Mathematics Questions

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

1. Q721
   A card is ​drawn from a deck of 52 ​cards. The ​event E ​is that card is ​not an ace of hearts. ​The number ​of outcomes favourable to ​E is

   1. (a)$4$
   2. (b)$13$
   3. (c)$48$
   4. (d)$51$
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2. Q722
   The probability of ​getting ​a bad egg ​in ​a lot of 400 is ​0.035. The number ​of bad eggs in the ​lot is

   1. (a)$7$
   2. (b)$14$
   3. (c)$21$
   4. (d)$28$
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3. Q723
   A girl calculates that the probability of her ​winning the ​first ​prize in a ​lottery is $0.08$. If $6000$ ​tickets are sold, how ​many ​tickets has ​she bought?

   1. (a)$40$
   2. (b)$240$
   3. (c)$480$
   4. (d)$750$
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4. Q724
   One ticket is ​drawn ​at ​random from a bag containing tickets numbered 1 to 40. ​The ​probability that ​the ​selected ticket has a number which is ​a multiple of 5 is

   1. (a)$\frac{1}{5}$
   2. (b)$\frac{3}{5}$
   3. (c)$\frac{4}{5}$
   4. (d)$\frac{1}{3}$
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5. Q725
   Someone is asked to ​take a number ​from ​1 ​to ​100. ​The probability that it is a prime is

   1. (a)$\frac{1}{5}$
   2. (b)$\frac{6}{25}$
   3. (c)$\frac{1}{4}$
   4. (d)$\frac{13}{50}$
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6. Q726
   A school ​has five houses A, ​B, C, D and E. A class has 23 students, 4 from ​house A, 8 from house B, 5 from house C, 2 ​from house D and rest from house E. A single student is selected at random to be ​the class monitor. The probability that the selected student is ​not from A, B and ​C is

   1. (a)$\frac{4}{23}$
   2. (b)$\frac{6}{23}$
   3. (c)$\frac{8}{23}$
   4. (d)$\frac{17}{23}$
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7. Q727
   The median ​of ​an ungrouped ​data and the median ​calculated when the same data ​is grouped are always the same. Do you think ​that this is a ​correct statement? Give reason.
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8. Q728
   In calculating the mean of grouped data, grouped in ​classes of equal width, ​we may use the formula $\bar{x}=a+\frac{f_i{d}_i}{f_i}$ where $a$ is the assumed mean. $a$ ​must be ​one of the ​mid-points of ​the ​classes. ​Is the last statement correct? Justify your answer.
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9. Q729
   Is it ​true to ​say that the mean, mode and median ​of ​grouped ​data will always be different? ​Justify your answer.
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10. Q730
    Will the ​median class and ​modal ​class of ​grouped data ​always be different? Justify ​your ​answer.
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11. Q731
    In a ​family having three children, ​there may be no girl, one ​girl, two ​girls or ​three girls. So, the ​probability of ​each is $\frac{1}{4}$. Is this ​correct? Justify your answer.
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12. Q732
    A game consists of spinning an arrow which ​comes to rest pointing ​at one ​of the regions ​(1, 2 or 3) (Fig. 13.1). Are ​the outcomes 1, 2 ​and 3 equally likely to occur? Give reasons.

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13. Q733
    Apoorv throws two dice once and ​computes ​the product of the ​numbers ​appearing on ​the dice. Peehu throws one die and squares ​the number that appears on it. Who has the better chance of getting the number ​36? Why?
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14. Q734
    When we ​toss a ​coin, ​there ​are two possible outcomes ​- Head or Tail. Therefore, ​the probability of each outcome is $\frac{1}{2}$. Justify your answer.
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15. Q735
    A student ​says that ​if you throw a ​die, it will show ​up 1 or ​not 1. ​Therefore, the probability of getting 1 and the probability ​of getting 'not 1' each is equal to $\frac{1}{2}$. Is this correct? Give reasons.
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16. Q736
    I toss ​three coins ​together. The possible outcomes are no ​heads, 1 head, 2 heads ​and ​3 heads. So, I ​say that probability of no heads ​is $\frac{1}{4}$. What is wrong with ​this conclusion?
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17. Q737
    If you toss a coin 6 times ​and ​it ​comes down heads ​on each ​occasion, ​can you say that the probability of getting a head is 1? ​Give reasons.
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18. Q738
    Sushma tosses a coin 3 times ​and gets tail each ​time. Do you think that the outcome of next toss ​will ​be ​a tail? Give reasons.
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19. Q739
    If I toss ​a coin 3 times and get head each time, should ​I ​expect a tail ​to have a ​higher ​chance in the 4th ​toss? ​Give reason in support of your answer.
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20. Q740
    A bag contains slips numbered from 1 to 100. If Fatima chooses a slip ​at ​random ​from the bag, it will either be an odd number or ​an even number. Since this ​situation ​has only two possible outcomes, so, the probability of ​each is $\frac{1}{2}$. Justify.
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