# Class 12 Mathematics Sample Paper

Refer to below provided Class 12 Mathematics Sample Paper with solutions. These Guess papers for Mathematics Class 12 have been designed based on the latest examination guidelines and paper pattern issued by CBSE. We have provided all Sample Papers for Class 12 Mathematics with answers. You can click on the links below to access the practice papers for free.

## CBSE Sample Papers for Class 12 Mathematics

## Class 12 Mathematics Sample Paper Term 2 Set A

**Section – A**

**1. Find: ∫1/ ^{dx}cos^{2}x(1=tanx)^{2}**

^{}

**OR**

**Evaluate:∫dx/1- tanx**

**Answer:**We have given

**2. Determine the order and degree of the following differential equationd ^{2}y/dx^{2} =cos3x+sin3x **

** Determine the order and degree of the following differential equation:** d/dx(dy/dx)=5

Sol. Here, d/dx(dy/dx)=5

⇒ d

^{2}y/dx

^{2}=5 ⇒ [d

^{2}y]/dx

^{2}]-

^{1}=5

∴ order = 2 and degree = 1

and sum = 2 + 1 = 3.

**Answe:**d

^{2}y/dx2-cos3x=0

The highest order derivative present in the differential equation is

d

^{2}y/dx

^{2}. Therefore, its order is two.

It is a polynomial equation in d

^{2}y/dx

^{2}and the power raised to d

^{2}y/dx

^{2}is 1.

Hence, its degree is one.

**3. Find a vector r equally inclined to the three axes and whose magnitude is 3√ 3 units.**

**Answer: ** We have

Since, r^{→} is equally inclined to the three axes, direction consines of the unit vector r^{→} will be same.

i.e. l = m = n

Now we know that,

**4. Find the value of λ such that the line x-2/6=y-1/λ==z+5/-4 is perpendicular to the plane 3x–y–2z = 7.**

**Answer: ** Given that line x-2/6=y-1/λ/-1=z+5/-4 is perpendicular to plane 3x – y – 2z = 7

6/3=λ/-1/-4/-2

[∴ When a line is perpendicular to a plane, their direction ratios are proportional]

**5. Three persons A, B and C, fire at a target in turn, starting with A. Their probability of hitting the target are 0.4, 0.3 and 0.2 respectively. Find the probability of two hits. **

**Answer: ** Here,

**6. A die is rolled. Consider the events**

A = {2,4,6}, B = {4,5}, C = {3,4,5,6}

Find P[A ∪ B/C]. **Answer: **

### **Section – B**

**7. Evaluate :∫ _{0}π/2 log sinx dx**

**Answer:**

**8. Solve the following differential equation :**

**dy/dx+y =cos x- sin xORGiven that dy/dx= e-2y and if x = 5, then y = 0. When y = 3, then find the value of x.**

**Answer:**Given differential equation is

dy/dx+y=cosx-sinx …(1)

**9. Using vectors, find the area of a triangle with vertices A (1, 1, 2), B (2, 3, 5) and C(1, 5, 5).**

**Answer: **

**10. Find the shortest distance between the following pair of lines :ORFind the cartesian equation of the line passing through the point A (1, 2, –4) and perpendicular to the lines:x-3/1=y-5/-2=z-7/1 and x+1/7=y+1/-6=z+1/1ORFind the cartesian equation of the line passing through the point A (1, 2, –4) and perpendicular to thelines:x-4/2=y-2/3=z-3/4 and x-1/1=y+2/-3=z-3/5**

**Answer:**

### **Section – C**

**11. Evaluate :∫3x+4/(x-1)(x-3) ^{dx}**

^{}

**Answer:**Let

Put

**12. Find the area of the region enclosed between the parabola 4y = 3×2 and the line 3x – 2y + 12 = 0.ORFind the area of the region quadrant enclosed by x-axis, line x = √3y and the circle x**

^{2}+ y

^{2}= 4.

**Answer:**

**13. Find the distance of point **

from the line

measured parallel to the plane x – y + 2z –3 = 0.

**Answer: **

**14. In an office three employees Vinay, Sonia and Iqbal process incoming copies of a certain from. Vinay processes 50% of the forms. Sonia processes 20% and Iqbal processes the remaining 30% of the forms.****Vinay has an error rate of 0.06%, Sonia has an error rate of 0.04% and Iqbal has an error rate of 0.03%. **

Based on the above information answer the following:

(i) The total probability of committing an error in processing the form is?

(ii) The manager of the company wants to do a quality check. During inspection he selects a form at random from the days output of processed forms. If the form selected at random has an error, the probability that the form is NOT processed by Vinay is?**Answer: **