Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of types A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 4 hours available for assembling. The profit is ₹ 50 each for type A and ₹60 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximize profit? Formulate the above  LPP and solve it graphically and find the maximum profit.

Find: `int_  (cos"x")/((1 + sin "x") (2+ sin"x")) "dx"`

Write the value of `|(a-b, b- c, c-a),(b-c, c-a, a-b),(c-a, a-b, b-c)|`

On her birthday Seema decided to donate some money to children of an orphanage home. If there were 8 children less, everyone would have got ₹ 10 more. However, if there were 16 children more, everyone would have got ₹ 10 less. Using the matrix method, find the number of children and the amount distributed by Seema. What values are reflected by Seema’s decision?

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi-vertical angle α is one-third that of the cone and the greatest volume of the cylinder is `(4)/(27) pi"h"^3 tan^2 α`.

Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`

Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`

Find: `int sin^-1 (2x) dx.`

Solve the differential equation: x dy - y dx = `sqrt(x^2 + y^2)dx,` given that y = 0 when x = 1.

If `sin^-1((x^5 - y^5)/(x^5 + y^5)) = pi/(6), "show that" "dy"/"dx" = x^4/(3y^4)`

Differentiate `sin^-1((2x)/(1 + x^2))w.r.t. cos^-1((1 - x^2)/(1 + x^2))`

If `x^7 * y^9 = (x + y)^16`, then show that `dy/dx = y/x`

If x = a t⁴ y = 2a t² then `("d"y)/("d"x)` = ______

Find the principal value of cos^–1x, for x = `sqrt(3)/2`.

Find the value of `cos^-1(cos  (13pi)/6)`.

Find the value of `tan^-1 (tan  (9pi)/8)`.

Prove that tan(cot^–1x) = cot(tan^–1x). State with reason whether the equality is valid for all values of x.

Find the value of `sec(tan^-1  y/2)`

Find value of tan (cos^–1x) and hence evaluate `tan(cos^-1  8/17)`

Find the value of `sin[2cot^-1 ((-5)/12)]`