HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the vector equation of the line passing through the point (–2, 1, 4) and perpendicular to the plane `barr*(4hati - 5hatj + 7hatk)` = 15

Find the equation of the plane which contains the line of intersection of the planes x + 2y + 4z = 4 and 2x – 3y – z = 9 and which is perpendicular to the plane 4x – 3y + 5z = 10.

Find the point of intersection of the line `(x + 1)/2 = (y - 1)/3 = (z - 2)/1` with the plane x + 2y – z = 6.

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

The perpendicular distance of the plane `bar r. (3 hat i + 4 hat j + 12 hat k) = 78` from the origin is ______.

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 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 :

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

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

∀ x ∈ A, x + 5 < 12.

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

∃ x ∈ A, such that x + 7 ≥ 11.

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

∀ x ∈ A, 3x ≤ 25.