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

Find the differential equation of the family of circles passing through the origin and having their centres on the x-axis

Find the differential equation of the family of parabolas with vertex at (0, –1) and having axis along the y-axis

Find the differential equations of the family of all the ellipses having foci on the y-axis and centre at the origin

Find the differential equation corresponding to the family of curves represented by the equation y = Ae^8x + Be ^–8x, where A and B are arbitrary constants

Find the differential equation of the curve represented by xy = ae^x + be^–x + x²

Choose the correct alternative:

The slope at any point of a curve y = f(x) is given by `("d"y)/("d"x) - 3x^2` and it passes through (-1, 1). Then the equation of the curve is

The probability density function of X is given by
`f(x) = {{:(kx"e"^(-2x),  "for"  x > 0),(0,  "for"  x ≤ 0):}`
Find the value of k

The probability density function of X is `f(x) = {(x, 0 < x < 1),(2 - x, 1 ≤ x ≤ 2),(0, "otherwise"):}`
Find P(0.2 ≤ X < 0.6)

The probability density function of X is `f(x) = {(x, 0 < x < 1),(2 - x, 1 ≤ x ≤ 2),(0, "otherwise"):}`
Find P(1.2 ≤ X < 1.8)

The probability density function of X is `f(x) = {(x, 0 < x < 1),(2 - x, 1 ≤ x ≤ 2),(0, "otherwise"):}`
Find P(0.5 ≤ X < 1.5)

Suppose the amount of milk sold daily at a milk booth is distributed with a minimum of 200 litres and a maximum of 600 litres with probability density function
`f(x) = {{:(k, 200 ≤ x ≤ 600),(0, "otherwise"):}`
Find the value of k

Suppose the amount of milk sold daily at a milk booth is distributed with a minimum of 200 litres and a maximum of 600 litres with probability density function
`f(x) = {{:(k, 200 ≤ x ≤ 600),(0, "otherwise"):}`
Find the distribution function

Suppose the amount of milk sold daily at a milk booth is distributed with a minimum of 200 litres and a maximum of 600 litres with probability density function
`f(x) = {{:(k, 200 ≤ x ≤ 600),(0, "otherwise"):}`
Find the probability that daily sales will fall between 300 litres and 500 litres?

The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for"  x > 0),(0,"for"  x ≤ 0):}`
Find the value of k 

The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for"  x > 0),(0,"for"  x ≤ 0):}`
Find the distribution function

The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for"  x > 0),(0,"for"  x ≤ 0):}`
Find P(X < 3)

The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for"  x > 0),(0,"for"  x ≤ 0):}`
Find P(5 ≤ X)

The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for"  x > 0),(0,"for"  x ≤ 0):}`
Find P(X ≤ 4)

If X is the random variable with probability density function f(x) given by,
`f(x) = {{:(x + 1",", -1 ≤ x < 0),(-x +1",",   0 ≤ x < 1),(0, "otherwise"):}`
then find the distribution function F(x)

If X is the random variable with probability density function f(x) given by,
`f(x) = {{:(x + 1",", -1 ≤ x < 0),(-x +1",",   0 ≤ x < 1),(0, "otherwise"):}`
then find P(– 0.5 ≤ x ≤ 0.5)