# Maths Sample Paper for Class 12 CBSE

Central Board of Secondary Education is the most finest and reputed Board of Education that maintain the quality standards in the field of Education for both private as well as public Schools across the country. To get excellent marks in the Board Exams conducted by CBSE is like a dream come true for any of the appearing candidate. Here I have tried to prepare** Maths Sample Paper for Class 12 CBSE Board** to help in order to get good marks in your Board Exams. Maths is one of the most interesting subject but at the same time it demands for proper concentration to solve the questions. A little mistake is sufficient enough to extract your marks. So, practice the given sample paper to prepare well for the exams.

This is the **10th Maths Sample Paper for Class 12 CBSE** series and you will find more sample Papers from the links given below this sample paper. We will soon update more mathematics sample papers for class 12 in this series for for guide you.

**General Instruction for the Maths Sample Paper for Class 12 CBSE:**

**1)** All questions are compulsory.

**2)** The question paper consists of 30 questions divided into three section A comprises of 10 questions of one mark each, section B comprises of 15 questions of four marks each and section C comprises of 05 questions of six marks each.

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

**4)** Marks are allotted to each question for your convenience.

**Section – A**

**Q 1.** What is the principal value of cos^(-1)〖(cos〖2π/3〗 )+ 〗 sin^(-1)〖(sin(((2π/3)?**[1]**

**Q 2.** For what value of x, the following matrix is singular ? [■( 5-x&x+1@2&4)]. **[1]**

**Q 3.** Give an example of a relation which is reflexive and transitive but not Symmetric.**[1]**

**Q 4.** If x = a cos t and y = a sin t. Find dy/dx. **[1]**

**Q 5.** If f: R→R is defined by f(x) = 3x + 2, define fof (x).v **[1]**

**Q 6.** If |■(x&x@1&x)| = |■(3&4@1&2)| , write the positive value of x.**[1]**

**Q 7.** The radius of a circle is increasing at the rate of 0.7 cm/s. what is the rate of increasing of its circumference? **[1]**

**Q 8.** Find the value of x for which is a unit vector. **[1]**

**Q 9.** Show that the points (2,3,4), (-1,-2,1),(5,8,7) are collinear. **[1]**

**Q 10.** Evaluate : ∫_1^(√3)▒dx/(1+x^2 ). **[1]**

**Section – B**

**Q 11.** Using properties of determinants, prove that | ■(-bc&b^2+bc&c^2+bc@a^2+ac&-ac&c^2+ac@a^2+ab&b^2+ab&-ab) |= (ab+bc+ca)^3. **[4]**

**Q 12**. Prove the following : 〖cot〗^(-1)[(√(1+sinx)+√(1-sinx))/√(1+sinx-√(1-sinx))]= x/2,x є(0,π/4 ).**[4]**

**Q 13.** Differentiate 〖sin〗^(-1)(2x√(1- x^2 )) with respect to 〖cos〗^(-1)((1- x^2)/(1+ x^2 )).**[4]**

**Q 14.** Find the shortest distance between the lines, whose equations are **[4]**

(x-8)/3=(y+9)/(-16)=(10-z)/(-7) and (x-5)/3=(58-2y)/(-16)=(z-5)/(-5) .**[4]**

**Q 15.** Find the value of a for which the function f defined as f (x) = {■(asin (π( x+1), )/2 ,x ≤0@tan〖x-sinx〗/x^3 ,x>0)┤ is continuous at x = 0. **[4]**

**Q 16.** Use Rolle’s theorem to find the condition for the polynomial equation f(x)=0 to have a repeated real root .Hence or otherwise prove that

1+ x/1!+x^2/2!+x^3/3!+⋯+x^n/n!=0,can not have repeated root. **[4]**

**Q 17.** Find the mean number of heads in three tosses of a fair coin.**[4]**

**Q 18.** Evaluate ∫_0^1▒(3x^2+2x+1) dx. as the limit of the sum. **[4]**

**Q 19.** Solve the differential equation :〖cos〗^2x dy/dx+y=tanx. **[4]**

**Q 20**. For what λ € R the system of equations [**4]**

2x – y + 3=0

X + λy +7=0

3x + 2y-2=0

Is consistent ? solve the equations for that value of λ.

**Q 21.** Evaluate the equation

lim┬(x→0)〖(∛(1+x^2 )-1)/(x^2)〗 . **[4]**

Q 2**2.** Find the domain and range of f(x)=(x2-3x+2)/x2+x-6. **[4]**

**Q 23.** Evaluate: ∫_0^(π/2)▒〖2sinxcosx 〖tan〗^(-1)〖(sinx )□(24&dx)〗 **[4]**

**Q 24.** Let f(x)=1+x , 0<=x<=2 **[4]**

3-x , 2<x<=3.

Determine f{f(x)} and hence find the points of discontinuity and non differentiability. Also, draw the graph of f{f(x)} at [0,3].** [4]**

**Q 25.**Find the equation of the tangent line to the curve y = x2 – 2x+7 is parallel to the line

2x – y + 9 = 0 .

**[4]**

**Section – C**

**Q 26.** Solve the differential equation: (tan-1y – x)dy = (1 + y2) dx.**[5]**

**Q 27.** Consider f : R→[-5,∞) given by f(x) = 9×2+6x-5. Show that f is Invertible.

Find the inverse of f. **[5] **

**Q 28.** Use product [■(1&-1&2@0&2&-3@3&-2&4)][■(-2&0&1@9&2&-3@6&1&-2)] to solve the system of equations :

x– y + 2z = 1 , 2y – 3z = 1 and 3x – 2y +4z = 2. **[5]**

**Q 29.** Every gram of wheat provides 0.1 g of proteins and 0.25 g of carbohydrates. The corresponding values for rice are 0.05g and 0.5 g respectively. Wheat costs Rs. 4 per kg and rice Rs. 6 per kg. The minimum daily requirements of proteins and carbohydrates for an average child are 5 g and 200 g respectively. In what qualities should wheat and rice in the daily diet to provide minimum daily requirements of proteins and carbohydrates at minimum cost. Form a L.P.P. and solve it graphically. **[5]**

**Q 30.** A window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 m, find the dimensions of the rectangle that will produce the largest area of the window. **[5]**

We always welcomed your valuable thoughts about the paper pattern or the content of this Maths Sample Paper for Class 12 CBSE. Put your views in the below comment section for the further improvement of this Maths Sample Paper.

**BEST OF LUCK FOR YOUR PREPARATIONS…!!!**

**NOTE:** To get pdf of above sample paper,follow:

**Maths Sample Paper for Class 12 CBSE**

To get pdf of more maths sample paper, follow:

**1) CBSE Maths Sample Paper for Class 12**

**2) CBSE 12th Maths Sample Paper**

**For more Sample papers click on the following links.**

**1) CBSE Sample Papers for Class 12th Maths**

**2) Sample Paper for Mathematics CBSE Class 12**

**3) Sample Question Papers for Class 12 CBSE Maths**

**4) Sample Paper for Class 12 CBSE Mathematics**

**5) CBSE Mathematics Sample Papers for Class 12**

**6)** **Sample Paper of Class 12th CBSE Maths**

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