Class 12 is an important step for students in which they face a national level competition. Scores in class 12 have their own weightage in many graduation and post graduation competitions. Mathematics is a highly scoring subject although it demands much practice. For helping students to prepare oureducation.in is presenting MP Board Class 12 Maths Sample Paper. We hope this paper will be helpful for you.

**Time- 3.00 hr** **Marks-100**

**Instruction :**

- All questions are compulsory
- There is no overall choise. Question paper consist of 25 Questions divide into 5 sections A,B,C,D & E. Each sections comprises 5 questions and carry 2,3,4,5 & 6 marks respectively.
- Use of calci is not permitted.
- An additional 15 min time has been allotted to read this question papper.

**Section- A**

- Y= (sinx + 3cosx) / tanx. Find dy/dx.
- A man was going 15m in north direction & then he turns in left direction & move forward
MP Board Class 12 Maths Sample Paper

10m. What is the distance from starting point to end point?

- If dy/dx= tanx-3x + 3cosx. Find the value of y.
- What was the integral of x sinx ?
- A+B=15, A-B= 10. Find the value of A*B ?

**Section- B**

- If A&B is a symmetric matrix. Prove that AB +BA is also a symmetric matrix.
- Find the eq of line which passing through point (3,3,5) & parallel to the vector 3i+4j+7k.
- Find the principle value of tan(-π/2S)
- If matrix A=(3,4,5). Find AA* where A* is the transpose of A.
- A= 3i+4j+8k & B=4i+6j+6k. Find A*B.

**Section- C**

- Find the position vector of mid point of the vectoc joining the points (3,5,7) & (5,7,7)
- Line y= mx+7 is a tangent of a curve y^2=4x. Find the value of m
- 2x=3y=tanx. Find dy/dx
- A is the non singular Square matrix of order 3. Find adj A.
- Find the area of region lying in the first quadrant & bounded by y^2=4x, x=0, y=1&y=4

**Section- D**

- Find the vector eq of a plane which is at the distance of 9 units from the origin & normal to the vector 3i+5j+7k.
- If P be the coordinate be (3,4,6). Find the equation of the plane passing through P & perpendicular to OP.
- Solve the linear equation by matrix method 3x+4y+6z=12, 4x+5y+7z=34, 3x+5y+7z=4.
- A family has two children. Find the probability that both are boys, if it is known that

(i) At least one of the children is a boy.

(ii) The elder child is boy.

- Find the equation of the plane passing through the points (3,5,7) & (4,5,8) & parallel to the line x-1/2 = y-3/5= z/2.

**Section- E**

- Using integration find the area of triangle ABC, coordinate of whose vertex is A(2,5) B(4,6) C(5,5).
- Solve the equation dy/dx + 15y = 3x.
- Find the integral of ( 1+ x)/(3+ x^2)
- If p(A)=1/3 & p(B)= 1/2 & p(A) & p(B) is the mutually exclusive event then find p(AUB)
- IF trace of a matrix is 13 & determinant is 3 then defines its eigen value.

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MP Board Model Paper Class 12th

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