As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.

Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced.

**Q1.**Fifteen coupons are numbered 1 to 15. Seven coupons are selected at random, one at a time with replacement. The probability that the largest number appearing on a selected coupon be 9, is

(c) Probability of each case =9/15=3/5

^{7}

**Q2.**The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively. Then, P(X>6) is equal to

(c) Given, np=4,npq=2

^{8}C

_{7}(1/2)

^{7}(1/2) +

^{8}C

_{8}(1/2)

^{8}

**Q3.**A bag contains 7 red and 2 white balls and another bag contains 5 red and 4 white balls. Two balls are drawn, one from each bag. The probability that both the balls are white, is

(c) Required probability =

^{2}C

_{1}×

^{4}C

_{1}/

^{9}C

_{1}×

^{9}C

_{1}=8/81

**Q4.**A pair of dice is rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is

(a) Explaination not available

**Q5.**A and B are two independent events such that P(A) 1/2 and P(B)=1/3,then P(neither A nor B)is equal to

(d) Since, A and B are independent events.

^{c}∩B

^{c})=1-P(A∪B) =1-2/3=1/3

**Q6.**A five digit number is chosen at random. The probability that all the digit are distinct and digits at odd places are odd and digits at even place are even, is

(d) Total number of 5 digit number =9×10×10×10×10=90000

**Q7.**A and B are the independent events. The probability that both occur simultaneously is 1/6 and the probability that neither occur is 1/3. The probability of occurrence of the events A and B is

(b) Given, P(A∩B)=1/6

^{c}∩B

^{c})=1/3

^{c})P(B

^{c})=1/3

**Q8.**If A and B are two independent events, then A and B

^{c}are

(b) We have, P(A∩B)=P(A)P(B)

^{c})=P(A)-P(A∩B)

^{c})=P(A)-P(A)P(B)=P(A)P(B

^{c})

^{c}are independent events

**Q9.**The probability that the same number appear on throwing three dice simultaneously, is

(a) Total number of favorable cases =6

**Q10.**If A and B are two independent events, the probability that both A and B occur is 1/8 and the probability that neither of them occurs is 3/8. The probability of the occurrence of A, is

(a) Since A and B are independent events

^{c}∩B

^{c})=3/8

^{c})P(B

^{c})=3/8

^{c}∩B

^{c})=3/8

^{2}-x{P(A)+P(B)}+P(A)P(B)=0

^{2}-3/4 x+1/8=0

^{2}-6 x+1=0