HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Divide the number 100 into two parts so that the sum of their squares is minimum.

Find the point on the curve y² = 4x, which is nearest to the point (2, 1).

A box with a square base is to have an open top. The surface area of box is 147 sq. cm. What should be its dimensions in order that the volume is largest?

Write converse, inverse and contrapositive of the following statement.

If x < y then x² < y² (x, y ∈ R)

Write converse, inverse and contrapositive of the following statement.

A family becomes literate if the woman in it is literate.

Write converse, inverse and contrapositive of the following statement.

If surface area decreases then pressure increases.

Write converse, inverse and contrapositive of the following statement. "If voltage increases then current decreases".

Find `bb((d^2y)/(dx^2))` of the following:

x = 2at², y = 4at

If y = `"e"^("m"tan^(-1)x`, show that `(1 + x^2) ("d"^2y)/("d"x^2) + (2x - "m")("d"y)/("d"x)` = 0

If y = cos(m cos^–1x), then show that `(1 - x^2) ("d"^2y)/("d"x^2) - x("d"y)/("d"x) + "m"^2y` = 0

 Check whether the vectors `2hati +2hatj +3hatk,-3hati +3hatj +2hatk and 3hati + 4hatk` From a triangle or not.

If `4hati - 5hatj + hatk, 2hati + 3hatj + 3hatk` and `xhati + yhatj + zhatk` represent the sides AB, BC and AC respectively of a triangle ABC, then find x, y, z.

Check whether the vectors `2hati + 2hatj +3hatk, -3hati +3hatj +2hatk` and `3hati +4hatk` form a triangle or not.

If y = sin^–1x, then show that `(1 - x^2) (d^2y)/(dx^2) - x * dy/dx` = 0

If x = cos θ and y = sin³θ, show that `y(d^2y)/(dx^2) + (dy/dx)^2` = 3sin²θ(5cos²θ – 1)

Check whether the vectors `2hati + 2hatj+ 3hatk`, `-3hati + 3hatj +2hatk` and `3hati + 4hatk` form a triangle or not.

Check whether the vectors `2hati + 2hatj + 3hatk , -3hati + 3hatj + 2hatk and 3hati + 4hatk` form a triangle or not.

The negation of p ∧ (q → r) is ______________.

Without using truth tabic show that ~(p v q)v(~p ∧ q) = ~p

Without using the truth table show that P ↔ q ≡ (p ∧ q) ∨ (~ p ∧ ~ q)