HSC Science (Electronics) 12th Standard Board Exam - Maharashtra State Board Important Questions

The integrating factor of linear differential equation `x dy/dx + 2y = x^2 log x` is ______.

The general solution of `(dy)/(dx)` = e^−x is ______.

Select and write the correct alternative from the given option for the question 

Differential equation of the function c + 4yx = 0 is

Select and write the correct alternative from the given option for the question

The order and degree of `(("d"y)/("d"x))^3 - ("d"^3y)/("d"x^3) + y"e"^x` = 0 are respectively

Select and write the correct alternative from the given option for the question

The solution of `("d"y)/("d"x)` = 1 is

State the degree of differential equation `e^((dy)/(dx)) + (dy)/(dx)` = x

Form the differential equation of y = (c₁ + c₂)e^x 

Solve the differential equation `("d"y)/("d"x) + y` = e^−x 

Solve the differential equation (x² – yx²)dy + (y² + xy²)dx = 0

Find the differential equation by eliminating arbitrary constants from the relation x² + y² = 2ax

Solve: `("d"y)/("d"x) + 2/xy` = x² 

Write the degree of the differential equation (y''')² + 3(y") + 3xy' + 5y = 0

Solve the differential equation

`y (dy)/(dx) + x` = 0

Form the differential equation of all lines which makes intercept 3 on x-axis.

Find the particular solution of the differential equation `dy/dx` = e^2y cos x, when x = `π/6`, y = 0

A particle is moving along the X-axis. Its acceleration at time t is proportional to its velocity at that time. Find the differential equation of the motion of the particle.

Solve:

`1 + (dy)/(dx) = cosec (x + y)`; put x + y = u.

The time (in minutes) for a lab assistant to prepare the equipment for a certain experiment is a random variable taking values between 25 and 35 minutes with p.d.f 

`f(x) = {{:(1/10",", 25 ≤ x ≤ 35),(0",", "otherwise"):}`

What is the probability that preparation time exceeds 33 minutes? Also, find the c.d.f. of X.

The expected value of the number of heads obtained when three fair coins are tossed simultaneously is

(A) 1

(B) 1.5

(C) 0

(D) -1

The probability distribution of X, the number of defects per 10 metres of a fabric is given by

Find the variance of X