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

If `|[x+1,x-1],[x-3,x+2]|=|[4,-1],[1,3]|`, then write the value of x.

Evaluate : `intsin(x-a)/sin(x+a)dx`

Show that the differential equation 2y^x/y dx + (y − 2x e^x/y) dy = 0 is homogeneous. Find the particular solution of this differential equation, given that x = 0 when y = 1.

Solve the differential equation :

`y+x dy/dx=x−y dy/dx`

If A =  `([cos alpha, sin alpha],[-sinalpha, cos alpha])` , find α satisfying 0 < α < `pi/r`when `A+A^T=sqrt2I_2` where A^T is transpose of A.

Show that the differential  equation `2xydy/dx=x^2+3y^2`  is homogeneous and solve it.

Find the particular solution of the differential equation:

2y e^x/y dx + (y - 2x e^x/y) dy = 0 given that x = 0 when y = 1.

If `A=[[1,2,2],[2,1,2],[2,2,1]]` ,then show that `A^2-4A-5I=0` and hence find A^-1.

Find the absolute maximum and absolute minimum values of the function f given by f(x)=sin²x-cosx,x ∈ (0,π)

If `A=([2,0,1],[2,1,3],[1,-1,0])` find A² - 5A + 4I and hence find a matrix X such that  A² - 5A + 4I + X = 0

Find the local maxima and local minima, of the function f(x) = sin x − cos x, 0 < x < 2π.

Two tailors, A and B, earn Rs 300 and Rs 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP

Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`

Find  A + B

Compute the following:

`[(a,b),(-b, a)] + [(a,b),(b,a)]`

Compute the following:

`[(a^2+b^2, b^2+c^2),(a^2+c^2, a^2+b^2)] + [(2ab , 2bc),(-2ac, -2ab)]`

Compute the following: 

`[(-1,4, -6),(8,5,16),(2,8,5)] + [(12,7,6),(8,0,5),(3,2,4)]`

Compute the following:

`[(cos^2x, sin^2 x),(sin^2 x ,cos^2 x)]+[(sin^2 x, cos^2 x), (cos^2 x, sin^2 x)]`

If F(x) = `[(cosx, -sinx,0), (sinx, cosx, 0),(0,0,1)]`  show that F(x)F(y) = F(x + y)

Let A be a nonsingular square matrix of order 3 × 3. Then |adj A| is equal to ______.

Examine the consistency of the system of equations.

x + 2y = 2

2x + 3y = 3