# Class 12 Mathematics Sample Paper

We have provided Class 12 Mathematics Sample Paper as per the latest CBSE examination pattern for the current academic year. The following CBSE Sample Papers for Class 12 Mathematics has been prepared based on the guess papers issued recently. Students will be able to practice these papers and get good marks in upcoming Mathematics exams for Class 12.

## Class 12 Mathematics Sample Paper Term 2 With Solutions Set A

### Section – A

1. A problem of mathematics is given to 3 students whose chances of solving are
1/2
1/3
1/4
What is the probability that the problem will be solved?
Answer: Let A, B, C be the respective events of solving the problem.
Then,

Clearly A, B, C are independent events and the problem will be solved if at least one student solves it.
Required probability

2. If A(1, 2, – 2) and B(3, – 4, 5) are two points, find the direction cosines of OA, OB and AO.
Answer: The direction cosines of OA are proportional to 1 – 0, 2 – 0, – 2 – 0 or 1, 2, – 2.
Hence, the actual direction cosines of OA are :

OR
1/3,2/3,-2/3

Therefore, the direction cosines of A O will be −1/3,-2/3,2/3·
Similarly, the direction cosines of OB will be///////
OR

3. Find the solution of the differential equation:
dy/dx=x/x2+1
Integrating both side

4. Find:∫ex(sin4x-4/1-cos4x)dx
OR
Evaluate:∫dx/1+ tanx·

OR

5. If  b  , and c are unit vectors such that a+ b+ c = 0 , then find the value of a· b+ b· c+ c· a .

6. If P(not A) = 0.7, P(B) = 0.7 and P(B/A) = 0.5, then find P(A/B) and P(A ∪ B).

### Section – B

7. Find the cartesian equation of the plane passing through points A(0, 0, 0) and B(3, –1, 2), parallel to the
line x -4/1=y+3/-4 =z+1/7.
OR
Find the vector equation of the line passing through the point (1, 2, – 4) and perpendicular to the two lines:
x-8/3=y+19/-16=z-10/7 and x -15/3= y-29/8=z-5/-5

OR

8. Find the area of parallelogram, whose diagonals are a =3î +j -2k^ and  b=î-3j+4k^
Answer: Let ABCD be a parallelogram and its diagonals are

9. Solve the differential equation:
y+xdy/dx=x-ydy/dx
OR
Find a particular solution of the differential equation (x +1) dy/dx
= 2e-y-1given y = 0, when x = 0.

OR

10. Evaluate:∫dx/2 sin2 x+5 cos2 x

### Section – C

11.Evaluate:∫42x/x2+1dx

12. Using integration, find the area bounded by the curve x2 = 4y and the line x = 4y – 2.
OR
Find the area of the region:
{(x, y) : y2≤ 4x, 4x2 +4y2 ≤ 9}

OR

13. Find the vector and cartesian equation of the plane containing the two lines