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

Write the negation of the following:

∃ x ∈ A, such that x + 9 ≤ 15.

Write the negation of the following:

Some triangles are equilateral triangle.

Find the distance of the point `4hat"i" - 3hat"j" + hat"k"` from the plane `bar"r".(2hat"i" + 3hat"j" - 6hat"k")` = 21.

Find the distance of the point (1, 1 –1) from the plane 3x +4y – 12z + 20 = 0.

Solve the following:

Find the distance of the point `3hat"i" + 3hat"j" + hat"k"` from the plane `bar"r".(2hat"i" + 3hat"j" + 6hat"k")` = 21.

Solve the following :

Find the distance of the point (13, 13, – 13) from the plane 3x + 4y – 12z = 0.

Find the maximum and minimum of the following functions : y = 5x³ + 2x² – 3x.

Find the maximum and minimum of the following functions : f(x) = 2x³ – 21x² + 36x – 20

Find the maximum and minimum of the following functions : f(x) = x³ – 9x² + 24x

Find the maximum and minimum of the following functions : f(x) = `x^2 + (16)/x^2`

Find the maximum and minimum of the following functions : f(x) = x log x

Find the maximum and minimum of the following functions : f(x) = `logx/x`

Divide the number 30 into two parts such that their product is maximum.

Divide the number 20 into two parts such that sum of their squares is minimum.

A wire of length 36 metres is bent in the form of a rectangle. Find its dimensions if the area of the rectangle is maximum.

A ball is thrown in the air. Its height at any time t is given by h = 3 + 14t – 5t². Find the maximum height it can reach.

Find the largest size of a rectangle that can be inscribed in a semicircle of radius 1 unit, so that two vertices lie on the diameter.

An open cylindrical tank whose base is a circle is to be constructed of metal sheet so as to contain a volume of `pia^3`cu cm of water. Find the dimensions so that the quantity of the metal sheet required is minimum.

The perimeter of a triangle is 10 cm. If one of the side is 4 cm. What are the other two sides of the triangle for its maximum area?

A box with a square base is to have an open top. The surface area of the box is 192 sq cm. What should be its dimensions in order that the volume is largest?