# Sample Paper of Class 12th CBSE Maths

Mar 11 • Board Sample Papers • 4207 Views • 5 Comments on Sample Paper of Class 12th CBSE Maths

Central Board of Secondary Education is the most toughest Board that students needs to appear.The Board conducts Board Exam every year for the class 10th and 12th once thus, to perform well in these exam is the dream to every appearing student. Here, in this post I have tried to made available Maths Sample Paper for Class 12 CBSE, which is based on the paper pattern. The choice of questions are made to give an appropriate idea of type of questions asked in the exam so that students will able to secure good marks in their Final exams. To practice more you can also take help from Maths Sample Paper for Class 12 CBSE.

This is the 4th Maths Sample Paper for Class 12 CBSE in the sample paper series.  Very soon I will update more sample paper for Class 12 students to check board students preparation.

Time: 3 Hours                                                                                                        Max. Marks:100

General Instructions:

1. All question are compulsory.
2. The question paper consists of 29 questions divided into three sections A, B and C.

Section A comprises of 10 questions of one mark each.

Section B comprises of 12 questions of four marks each.

Section C comprises of 7 questions of six marks each.

4. Use of calculators is not permitted.

5. There is no overall choice. However, internal choice has been provided in 4 questions of four marks each and 2 questions of six marks each.

SECTION-A
(Question number 1 to 10 carry ONE mark each)

1) EVALUATE: ∫ xsin 3x dx

2) EVALUATE:-
π/4
ʃ tan^2 x dx
0
3) If the binary operation ‘*’ on the set ‘z’ is defined by a*b=a+b-5,then find the identity element with respect to ‘*’.

4) If AB=A and BA=B,then show that A^2=A,B^2=B.

5) Find the magnitude of vector a =(i+3j-2k)*(-i+3k).

6) P(6,3,2),Q(5,1,4) and R(3,3,5) are the vertices of triangle PQR. Find angle pqr.

7) Find the vector from the origin O to the centroid of the triangle whose vertices are (1,-1,2),(2,1,3) and (-1,2,1).

8) Find the area of triangle whose vertices are A(3,-1,2),B(1,-1,-3) and C(4,-3,1)

9) If A^2-A+I=0 ,find A inverse.

10) Find the principal argument of tan^-1(1).

SECTION-B
(Question number 11 to 22 carry FOUR mark each)

11) EVALUATE: ʃ(sin x/1+sin x )dx

12) Let R be a relation on the set of all lines in a plane defined by (l1,l2)ɛ R line l1 is parallel to l2.

Or Show that the relation ‘is congruent to’ on set of all triangles in a plane is an equivalence relation.

13) If y=(3*e^2x)+2*e^3x,prove that f’’(x)-5*f’(x)+6y=0.

Or  If y=sin^-1 (x),show that (1-x^2)*f’’(x)-x*f’(x)=0

14) Find the equation of all lines having slope 2 and being tangent to the curve y+(2/(x-3)).

Or  Find points on the curve ((x^2/)4) +((y^2)/25) at which the tangents are
(i) parallel to x-axis                                                                                (ii) parallel to y-axis.

15) Prove that :tan^-1 (1/5) +tan^-1(1/7) +tan^-(1/3)+tan^-(1/8)=pi/4

16) Show that angles between diagonal of a cube is cos^-1(1/3).

Or A line makes angles a,b,c,d with the 4 diagonals of a cube then prove that cos^2 (a)+cos^2(b)+cos^2(c)+cos^2(d)=4/3

17) Find the differential equation of all the circles touching the x-axis at the origin.

18) Solve :2y*e^(x/y)dx+(y-2x*e^(x/y)dy=0

19) Prove that:If A and B are square matrices of same order such that AB=BA,then prove that by induction that A(B)^n=((B)^N)A.Further prove that (AB)^n=(A^n)(B^N)

20) A man takes a step forward with probability 0.4 and backwards with probability 0.6.find the probability that at the end of eleven steps he is just one step away from the starting point.

21) Discuss the continuity of the function f defined by F(x)=x+2;if x1

22) Find the derivative of f given by f(x)=tan^-1 (x) assuming it exists.

Or  Find the derivative of f given by f(x)=sin^-1 (x) assuming it exists.

SECTION-C
(Question number 23 to 29 carry SEVEN mark each)

23) A manufacturer of a line of patent medicines is preparing a production plan on medicines A and B.There are sufficient ingredients available to make 20000 bottles of A and 40000 bottles of B but there are only 45000 bottles into which either of medicines can be put.Furthermore,it takes 3 hours to prepare enough material to fill 1000 bottles of B and there are 66 hours available for this operation.The profit is Rs. 8 per bottle for A and Rs.7 for bottle B.Formulate this problem as a linear problem.

24) Using the integration,find the area of the region bounded between the lines x=2 and the parabola y^2=8x.

Or Using integration,find the area of the triangular region,the equations of whose sides are y=2x+1,y=3x+1 and x=4.

25) Show that the volume of the largest cone that can be inscribed in a sphere of radius R IS 8/27 of the volume of the sphere.

Or An open box with a square base is to be made out of a given quantity of cardboard of area c^2 square units.Show that the maximum volume of the box is c^3/6*(3)^1/2 units.

26) EVALUATE:ʃ(3sin x+2 cos x)/(3 cos x +2sin x) dx

Or EVALUATE: ʃ(3cos x +2)/(sin x+2 cos x+3) dx

27) A card from a pack of 52 card is lost.From the remaining cards of the pack,two cards are drawn and are found to be hearts .Find the probability of the the missing card to be a heart.

28) Find the equation of plane passing through the line of intersection of the planes 2x+y-z=3,5x-3y+4z+9=0 and parallel to the line (x-1)/2 =(y-3)/4 =(z-5)/5.

29) Use matrix method to examine the following system of equations for consistency or inconsistency-2y=3,6x-3y=5.

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All the Best for your Exam Preparations..!!!!