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

Find `int (cos theta)/((4 + sin^2 theta)(5 - 4 cos^2 theta)) d theta`

Maximise Z = x + 2y subject to the constraints

`x + 2y >= 100`

`2x - y <= 0`

`2x + y <= 200`

Solve the above LPP graphically

Determine the product `[(-4,4,4),(-7,1,3),(5,-3,-1)][(1,-1,1),(1,-2,-2),(2,1,3)]` and use it to solve the system of equations x - y + z = 4, x- 2y- 2z = 9, 2x + y + 3z = 1.

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 `(dy)/(dx)` at x = 1, y = `pi/4` if `sin^2 y + cos xy = K`

Prove that if E and F are independent events, then the events E and F' are also independent. 

Let A = `((2,-1),(3,4))`, B = `((5,2),(7,4))`, C= `((2,5),(3,8))` find a matrix D such that CD − AB = O

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

Use product `[(1,-1,2),(0,2,-3),(3,-2,4)][(-2,0,1),(9,2,-3),(6,1,-2)]` to solve the system of equations x + 3z = 9, −x + 2y − 2z = 4, 2x − 3y + 4z = −3

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

if `y = sin^(-1) (6xsqrt(1-9x^2))`, `1/(3sqrt2) < x < 1/(3sqrt2)` then find `(dy)/(dx)`

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

Find the particular solution of the differential equation

`tan x * (dy)/(dx) = 2x tan x + x^2 - y`; `(tan x != 0)` given that y = 0 when `x = pi/2`

if the matrix A =`[(0,a,-3),(2,0,-1),(b,1,0)]` is skew symmetric, Find the value of 'a' and 'b'

Given `A = [(2,-3),(-4,7)]` compute `A^(-1)` and show that `2A^(-1) = 9I - A`

Evaluate `int (cos 2x + 2sin^2x)/(cos^2x) dx`

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]]`