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

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

If z = x + iy is a complex number such that Im `((2z + 1)/("i"z + 1))` = 0, show that the locus of z is 2x² + 2y² + x – 2y = 0

Obtain the Cartesian form of the locus of z = x + iy in the following cases:

[Re(iz)]² = 3

Obtain the Cartesian form of the locus of z = x + iy in the following cases:

Im[(1 – i)z + 1] = 0

Obtain the Cartesian form of the locus of z = x + iy in the following cases:

|z + i| = |z – 1|

Obtain the Cartesian form of the locus of z = x + iy in the following cases:

`bar(z) = z^-1`

Show that the following equations represent a circle, and, find its centre and radius.

|z – 2 – i| = 3

Show that the following equations represent a circle, and, find its centre and radius.

|2z + 2 – 4i| = 2

Show that the following equations represent a circle, and, find its centre and radius.

|3z – 6 + 12i| = 8 

Obtain the Cartesian equation for the locus of z = x + iy in the following cases:

|z – 4| = 16

Obtain the Cartesian equation for the locus of z = x + iy in the following cases:

|z – 4|² – |z – 1|² = 16

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If  `|"z" - 3/2|`, then the least value of |z| is