HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

If the probability of success in a single trial is 0.01. How many trials are required in order to have a probability greater than 0.5 of getting at least one success?

In binomial distribution with five Bernoulli’s trials, the probability of one and two success are 0.4096 and 0.2048 respectively. Find the probability of success.

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

x³ + y³ = 4ax

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

Ax² + By² = 1

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = A cos (log x) + B sin (log x)

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y² = (x + c)³

Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = Ae^5x + Be^-5x 

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

(y - a)² = 4(x - b)

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = a + `"a"/"x"`

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = c₁e^2x + c₂e^5x 

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

c₁x³ + c₂y² = 5

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = e^−2x (A cos x + B sin x)

Form the differential equation of family of lines having intercepts a and b on the co-ordinate ares respectively.

Find the differential equation all parabolas having a length of latus rectum 4a and axis is parallel to the axis.

Find the differential equation of the ellipse whose major axis is twice its minor axis.

Find the differential equation of all circles having radius 9 and centre at point (h, k).

Form the differential equation of family of lines parallel to the line 2x + 3y + 4 = 0.

Form the differential equation of all parabolas whose axis is the X-axis.

In the following example verify that the given expression is a solution of the corresponding differential equation:

xy = log y +c; `"dy"/"dx" = "y"^2/(1 - "xy")`