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

Find the point of intersection of the lines given by x² + 3xy + 2y² + x – y – 6 = 0

Find the values of p and q if the equation px² – 6xy + y² + 18x – qy + 8 = 0 represents a pair of parallel lines.

If Rolle's theorem holds for the function f(x) = x³ + bx² + ax + 5, x ∈ [1, 3] with c = `2 + 1/sqrt(3)`, find the values of a and b.

Draw the rough graph and shade the feasible region for the inequalities x + y ≥ 2, 2x + y ≤ 8, x ≥ 0, y ≥ 0.

If x – y ≥ 8, x ≥ 3, y ≥ 3, x ≥ 0, y ≥ 0 then find the coordinates of the corner points of the feasible region.

Evaluate:

`int x/((x + 2)(x - 1)^2)dx`

Find feasible solution for the following system of linear inequation graphically.

3x + 4y ≥ 12, 4x + 7y ≤ 28, x ≥ 0, y ≥ 0

A body is heated at 110°C and placed in air at 10°C. After 1 hour its temperature is 60°C. How much additional time is required for it to cool to 35°C?

Find the angle between the planes `bar r.(2bar i+barj-bark)=3 and bar r.(hati+2hatj+hatk)=1`

Find the expected value, variance and standard deviation of random variable X whose probability mass function (p.m.f.) is given below: 

The probability that a certain kind of component will survive a check test is 0.6. Find the probability that exactly two of the next four components tested will survive.

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

If the population of a country doubles in 60 years, in how many years will it be triple under
the assumption that the rate of increase in proportional to the number of inhabitants?
[Given : log 2 = 0.6912 and log 3 = 1.0986.]

Solve the differential equation `y - x dy/dx = 0`

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

Find the variance of X

Find the area of the region bounded by the curves y² = 4x and 4x² + 4y² = 9 with x > = 0.

Let the p. m. f. of a random variable X be __

P(x) = `(3-x)/10` for x = -1,0,1,2

= 0                        otherwise

Then E(X ) is ________.

Find the variance and standard deviation of the random variable X whose probability distribution is given below :

The acute angle between the two planes x+y+2z = 3 and 3x -2y +2z = 7 ________.

If A = {1, 2, 3, 4, 5, 6, 7, 8, 9}, determine the truth value of the following statement:

∃ x ∈ A such that x + 8 = 15