Mathematics is one of the most interesting subject but at the same time it is the toughest subject to prepare. But with little concentration and attention, one will able to perform well in this subject. Here in this post, I have prepared following CBSE Sample Papers Class 12 Maths for appearing students of Board Exam which is according to latest pattern. The marks assigned to each module are according to the actual CBSE Exam Paper. Sample papers are generally preferred to check the preparation before going for exam, to know which topic require more attention. The given **CBSE Sample Papers Class 12 Maths** is designed for the same purpose.

This is the **3rd**** Sample Paper** of Maths Sample Paper series and we will very soon update more mathematics soon.

**CBSE Sample Papers Class 12 Maths**

**General Instructions:**

1) All questions are compulsory.

2) The question paper consists of 29 questions divided into three sections A, B and C.

**Section A** consists of 10 questions of 1 mark each.

**Section B** consists of 12 questions of 4 marks each.

** Section C** comprises of 7 questions of 6 marks each.

3) Use of calculators is not permitted.

4) There is no overall choice. However internal choices are there.

5) All questions in section A are to be answered in one word, one sentence or as per the requirement of the question.

**SECTION-A**

**(Question number 1 to 10 contains ONE mark each)**

**1) **Two definite sets **A** and **B** consist of **m** and **n** elements respectively. The number of subsets in A exceeds that of B by 112. Find the value of **m** and **n**.

**2) **Find the angle between the vectors (a-b) and (a+b) when vector a=(1,1,4) and vector b=(1,-1,4).

**3) **f(x)=(x**^2**-10x+25)**/**(x**^2**-7x+10) for x ≠ 5 and f is continuous at x=5,the find the value of f(5).

**4)** A=[(1 1 1),(b+c c+a a+b),(b+c-a c+a-b a+b-c),](row-wise),then find determinant of A.

**5) ** A=[(4 2),(3 1)](row-wise) Then find the inverse of A.

**6)** Find the value of COS**^-1**(pi/3-Sin**^-1**(1/2)).

**7)** Find the value of X,Y,Z & t when the following matrices are equal [(x+y y-z),(5-t 7+x)] , and [(t-x z-t),(z-y x+z+t)] (row-wise).

**8)** The position vectors of the points A and B are 5i-2j and -4i+3j respectively. Find the position vectors of the trisection points of the line segment AB .

**9)** Find the ratio in which the line joining (2, 4, 5) and (3, 5,-4) is divided by the y-z plane.

**10)** Find the order and degree of the differential equation dy/dx+1/dy/dx=6 d^(3)y/d^(3)y.

**Section-B**

**(Question number 11 to 22 contains FOUR marks each)**

**11)** **(i)** A bag contains 3 red and 5 black balls and a second bag contains 6 red and 4 black balls. A ball is drawn from each bag. Find the probability that both are (i) red, and (ii) black.

**OR**

**(ii)** Find the probability that a leap year has 53 Sundays.

**12)** If ∆=[(1+a 1 1),(1 1+b 1),(1 1 1+c)] (row-wise) , then for non zero a, b, c, if mod ∆ =0. Find the value of 1/a+1/b+1/c .

**13)** Sin^(-1)θ+Sin^(-1) (1-θ)=Cos^(-1)θ . Find the value of θ.

**14)** Prove that the function f(x)=Sin(pi * mod(x)) is continuous at x=0 but is not differentiable there.

**15)** If vector A, vector B,& vector C are perpendicular to vector(b+c), vector(c+a) and vector(a+b) respectively and, if modulus of vector(a+b)=6,vector(b+c)=8 and vector(c+a)=10, then find the value of mod vector(a+b+c).

**16)** If the straight lines x=1+s, y=-3-λs, z=1+λs and , y=1+t, z=2-t, with parameter s and t respectively, are co-planner, then find the value of λ.

**17)** Find dy/dx of the following y=tan^(-1)(x/1+√(1+x^2))+ Sin(2 tan^(-1)√(1-x/1+x)).

**18)** If x=e^t Sin t , y=e^t Cos t, t is a parameter, then find d^2y/dx^2 at (1,1).

**19) **Solve ∫ dx/Cos(5+3 Cos x)

**20)** Solve ∫Sin 2x dx/(Sin x +Cos x)^2

**21)** definite integral with lower power ‘0’ and higher power ‘pi’ ∫mod(Sin x + Cos x)dx

**22)** A relation R on the set of integers Z is defined as follows:(x,y) ε R implies that x ε Z, mod X ≤4 and Y= MOD(x+1). Find the domain and range of R.

**SECTION-C**

**(Question number 23 to 29 contains SIX marks each)**

**23)** Three faces of a fair die are yellow, two faces are red and one blue. The die is tossed three times. Find the probability that the colors yellow, red and blue appear in the 1^{st}, 2^{nd} and 3^{rd} tosses respectively.

**OR**

(ii) A bag contains 8 red balls and 5 white balls. Two successive draws of 3 balls are made without replacement. Find the probability that the first drawing will give 3 white balls and the second three red balls.

**24)** A dealer in rural area wishes to purchase a number of sewing machines. He has only Rs 5670.00 to invest and space for at most 20 items. An electronic sewing machine costs him Rs 360.00 and a manually operated machine Rs 240.00. He can sell an electronic sewing machine at a profit of Rs 22.00 and a manually operated machine at profit of Rs 18.00. Assuming that he can sell all the items that he can buy how should he invest his money in order to maximize his profit. Make it a linear programming problem and solve it graphically. Keeping the rural background in mind justify the ‘values’ to be promoted for the selection of the manually operated machine.

**25) ** A variable plane x/a + y/b + z/c at a unit distance from origin cuts the co-ordinate axes at A, B and C. Centroid (x, y, z) satisfies the equation 1/x^2 + 1/y^2 + 1/z^2 . Find the value of k.

**26)** Solve the differential equation**(any one)**:

(i) x(y dx+ x dy) Cos(xy)+ Sin(xy) dx=0

(ii) (xy^2 + e^(1/x^3))dx – x^2y dy=0; given y=0, when x=1.

**27)** Find the abscissa of the point on the curve xy=(c+x)^2 , the normal at which cuts off numerically equal intercepts from the axes of co-ordinates.

**28)** Show that, the area bounded by the parabola y^2=4ax and a double ordinate, is two- thirds of the rectangle formed by this ordinate and the abscissa.

**29) **If A=[(3 2 -1),(1 1 1),(5 1 -1)] (row-wise), show that A*.A^-1=A^-1*A . Hence solve the following system of equations : x+2y-3z=-4, 2x+3y+2z=2, 3x-3y-4z=11.

**Click following to get pdf of previous year CBSE Sample Papers Class 12 Maths**

**Sample Question Paper for Class 12 CBSE 2013****CBSE Sample Papers 2012 for Class 12 Maths****Sample Papers for Class 12 CBSE Mathematics 2010****CBSE Class 12 Maths Question Paper 2009**

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

**SET-1 CBSE Sample Papers for Class 12th Maths****SET-2 CBSE Maths Sample paper for Class 12****SET-4****Sample Paper of Class 12th CBSE Maths****SET-5 Sample Paper for Class 12 CBSE Mathematics****SET-6****Class 12 CBSE Maths Sample Papers****SET-7****CBSE 12th Maths Sample Paper****SET-8****CBSE Maths Sample Paper for Class 12**

If you want something more to add, please let me know through the comment section given below the post.**Best of Luck for your Exam..!!!!**

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