CBSE 12 Maths Question Paper-2019

Find the area of the region lying above the x-axis and included between the circle x² + y² = 8x and inside of the parabola y² = 4x.

Using the vector equation of a plane, find the vector and Cartesian equations of the plane passing through the points (2, 2, -1), (3, 4, 2), and (7, 0, 6).

Find the vector equation of the plane passing through the point (4, 3, 1) and parallel to the plane obtained above.

A manufacturer has three machine operators A, B, and C. The first operator A produces 1% defective items, whereas the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B on the job 30% of the time and C on the job for 20% of the time. What is the probability that a defective item chosen at random was produced by operator A?

Find the least expensive tank with a rectangular base and open at the top, having a volume of 8 m³, where the cost for the base is ₹70 per m² and the sides are ₹45 per m².

What is the solution to the system of equations?
x + y + z = 6, x + 2z = 7, 3x + y + z = 12

What is the inverse of the matrix?
A =
1 1 1
1 0 2
3 1 1

Find the area of the triangle with vertices A(2, 5), B(4, 7), and C(6, 2).

Find the probability that a defective item chosen from a stockpile of items produced by operators A, B, and C was produced by operator A. A produces 1% defective items, B produces 5%, and C produces 7%. A works 50% of the time, B 30%, and C 20%.

Using elementary operations, find the inverse of the matrix A = 1 2 -2
-1 3 0
0 -2 1

Find the cost of constructing a tank with a rectangular base and open at the top, having a volume of 8 m³, where the cost for the base is ₹70 per m² and the sides are ₹45 per m².

What is the inverse of the following matrix?
A =
1 1 1
1 0 2
3 1 1

Find the solution to the system of equations:
x + y + z = 6, x + 2z = 7, 3x + y + z = 12

What is the inverse of the matrix?
A =
1 1 1
1 0 2
3 1 1

Solve the system of equations using matrix inverse.
x + y + z = 6
x + 2z = 7
3x + y + z = 12
What are the values of x, y, and z?

Find the least expensive tank with a rectangular base and open at the top, having a volume of 8 m³, where the cost for the base is ₹70 per m² and the sides are ₹45 per m².

What is the solution to the system of equations?
x + y + z = 6
x + 2z = 7
3x + y + z = 12

Using integration, find the area of triangle ABC, whose vertices are A(2, 5), B(4, 7), and C(6, 2).

What is the inverse of the matrix?
A =
1 1 1
1 0 2
3 1 1

Find the probability that a defective item chosen from a stockpile of items produced by operators A, B, and C was produced by operator A. A produces 1% defective items, B produces 5%, and C produces 7%. A works 50% of the time, B 30%, and C 20%.

Using elementary operations, find the inverse of the matrix A = 1 2 -2
-1 3 0
0 -2 1

What is the solution to the system of equations?
x + y + z = 6
x + 2z = 7
3x + y + z = 12

What is the cost of constructing a tank with a rectangular base and open at the top, having a volume of 8 m³, where the cost for the base is ₹70 per m² and the sides are ₹45 per m²?

Using integration, find the area of triangle ABC, whose vertices are A(2, 5), B(4, 7), and C(6, 2).

What is the inverse of the matrix?
A =
1 1 1
1 0 2
3 1 1