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

Feasible region (shaded) for a LPP is shown in the Figure Minimum of Z = 4x + 3y occurs at the point ______.

The common region determined by all the linear constraints of a LPP is called the ______ region.

Three machines E₁, E₂, E₃ in a certain factory produced 50%, 25% and 25%, respectively, of the total daily output of electric tubes. It is known that 4% of the tubes produced one each of machines E₁ and E₂ are defective, and that 5% of those produced on E₃ are defective. If one tube is picked up at random from a day’s production, calculate the probability that it is defective.

Find the probability that in 10 throws of a fair die a score which is a multiple of 3 will be obtained in at least 8 of the throws.

Let A and B be two events. If P(A) = 0.2, P(B) = 0.4, P(A ∪ B) = 0.6, then P(A|B) is equal to ______.

If P(A) = `4/5`, and P(A ∩ B) = `7/10`, then P(B|A) is equal to ______.

If P(A ∩ B) = `7/10` and P(B) = `17/20`, then P(A|B) equals ______.

If P(A) = `3/10`, P(B) = `2/5` and P(A ∪ B) = `3/5`, then P(B|A) + P(A|B) equals ______.

If P(A) = `2/5`, P(B) = `3/10` and P(A ∩ B) = `1/5`, then P(A|B).P(B'|A') is equal to ______.

If P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6, then P(A ∪ B) is equal to ______.

In maximization problem, optimal solution occurring at corner point yields the ____________.

The radius of a cylinder is increasing at the rate of 3 m/s and its height is decreasing at the rate of 4 m/s. The rate of change of volume when the radius is 4 m and height is 6 m, is ____________.

A particle is moving along the curve x = at² + bt + c. If ac = b², then particle would be moving with uniform ____________.

The rate of change of area of a circle with respect to its radius r at r = 6 cm is ____________.

Total revenue in rupees received from the sale of x units of a product is given by R(x)= 3x²+ 36x + 5. The marginal revenue, when x = 15 is ____________.

If the rate of change of the area of the circle is equal to the rate of change of its diameter then its radius is equal to ____________.

The rate of change of volume of a sphere is equal to the rate of change of the radius than its radius equal to ____________.

If the rate of change of volume of a sphere is equal to the rate of change of its radius then the surface area of a sphere is ____________.

A man 1.6 m tall walks at the rate of 0.3 m/sec away from a street light that is 4 m above the ground. At what rate is the tip of his shadow moving? At what rate is his shadow lengthening?

Find the direction ratio and direction cosines of a line parallel to the line whose equations are 6x − 12 = 3y + 9 = 2z − 2