Arts (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

Integrate the functions:

`1/(1 - tan x)`

Integrate the functions:

`sqrt(tanx)/(sinxcos x)`

Integrate the functions:

`(1+ log x)^2/x`

Integrate the functions:

`((x+1)(x + logx)^2)/x`

Integrate the functions:

`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`

`(10x^9 + 10^x log_e 10)/(x^10 + 10^x)  dx` equals:

`int (dx)/(sin^2 x cos^2 x)` equals:

Solve the differential equation `(tan^(-1) x- y) dx = (1 + x^2) dy`

Maximise Z = x + 2y subject to the constraints

`x + 2y >= 100`

`2x - y <= 0`

`2x + y <= 200`

Solve the above LPP graphically

Show that the surface area of a closed cuboid with square base and given volume is minimum, when it is a cube.

Solve the following linear programming problem graphically :

Maximise Z = 7x + 10y subject to the constraints

4x + 6y ≤ 240

6x + 3y ≤ 240

x ≥ 10

x ≥ 0, y ≥ 0

Find the general solution of the differential equation `dy/dx - y = sin x`

Solve the following L.P.P. graphically: 

Minimise Z = 5x + 10y

Subject to x + 2y ≤ 120

Constraints x + y ≥ 60

x – 2y ≥ 0 and x, y ≥ 0

Solve the differential equation `x dy/dx + y = x cos x + sin x`,  given that y = 1 when `x = pi/2`

Find the vector and Cartesian equations of a line passing through (1, 2, –4) and perpendicular to the two lines `(x - 8)/3 = (y + 19)/(-16) = (z - 10)/7` and `(x - 15)/3 = (y - 29)/8 = (z - 5)/(-5)`

Solve the following L.P.P. graphically Maximise Z = 4x + y 

Subject to following constraints  x + y ≤ 50

3x + y ≤ 90,

x ≥ 10

x, y ≥ 0

A metal box with a square base and vertical sides is to contain 1024 cm³. The material for the top and bottom costs Rs 5 per cm2 and the material for the sides costs Rs 2.50 per cm2. Find the least cost of the box

Solve the following L.P.P graphically: Maximise Z = 20x + 10y

Subject to the following constraints x + 2y ≤ 28,

3x + y ≤ 24,

x ≥ 2,

 x, y ≥ 0

An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when the depth of the tank is half of its width. If the cost is to be borne by nearby settled lower-income families, for whom water will be provided, what kind of value is hidden in this question?

Find x, y, a and b if

`[[2x-3y,a-b,3],[1,x+4y,3a+4b]]`=`[[1,-2,3],[1,6,29]]`