Mathematics Questions

Browse 1,240 Mathematics questions with expert-verified, step-by-step solutions — NCERT, exemplar and previous-year questions, organised by chapter.

1. Q201
   The table ​below shows the ​daily ​expenditure on food ​of 25 households ​in a locality. ​Find the mean daily expenditure on food by ​a suitable method.
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2. Q202
   The following ​distribution gives the ​state-wise ​teacher-student ratio in higher ​secondary schools of India. Find the mode ​and mean of this data. Interpret the ​two measures.
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3. Q203
   The ​given distribution ​shows the number ​of runs scored by some top ​batsmen ​of the world in one-day ​international cricket matches. Find ​the mode of the data.
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4. Q204
   A student noted the number of ​cars passing ​through a spot on a road for ​100 periods ​each of 3 minutes and ​summarised it ​in the table given below. Find the mode ​of the ​data.
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5. Q205
   Complete the following statements:

   1. (i)Probability of an event E + Probability of the event 'not E' = ​____.
   2. (ii)The probability of an ​event that cannot happen ​is ____. Such ​an event is called ____.
   3. (iii)The probability of an event that is certain to happen is ____. ​Such an ​event is called ____.
   4. (iv)The sum of the probabilities of all the elementary events of an experiment is ____.
   5. (v)The probability of an event is greater than or equal ​to ____ and less than or equal to ____.
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6. Q206
   Which of the following experiments have ​equally likely outcomes? Explain.

   1. (i)A driver attempts to start a ​car. The car starts or ​does not start.
   2. (ii)A player attempts to shoot ​a basketball. She/he shoots or misses the shot.
   3. (iii)A trial is made ​to ​answer a true-false question. The answer is right or wrong.
   4. (iv)A baby is ​born. It is a boy or a girl.
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7. Q207
   Why is tossing a coin considered to be a fair way of ​deciding ​which team should get ​the ball ​at the beginning of ​a ​football game?
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8. Q208
   Which of ​the ​following ​cannot ​be the probability ​of ​an event?

   1. (a)$\frac{2}{3}$
   2. (b)$-1.5$
   3. (c)$15\%$
   4. (d)$0.7$
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9. Q209
   If $P(E)=0.05$, what ​is ​the ​probability ​of 'not E'?
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10. Q210
    A bag contains lemon flavoured ​candies only. Malini takes out one candy ​without looking into the bag. What is the probability ​that she takes ​out

    1. (i)​an orange ​flavoured candy? ​
    2. (ii)a lemon flavoured candy?
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11. Q211
    It ​is given that in ​a group of 3 ​students, the probability of ​2 students not having the same birthday is $0.992$. What is the probability that ​the 2 ​students have ​the same ​birthday?
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12. Q212
    A bag ​contains $3$ red balls ​and $5$ black balls. A ball is drawn at random from the bag. What is the probability that the ball ​drawn ​is

    1. (i)red?
    2. (ii)​not ​red?
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13. Q213
    A ​box contains $5$ red marbles, $8$ white marbles and $4$ green marbles. One marble ​is taken out ​of the box at ​random. What is ​the ​probability that the marble taken out will be

    1. (i)​red?
    2. (ii)white?
    3. (iii)not green?
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14. Q214
    A piggy bank contains hundred 50p coins, fifty Rs 1 ​coins, ​twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out ​when ​the ​bank is turned upside down, what is the probability ​that ​the coin

    1. (i)will be a 50 p coin?
    2. (ii)will not ​be a Rs 5 coin?
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15. Q215
    Gopi buys ​a fish ​from a shop for his aquarium. The shopkeeper takes out one fish ​at ​random from a tank ​containing $5$ male ​fish and $8$ female fish (see Fig. 14.4). What is the ​probability that the fish taken out is a male fish?
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16. Q216
    A game ​of chance ​consists of spinning an arrow which comes ​to rest pointing at one of the ​numbers $1,2,3,4,5,6,7,8$ (see Fig. 14.5), and these are equally likely outcomes. What is ​the probability that it ​will point at

    1. (i)$8$? ​
    2. (ii)an ​odd number?
    3. (iii)a number greater than $2$?
    4. (iv)a number less than $9$?
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17. Q217
    A ​die is ​thrown ​once. Find ​the probability of getting

    1. (i)a prime number;
    2. (ii)a ​number lying ​between ​2 and ​6;
    3. (iii)an odd number.
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18. Q218
    One card is drawn from ​a well-shuffled ​deck of 52 cards. Find ​the probability ​of getting ​

    1. (i)a king of ​red colour
    2. (ii)a face ​card
    3. (iii)a red face card
    4. (iv)the jack of ​hearts
    5. (v)a spade
    6. (vi)the queen of diamonds
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19. Q219
    Five cards - the ten, jack, queen, king and ace of diamonds, are well-shuffled ​with their face downwards. One card is then picked up at random.

    1. (i)What is ​the probability that ​the card is the queen? ​
    2. (ii)If the ​queen is drawn and ​put aside, ​what is the probability that the second card picked up is (a) an ace? (b) a queen?
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20. Q220
    12 defective pens are ​accidentally mixed with 132 good ones. It is not possible ​to just look ​at a pen and tell whether ​or not ​it is ​defective. One pen is taken ​out at random from this lot. Determine the probability that the pen taken out is a good ​one.
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