Mathematics : Practice Questions and Answers

The length of the rectangle is changing at a rate of 4 cm/s and the area is changing at the rate of 8 cm/s. What will be the rate of change of width if the length is 4cm and the width is 1 cm.

The total cost N(x) in rupees, associated with the production of x units of an item is given by N(x) = 0.06x³ - 0.01x² + 10x - 200. Find the marginal cost when 5 units are produced.

If the circumference of the circle is changing at the rate of 5 cm/s then what will be rate of change of area of the circle if the radius is 6cm.

The rate of change of area of a square is 16 cm²/s. What will be the rate of change of side if the side is 4 cm?

The edge of a cube is increasing at a rate of 7 cm/s. Find the rate of change of area of the cube when x=6 cm.

If the rate of change of radius of a circle is 6 cm/s then find the rate of change of area of the circle when r=2 cm.

The total cost P(x) in rupees associated with a product is given by P(x) = 0.4x² + 2x - 50. Find the marginal cost if the number of units produced is 5.

The longest side of a triangle is 2 times the shortest side and the third side is 4 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

Find all pairs of consecutive odd positive integers both of which are smaller than 8 such that their sum is more than 10.

Rahul obtained 65 and 70 marks in first two tests. Find the minimum marks he should get in the third test to have an average of at least 60 marks.

If x-1>-x+7 then which is true?

If 2x+1 > 5 then which is true?

If x is a whole number and 10x≤then find solution set of x.

If x is a natural number and 20x≤then find solution set of x.

If x is a positive integer and 2x > 4, then which is true?

If x>7 then -x>-7 is ___________

If x>5 then 2x>10 is true or not?

If x>7 then which is impossible?

If x>7 then x+2>9 is true?