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Tuesday, January 9, 2018

CBSE CLASS 12 MATHS PRACTICE TEST PAPER FOR CONTINUITY, DIFFERENTIATION, APPLICATIONS OF DERIVATIVE

Class 12 Maths Practice Test Paper/ Mock Test Paper 

CBSE CLASS 12 MATHS PRACTICE PAPER

Topics : Continuity, Differentiation and Applications of Derivatives

  TIME – 1:30 Hr                                                                                                                  M.M. 50

Very short answer type question (1 Mark)

1. Find the point of discontinuity, if any, for the function f( x )= 1 x5 ;
2.Verify LMV theorem for the function f( x )=|x|in[ 1,1 ]

Short answers type questions. (2 marks)

3.Find two positive numbers whose sum is 15 and sum of whose squares is minimum.
4.Find the equation of the tangent to the curve y= 4x3 , if slope of the tangent is 2/3.
5.Verify Rolle’s theorem f( x )=sinx+cosxin[ 0, Π 2 ]
6.For what value of k, is the following function continuous at x = 0? f( x )={ k,x=0 sin5x 3x ,x0
7.A Particle moves along the curve y= 2 3 x 3 +1 .Find the points on the curve at which the y coordinates changes twice as fast as x coordinates.

Long answer type questions – I( 4 marks)

8.Prove that function f( x )= { k,x=0 x |x|+2 x 2 ,x0 is discontinuous at x = 0.
9. If x=2cosθcos2θandy=2sinθsin2θ,find ( d 2 y d x 2 ) θ= π 2
10.Find the intervals in which the function f given f( x )=sinx+cosx,0x2π 1. is strictly increasing or strictly decreasing.
11.Water is running into a conical tank of height 10 m and diameter 10 m at the top, at a constant rate of 18 m3/min. How fast is the water rising in the tank at any instant.
12.Show that the surface area of a closed cuboid with a square base and given volume is minimum, when it is a cube.

Long answer type questions – II( 6 marks)

13.Determine, the points on the curve y= 1 4 x 2 which are nearest to the point (0, 5).
14.A point on the hypotenuse of a right – angle triangle is at distances a and b from the sides of the triangle. Show that the minimum length of the hypotenuse is ( a 2 3 + b 2 3 ) 3 2

Also Read : CBSE Class 12 Maths Sample Paper 2018

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