HSC Science (Electronics) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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

The area bounded by the curve y = x³, the X-axis and the Lines x = –2 and x = 1 is ______.

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 area of the region bounded by the curve y² = 4x, the X-axis and the lines x = 1, x = 4 for y ≥ 0.

Find the area of the region bounded by the curve y = x² and the line y = 4.

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`.

Find `dy/dx` if ,

`x= e^(3t) , y = e^(4t+5)`

Evaluate:

`int 1/(1 + cosα . cosx)dx`