PUC Karnataka Science Class 12 - Department of Pre-University Education, Karnataka Question Bank Solutions for Mathematics

If `|[2x,5],[8,x]|=|[6,-2],[7,3]|`, write the value of x.

Show that the lines `(x+1)/3=(y+3)/5=(z+5)/7 and (x−2)/1=(y−4)/3=(z−6)/5` intersect. Also find their point of intersection

Find the distance of the point (−1, −5, −10) from the point of intersection of the line `vecr=2hati-hatj+2hatk+lambda(3hati+4hatj+2hatk) ` and the plane `vec r (hati-hatj+hatk)=5`

Find the value of a if `[[a-b,2a+c],[2a-b,3c+d]]=[[-1,5],[0,13]]`

Differentiate x^sinx+(sinx)^cosx with respect to x.

If `A=[[2,0,1],[2,1,3],[1,-1,0]]` , find A² − 5 A + 16 I.

Find the the differential equation for all the straight lines, which are at a unit distance from the origin.

Write the element a₁₂ of the matrix A = [a_ij]_{2 × 2}, whose elements aij are given by a_ij = e^2ix sin jx.

Using the method of integration, find the area of the triangular region whose vertices are (2, -2), (4, 3) and (1, 2).

Write the element a₂₃ of a 3 ✕ 3 matrix A = (a_ij) whose elements a_ij are given by `a_(ij)=∣(i−j)/2∣`

If `[[3x,7],[-2,4]]=[[8,7],[6,4]]`, find the value of x

Find the equation of the curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements?

If A = [a_ij] =`[[2,3,-5],[1,4,9],[0,7,-2]]`and B = [b_ij] `[[2,-1],[-3,4],[1,2]]`

Let A be a matrix of order 3 × 4. If R₁ denotes the first row of A and C₂ denotes its second column, then determine the orders of matrices R₁ and C₂

Construct a 2 × 2  matrix whose elements `a_(ij)`

are given by: `(i+j)^2/2`

Construct a 2 × 2 matrix whose elements a_ij are given by:

`aij=(i-j)^2/2`

Construct a 2 × 2 matrix whose elements a_ij are given by:

`a_(ij)=(i-2_j)^2/2`

Construct a 2 × 2 matrix whose elements a_ij are given by:

`a_(ij)= (2i +j)^2/2`

Construct a 2 × 2 matrix whose elements a_ij are given by:

`a_(ij)=|2_i - 3_i|/2`