The CBSE has scheduled the Class 12th Mathematics Examination 2020 on March 17, 2020. The students can go through the below-mentioned questions for chapter 6 - Application of Derivatives for the upcoming examination. These questions are based on the latest pattern prescribed by the CBSE Board.
Question 1- Find the dimensions of the rectangle of perimeter 36 cm which will sweep out a volume as large as possible, when revolved about one of its sides. Also, find the maximum volume.
Answer: 864 π cm3
Question 2- A metal box with a square base and vertical sides is to contain 1024 cm3. If the material For the top and bottom costs 5per cm2 and the material for the sides costs 2.50 per cm2. Then, find the least cost of the box.
Answer: Least cost of the box will be = ` 1920
Question 3- At what point, the slope of the curve y = -x3 + 3x2 + 9x - 27 is maximum? Also, find the maximum slope.
Answer: The maximum slope of the given curve is at x = 1. The maximum slope will be 12.
Question 4- At what points on the curve x2 + y2 - 2x - 4y + 1 = 0, the tangents a parallel to the Y- axis?
Answer: The required points are (- 1, 2) and (3, 2).
Question 5- Find the equation of the normal lines to the curve 3x2 -y2 = 8 which are parallel to the line x + 3y = 4.
Answer: The required equations are 3y + x = ± 8
Question 6- If the sum of lengths of the hypotenuse and a side of a right-angled triangle is given, then show that the area of the triangle is maximum when the angle between them is π / 3.
Answer: Area of the right-angled triangle is maximum when the angle between them is π / 3
Question 7- Find the points of local maxima, local minima and the points of inflexion of the function f(x) = x5 - 5x4 + 5x3 - 1. Also, find the corresponding local maximum and local minimum values.
Answer: Maximum value of y is given by 0 and the minimum value is given by - 298.
Question 8- A telephone company in a town has 500 subscribers on its list and collects fixed charges of 300 per subscriber per year. The company proposes to increase the annual subscription and it is believed that for every increase of 1 per one subscriber will discontinue the service. Find what increase will bring maximum profit?
Answer: The company should increase the subscription fee by 100 so that it has a maximum profit.
Question 9- Find the angle of intersection of the curves y = 4 - x2 and y = x2
Question 10- If x and y are the sides of two squares such that y = x - x2, then find the rate of change of the area of the second square with respect to the area of the first square.
Answer: 2x2 - 3x + 1
These were some of the important questions that can be expected in the upcoming CBSE Class 12th Mathematics Examination 2020 are based on the NCERT textbook, previous year papers and sample papers. The students can also go through the below-mentioned links: