Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

Find both the maximum and minimum values respectively of 3x⁴ - 8x³ + 12x² - 48x + 1 on the interval [1, 4].

The function f(x) = x⁵ - 5x⁴ + 5x³ - 1 has ____________.

Find the height of the cylinder of maximum volume that can be inscribed in a sphere of radius a.

Find the volume of the largest cylinder that can be inscribed in a sphere of radius r cm.

The area of a right-angled triangle of the given hypotenuse is maximum when the triangle is ____________.

Find the area of the largest isosceles triangle having a perimeter of 18 meters.

The coordinates of the point on the parabola y² = 8x which is at minimum distance from the circle x² + (y + 6)² = 1 are ____________.

The distance of that point on y = x⁴ + 3x² + 2x which is nearest to the line y = 2x - 1 is ____________.

The function `"f"("x") = "x" + 4/"x"` has ____________.

The combined resistance R of two resistors R₁ and R₂ (R₁, R₂ > 0) is given by `1/"R" = 1/"R"_1 + 1/"R"_2`. If R₁ + R₂ = C (a constant), then maximum resistance R is obtained if ____________.

Let f(x) = 1 + 2x² + 2²x⁴ + …… + 2¹⁰x²⁰. Then f (x) has ____________.

If A is a square matrix of order 3, |A′| = −3, then |AA′| = ______.

If f'(x) = `x + 1/x`, then f(x) is ______.

The solution set of the inequality 3x + 5y < 4 is ______.

The corner points of the shaded unbounded feasible region of an LPP are (0, 4), (0.6, 1.6) and (3, 0) as shown in the figure. The minimum value of the objective function Z = 4x + 6y occurs at ______.

If A is a square matrix of order 3 and |A| = 5, then |adj A| = ______.

P is a point on the line joining the points A(0, 5, −2) and B(3, −1, 2). If the x-coordinate of P is 6, then its z-coordinate is ______.

Prove that the function f is surjective, where f: N → N such that `f(n) = {{:((n + 1)/2",", if "n is odd"),(n/2",", if  "n is even"):}` Is the function injective? Justify your answer.

Solve the following Linear Programming Problem graphically:

Maximize Z = 400x + 300y subject to x + y ≤ 200, x ≤ 40, x ≥ 20, y ≥ 0

If A = `[(2, -3, 5),(3, 2, -4),(1, 1, -2)]`, find A^–1. Use A^–1 to solve the following system of equations 2x − 3y + 5z = 11, 3x + 2y – 4z = –5, x + y – 2z = –3