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

If 2x = `y^(1/m) + y^(-1/m)`, then show that `(x^2 - 1) (dy/dx)^2` = m²y²

`int x^2/sqrt(1 - x^6)dx` = ______.

If p, q are true statements and r, s are false statements, then write the truth value of the compound statement

(p `→` ∼ r) `→` (q ∧ s)

Form the differential equation whose general solution is y = a cos 2x + b sin 2x.

Food F₁ contains 2, 6, 1 units and food F₂ contains 1, 1, 3 units of proteins, carbohydrates, fats respectively per kg. 8, 12 and 9 units of proteins, carbohydrates and fats is the weekly minimum requirement for a person. The cost of food F₁ is Rs. 85 and food F₂ is Rs. 40 per kg. Formulate the L.P.P. to minimize the cost.

If y = `sqrt((1 - x)/(1 + x))`, then `(1 - x^2) dy/dx + y` = ______.

`int 1/(sin^2x cos^2x)dx` = ______.

Using the statements

p: Seema is fat,

q: Seema is happy,

Write the following statements in symbolic form;

1. Seema is thin and happy.
2. If Seema is fat then she is unhappy.

Evaluate:

`int(cos 2x)/sinx dx`

The perimeter of ΔABC is 20, ∠A = 60°, area of ΔABC = `10sqrt(3)`, then find the values of a, b, c.

If y = `log((x + sqrt(x^2 + a^2))/(sqrt(x^2 + a^2) - x))`, find `dy/dx`.

Evaluate:

`intsqrt(3 + 4x - 4x^2)  dx`

The sum of the slopes of the lines given by x² – 2λxy – 7y² = 0 is 4 times their product, then the value of λ is ______.

`int (cos4x)/(sin2x + cos2x)dx` = ______.

If y = `tan^-1((6x - 7)/(6 + 7x))`, then `dy/dx` = ______.

Write the negation of (p `leftrightarrow` q).

Evaluate:

`int sin^3x cos^3x  dx`

The side of a square is increasing at the rate of 0.5 cm/sec. Find the rate of increase of the perimeter when the side of the square is 10 cm long.

The p.m.f. of a random variable X is as follows:

P (X = 0) = 5k², P(X = 1) = 1 – 4k, P(X = 2) = 1 – 2k and P(X = x) = 0 for any other value of X. Find k.

Given below is the probability distribution of a discrete random variable x.

Find K and hence find P(2 ≤ x ≤ 3)