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# GATE 2022: Engineering Mathematics- 9 (App update required to attempt this test)

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Question 1

A bag contains 5 blue and 6 white balls. A ball is drawn at random and its color is noted and placed the another same color ball in the bag. The probability of getting blue ball in second draw is

Question 2

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

Question 3

A class of 12th students is composed of 4 batches A, B, C and D each consisting of 50 students. It is found that the sessional marks of students in math in batch B have mean of 6.5 and standard deviation of 2.1. The mean and standard deviation of the entire batch is 5.8 and 4.1 respectively. It is decided by the teacher to normalize the marks of all batches to have same mean and standard deviation as that of the entire class. Due to this the marks of a student in batch B are changed from 8.4 to

Question 4

Consider the continuous random variable with probability density function

The standard deviation of the random variable is

Question 5

An examination paper has 100 multiple choice questions of one mark with each question having four options. Each incorrect answer fetches -0.25 marks. Suppose there are 500 students choose their all answer randomly with uniform probability. The expected marks of sum of total marks obtained by the students is ---

Question 6

If mean and standard deviation of a binomial distribution are 3 and respectively, then binomial distribution is (q + p)n. The value of n is ________
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