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

Find the differential equation of the family of all the parabolas with latus rectum 4a and whose axes are parallel to the x-axis

Find the value of k. if 2x + y = 0 is one of the lines represented by 3x² + kxy + 2y² = 0

Find the cartesian co-ordinates of the point whose polar co-ordinates are `(1/2, π/3)`.

Form the differential equation of all lines which makes intercept 3 on x-axis.

Solve the following system of equations by the method of inversion.

x – y + z = 4, 2x + y – 3z = 0, x + y + z = 2

Solve the following differential equation:

`xsin(y/x)dy = [ysin(y/x) - x]dx`

(x² – y²)dx + 2xy dy = 0

`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`