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

If f(x) = x + 1, find `"d"/"dx"("fof") ("x")`

A company manufactures two types of cardigans: type A and type B. It costs ₹ 360 to make a type A cardigan and ₹ 120 to make a type B cardigan. The company can make at most 300 cardigans and spend at most ₹ 72000 a day. The number of cardigans of type B cannot exceed the number of cardigans of type A by more than 200. The company makes a profit of ₹ 100 for each cardigan of type A and ₹ 50 for every cardigan of type B. 

Formulate this problem as a linear programming problem to maximize the profit to the company. Solve it graphically and find the maximum profit.

If y = log (cos e^x) then find `"dy"/"dx".`

Solve the differential equation: `(1 + x^2) dy/dx + 2xy - 4x^2 = 0,` subject to the initial condition y(0) = 0.

Find `"dy"/"dx"`If x³ + x²y + xy² + y³ = 81

Find the maximum and minimum of the following functions : f(x) = `logx/x`

Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`

Evaluate: `int log ("x"^2 + "x")` dx

A rod of 108 m long is bent to form a rectangle. Find it’s dimensions when it’s area is maximum.

Which is greater, tan 1 or tan^–11?

The graph of inverse trigonometric function can be obtained from the graph of their corresponding trigonometric function by interchanging x and y axes.

If A = `[(x, 5, 2),(2, y, 3),(1, 1, z)]`, xyz = 80, 3x + 2y + 10z = 20, ten A adj. A = `[(81, 0, 0),(0, 81, 0),(0, 0, 81)]`

If A = `[(0, 1, 3),(1, 2, x),(2, 3, 1)]`, A^–1 = `[(1/2, -4, 5/2),(-1/2, 3, -3/2),(1/2, y, 1/2)]` then x = 1, y = ^–1.

If A and B are invertible matrices, then which of the following is not correct?

(A³)^–1 = (A^–1)³, where A is a square matrix and |A| ≠ 0.

`("aA")^-1 = 1/"a"  "A"^-1`, where a is any real number and A is a square matrix.

|A^–1| ≠ |A|^–1, where A is non-singular matrix.

|adj. A| = |A|², where A is a square matrix of order two.

Given f(x) = `1/(x - 1)`. Find the points of discontinuity of the composite function y = f[f(x)]

Differentiate `sqrt(tansqrt(x))` w.r.t. x