# Maths Sample Papers for Class 12 CBSE Board

CBSE is the short name of Central Board of Secondary Education which affiliates all the public as well as Private School. CBSE is govern by the Central Governing Body and the exams are conducted for AISSCE. In this post, I have tried to prepare Maths Sample Papers for Class 12 CBSE Board the 5th paper under the Sample Papers for Class 12 CBSE Mathematics Series and you will find more sample Papers in the below mentioned links. We will soon update more CBSE Mathematics Sample Papers for Class 12 also. Till than you can improve your practice by taking help from **CBSE Maths Sample Paper for Class 12.**

**S ample Paper for Class 12 CBSE Mathematics**

**MATHEMATICS **Time allowed : 3 hours Maximum marks : 100

**General Instructions are:**

**1.** All questions 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.

**3. **Use of calculators is not permitted.

**4.** All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.

**SECTION- A ****Question number 1 to 10 carry one mark each**

**1.** Evaluate: ʃ x sec^2 3x dx

**2.** Evaluate: ʃ sin 2x dx over limits from 0 to π/4.

**3**. On the set Z of integers, if the binary operation * is defined by a*b=a+b*2, then find the identity element.

**4.** A matrix has 16 elements. What are the possible orders it can have?

**5.** What do you mean by collinear vectors? Illustrate with an example.

**6.** Find the angle between the vectors with direction ratios proportional to 4,-3,5 and 3,4,5.

**7.** If [a-b,2b]= [2,6]. Then find the value of a and b.

**8.** Find the unit vector in the direction of a vector PQ, where P and Q are the points (1,2,3) and (4,5,6).

**9.** Write the principal argument of sec^-1 (2).

**10.** If A=diag (1 -1 2) and B=diag (2 3 -1), find A+B and 3A+4B.

**SECTION- B Question number 11 to 22 carry 4 marks each**

**11.** If f’(x)=( 1/sin(x-a) cos(x-b)) then find the value of f(x).

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

**13.** Differentiate the following function w.r.t x: e^cos^-1(√1-x^2).

**14**. Find the equation of the tangent line to the curve x=1-cosα, y=α-sinα at α=π/4.

**15.** Prove the following: 2 tan^-1 (1/5)+ sec^-1((5√2)/7)+2 tan^-1(1/8)=π/4.

** 16.** Find the length and the foot of the perpendicular from the point (7,14,5) to the plane 2x+4y z=2.

**17.** Solve: (dy/dx) + y sec x= tan x.

**18.** Solve: (3xy +y^2) dx + (x^2+xy)dy=0.

**19.** Using vectors prove that Medians of a triangle are concurrent.

**20.** Differentiate x^x with respect to x log x.

**21.** The mean and variance of a binomial distribution are 4 and 4/3 respectively, find P(X>=1).

**22.** Using determinants, find the area of the triangle whose vertices are (-2,4), (2,-6) and (5,4). Are the given points col-linear?

**SECTION- C Question number 23 to 29 carry 6 marks each**

**23.**A diet is to contain at least 400 units of carbohydrate, 500 units of fat, and 300 units of protein. Two food are available: F1, which costs Rs 2 per unit, and F2, which costs Rs 4 per unit. A unit of food F1 contains 10 units of carbohydrate, 20 units of fat, and 15 units of protein; a unit of food F2 contains 25 units of carbohydrate, 10 units of fat, and 20 units of protein. Find the minimum cost for a diet that consists of a mixture of these two food and also meets the minimum nutrition requirements. Formulate the problem as a linear programming problem.

**24.**Show that the triangle of maximum area that can be inscribed in a given circle is an equilateral triangle.

**OR**

Show that the semi-vertical angle of a right circular cone of given surface area and maximum volume is sin^-1(1/3).

**25.**Using integration, find the area of the triangle ABC whose vertices have coordinates A(2,5), B(4,7) and C(6,2).

**OR**

Find the area of the region enclosed by the parabola y^2=4ax and the chord y=mx.

**26.**In a test, an examiner either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he makes a guess is 1/3 and the probability that he copies the answer is 1/6.The probability that his answer is correct, given that he copied it, is 1/8. Find the probability that he knew the answer to the question ,given that he correctly answered it.

27.Evaluate the following: ʃ ((2x-3)/(x^2 +3x-18))dx

**OR**Solve the following: ʃ(x/(x^2+x+1))dx

**28.**Solve the following system of equations, using matrix method: X+2y+z=7, x+3z=11, 2x-3y=1

**29.**Find the equation of the plane through the points (1,0,-1),(3,2,2) and parallel to the line x-1/1= y-1/-2= z-2/3.

**Click following to get pdf of Maths Sample Papers for Class 12 CBSE Board**

**CBSE 12th Maths Sample Paper****CBSE Math Sample Paper Class 12****CBSE Class 12 Mathematics Question Paper**

**Click following to get more Maths Sample Papers for Class 12 CBSE Board**

**SET-1 CBSE Sample Papers for Class 12th Maths****SET-2 CBSE Maths Sample paper for Class 12****SET-3 CBSE Sample Papers Class 12 Maths****SET-4****Sample Paper of Class 12th CBSE Maths****SET-6****Class 12 CBSE Maths Sample Papers****SET-7****CBSE 12th Maths Sample Paper****SET-8****CBSE Maths Sample Paper for Class 12**

These are the some of the questions which has been asked in the final exams conducted by the CBSE BOARD.If you want something more to add then let me know through the comment section given below the post. **Wish you all the best for your exams.**

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