HSC Science इयत्ता १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

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The solution of the differential equation `2x ("d"y)/("d"x) - y = 3` represents

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The solution of the differential equation `("d")/("d"x) + 1/sqrt(1 - x^2) = 0` is

For the random variable X with the given probability mass function as below, find the mean and variance.

`f(x) = {{:(1/10, x = 2","  5),(1/5, x = 0","  1","  3","  4):}`

For the random variable X with the given probability mass function as below, find the mean and variance.

`f(x) = {{:((4 - x)/6,  x = 1","  2","  3),(0,  "otherwise"):}`

For the random variable X with the given probability mass function as below, find the mean and variance.

`f(x) = {{:(2(x - 1), 1 < x ≤ 2),(0, "otherwise"):}`

For the random variable X with the given probability mass function as below, find the mean and variance.

`f(x) = {{:(1/2 "e"^(x/2),  "for"  x > 0),(0,  "otherwise"):}`

Two balls are drawn in succession without replacement from an urn containing four red balls and three black balls. Let X be the possible outcomes drawing red balls. Find the probability mass function and mean for X

If µ and σ² are the mean and variance of the discrete random variable X and E(X + 3) = 10 and E(X + 3)² = 116, find µ and σ² 

Four fair coins are tossed once. Find the probability mass function, mean and variance for a number of heads that occurred

A commuter train arrives punctually at a station every half hour. Each morning, a student leaves his house to the train station. Let X denote the amount of time, in minutes, that the student waits for the train from the time he reaches the train station. It is known that the pdf of X is

`f(x) = {{:(1/30, 0 < x < 30),(0, "elsewhere"):}`
Obtain and interpret the expected value of the random variable X

The time to failure in thousands of hours of an electronic equipment used in a manufactured computer has the density function
`f(x) = {{:(3"e"^(-3x), x > 0),(0, "eleswhere"):}`
Find the expected life of this electronic equipment

The probability density function of the random variable X is given by

`f(x) = {{:(16x"e"^(-4x), x > 0),(0, x ≤ 0):}`
find the mean and variance of X

A lottery with 600 tickets gives one prize of ₹ 200, four prizes of ₹ 100, and six prizes of ₹ 50. If the ticket costs is ₹ 2, find the expected winning amount of a ticket

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Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins ₹ 36, otherwise he loses ₹ k², where k is the face that comes up k = {1, 2, 3, 4, 5}. The expected amount to win at this game in ₹ is

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A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is

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Four buses carrying 160 students from the same school arrive at a football stadium. The buses carry, respectively, 42, 36, 34, and 48 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying the randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on that bus. Then E(X) and E(Y) respectively are

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On a multiple-choice exam with 3 possible destructive for each of the 5 questions, the probability that a student will get 4 or more correct answers just by guessing is

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If P(X = 0) = 1 – P(X = 1). If E[X] = 3 Var(X), then P(X = 0) is

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If X is a binomial random variable with I expected value 6 and variance 2.4, Then P(X = 5) is

If 2 = x + iy is a complex number such that `|(z - 4"i")/(z + 4"i")|` = 1 show that the locus of z is real axis