HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Important Questions

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.

The solution of the differential equation `dx/dt = (xlogx)/t` is ______.

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 slope of the tangent to the curve x = sin θ and y = cos 2θ at θ = `π/6` is ______.

A random variable X has the following probability distribution:

then E(X)=....................

From a lot of 25 bulbs of which 5 are defective a sample of 5 bulbs was drawn at random with replacement. Find the probability that the sample will contain -

(a) exactly 1 defective bulb.

(b) at least 1 defective bulb.

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.

Probability distribution of X is given by

Find P(X ≥ 2) and obtain cumulative distribution function of X

Find the probability distribution of number of heads in two tosses of a coin.

From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.

A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.