    d) 1/σ1/\sigma
    Answer: b) σ2\sigma^2

  4. In grouped data, frequencies are multiplied by which value to calculate the mean?
    a) Cumulative frequencies
    b) Midpoints of the class
    c) Range of the class
    d) Class intervals
    Answer: b) Midpoints of the class

  5. Which step is necessary to calculate the variance of a dataset?
    a) Squaring deviations from the mean
    b) Finding the absolute deviations from the mode
    c) Multiplying deviations by cumulative frequencies
    d) Taking the square root of deviations from the mean
    Answer: a) Squaring deviations from the mean


MCQs for NEET, JEE, IIT, NIT, CUET, CTET, and SSC Entrance Exams: Your Ultimate Preparation Guide

Are you preparing for competitive exams like NEET, JEE, IIT, NIT, CUET, CTET, or SSC? Multiple Choice Questions (MCQs) are a proven way to enhance your preparation strategy. These MCQs are designed to strengthen your concepts, boost problem-solving skills, and improve time management—key elements to ace any entrance exam.

Why MCQs Are Essential for Competitive Exams?

  1. Concept Clarity: MCQs cover important topics, ensuring a deep understanding of fundamental concepts.
  2. Time Management: Practicing MCQs improves speed and accuracy, essential for high-stakes exams.
  3. Exam Pattern Familiarity: MCQs simulate the real exam pattern, helping you feel confident on the big day.

Benefits of Using These MCQs for NEET, JEE, IIT, and More

  • Targeted Preparation: Specially curated MCQs focus on the specific syllabus of exams like NEET, JEE, and CUET, making your study focused and efficient.
  • Wide Subject Coverage: Includes questions from Physics, Chemistry, Mathematics, Biology, and more.
  • Boosts Competitive Edge: High-quality MCQs ensure you're ready to tackle even the trickiest questions.

Exams These MCQs Help With:

  • NEET: For aspiring medical students.
  • JEE & IIT: For engineering and technical aspirants.
  • NIT Admissions: A stepping stone to prestigious National Institutes of Technology.
  • CUET: Common University Entrance Test for undergraduate programs.
  • CTET: A mandatory test for teachers.
  • SSC: Government job aspirants preparing for SSC exams.

Pro Tips to Use MCQs Effectively:

  1. Regular Practice: Dedicate time daily to solve topic-wise MCQs.
  2. Review and Revise: Go through solutions and explanations to understand your mistakes.
  3. Mock Tests: Attempt full-length MCQ tests to build exam stamina.

Get Started Now!

Our extensive MCQ collections are tailored to help you succeed in NEET, JEE, IIT, NIT, CUET, CTET, and SSC. Start practicing today and take a step closer to your dream career. Bookmark this page and share it with fellow aspirants.

Tags:

MCQs for NEET, JEE MCQs, IIT preparation, CUET questions, CTET practice, SSC MCQs, competitive exam tips, entrance exam success.

Make your preparation smarter, not harder. Let these MCQs guide your way to success!

at No comments:
Subscribe to: Posts (Atom)