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

Find all the points of local maxima and local minima of the function f(x) = (x - 1)³ (x + 1)²

Find the local minimum value of the function f(x) `= "sin"^4" x + cos"^4 "x", 0 < "x" < pi/2`

Find the points of local maxima and local minima respectively for the function f(x) = sin 2x - x, where `-pi/2 le "x" le pi/2`

If y `= "ax - b"/(("x" - 1)("x" - 4))` has a turning point P(2, -1), then find the value of a and b respectively.

Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x².

If y = x³ + x² + x + 1, then y ____________.

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 ____________.

Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2^nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3^rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.

The value of c in the particular solution given that y(0) = 0 and k = 0.049 is ______.

One card is drawn at random from a well-shuffled deck of 52 cards. In which of the following case is the events E and F independent?

E : ‘the card drawn is a spade’

F : ‘the card drawn is an ace’

One card is drawn at random from a well-shuffled deck of 52 cards. In which of the following case is the events E and F independent?

E : ‘the card drawn is black’

F : ‘the card drawn is a king’