HSC Science (Computer Science) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

`int cos^3x  dx` = ______.

Write `int cotx  dx`.

Find the length of the perpendicular drawn from the point P(3, 2, 1) to the line `overliner = (7hati + 7hatj + 6hatk) + λ(-2hati + 2hatj + 3hatk)`

Find separate equations of lines represented by x² – y² + x + y = 0.

Express the following compound statement symbolically:

Delhi is in India but Dhaka is not in Sri Lanka

Express the following compound statement symbolically:

3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25

In any ΔABC, prove that:

(b + c) cos A + (c + a) cos B + (a + b) cos C = a + b + c.

Prove that:

`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.

Evaluate:

`int 1/(1 + cosα . cosx)dx`

Show that the joint equation of a pair of straight lines through the origin is a homogeneous equation of second degree in x and y.

Evaluate:

`int sqrt((a - x)/x) dx`

If in ΔABC, `sin  A/2 * sin  C/2 = sin  B/2` and 2s is the perimeter of the triangle, then s = ______.

Evaluate:

`int(sqrt(tanx) + sqrt(cotx))dx`

Write the contrapositive of the inverse of the statement:

‘If two numbers are not equal, then their squares are not equal’.

From the following set of statements, select two statements which have similar meaning.

1. If a man is judge, then he is honest.
2. If a man is not a judge, then he is not honest.
3. If a man is honest, then he is a judge.
4. If a man is not honest, then he is not a judge.

The distance of the point (2, – 3, 1) from the line `(x + 1)/2 = (y - 3)/3 = (z + 1)/-1` is ______.

`int "cosec"^4x  dx` = ______.

The differential equation for a²y = log x + b, is ______.

Evaluate:

`int sin^2(x/2)dx`

Solve the differential equation

cos²(x – 2y) = `1 - 2dy/dx`