CBSE Sample Papers for Class 12 Maths Paper 2 are part of CBSE Sample Papers for Class 12 Maths. Here we have given CBSE Sample Papers for Class 12 Maths Paper 2.

## CBSE Sample Papers for Class 12 Maths Paper 2

Board |
CBSE |

Class |
XII |

Subject |
Maths |

Sample Paper Set |
Paper 2 |

Category |
CBSE Sample Papers |

Students who are going to appear for CBSE Class 12 Examinations are advised to practice the CBSE sample papers given here which is designed as per the latest Syllabus and marking scheme as prescribed by the CBSE is given here. Paper 2 of Solved CBSE Sample Paper for Class 12 Maths is given below with free PDF download solutions.

**Time: 3 Hours**

**Maximum Marks: 100**

**General Instructions:**

- All questions are compulsory.
- Questions 1-4 in section A are very short answer type questions carrying 1 mark each.
- Questions 5-12 in section B are short answer type questions carrying 2 marks each.
- Questions 13-23 in section C are long answer I type questions carrying 4 marks each.
- Questions 24-29 in section D are long answer II type questions carrying 6 marks each.

**SECTION A**

Question 1.

If A is a square matrix and |A| = 2, then write the value of |AA’| where A’ is the transpose of matrix A.

Question 2.

Find the distance between the parallel planes \(\vec { r } \cdot \left( 2\hat { i } -\hat { j } +3\hat { k } \right) =4\) and \(\vec { r } \cdot \left( 6\hat { i } -3\hat { j } +9\hat { k } \right) +13=0\)

Question 3.

Question 4.

If f(x) = |cos x| find the value of f'(\(\frac { 3\pi }{ 4 }\))

**SECTION B**

Question 5.

Find x and y if 2X + 3Y = \(\begin{pmatrix} 2 & 3 \\ 4 & 0 \end{pmatrix}\) and 3X + 2Y = \(\begin{pmatrix} 2 & -2 \\ -1 & 5 \end{pmatrix}\)

Question 6.

Question 7.

Find the approximate change in volume V of a cube of side x meter caused by increasing the side by 1%.

Question 8.

Check the differentiability of f(x) at x = 1

Question 9.

Find the vector and the Cartesian equation for the line through the points A (3, 4, -7) and B(5, 1, 6).

Question 10.

Show that x + y = tan^{-1}y is a solution of the differential equation y^{2}y’ + y^{2} + 1 = 0.

Question 11.

Question 12.

**SECTION C**

Question 13.

Question 14.

Question 15.

Question 16.

Question 17.

Question 18.

Question 19.

Question 20.

Form the differential equation representing the family of circles in the first quadrant which touches the both coordinate axis.

Question 21.

Find the general solution of the differential equation

Question 22.

Past records shows that 80% of the operations performed by a certain doctor were successful. If he performs 4 operations in a day, what is the probability that atleast 3 operations will be successful? Name any two life skills to be successful in life.

Question 23.

If set A = Q x Q. Let * be a binary operation on A defined by (a, b) * (c, d) = (ac, ad + b) where a, b, c, d ∈ Q; a ≠ 0, c ≠ 0 find the inverse and identity element of (a, b) ∈ A.

**OR**

Show that the relation R on the set A = {x ∈ Z : 0 ≤ x ≤ 12} given by R = {{a, b): |a – b| is a multiple of 4} is an equivalence relation.

**SECTION D**

Question 24.

Solve the following system of equations using matrix method

Question 25.

A library has to accommodate two different types of books on a shelf. The books are 6 cm and 4 cm thick and weigh 1 kg and 1.5 kg respectively. The shelf is 90 cm long and at most can support a weight of 21 kg. How the shelf should be filled with the books of two types in order to include maximum number of books. Form a LPP and solve it.

Question 26.

Find the intervals in which the function f(x) = (x – 1)^{3} (x + 2)^{2} is strictly increasing or strictly decreasing. Also find the points of local maximum and local minimum if any.

**OR**

If the sum of the surface areas of cube and a sphere is constant, what is the ratio of an edge of the cube to the diameter of the sphere when the sum of their volumes is minimum?

Question 27.

Find the value of \(\int _{ -1 }^{ 2 }{ \left( { x }^{ 2 }+7x-5 \right) } dx\) as a limit of sum.

**OR**

Using integration find the area of the region bounded by the line x – y + 2 = 0 and the curve x = √y and the y-axis.

Question 28.

In a class having 60% boys, 5% of the boys and 10% of the girls have an IQ of more than 150. A student is selected at random and found to have an IQ of more than 150. Find the probability that the selected student is a boy.

Question 29.

Find the shortest distance between the lines

**Solutions**

Solution 1.

|AA’| = |A| |A’| = |A|^{2} = 4

Solution 2.

distance = \(\frac { 25 }{ \surd 126 }\)

Solution 3.

a = 1, b = 5

Solution 4.

f(x) = -cos x

f'(\(\frac { 3\pi }{ 4 }\)) = \(\frac { 1 }{ \surd 2 }\)

Solution 5.

Solution 6.

Solution 7.

Volume is increased by 3%.

Solution 8.

Solution 9.

Solution 10.

Differentiate x + y = tan^{-1}y and get y^{2}y’ + y^{2} + 1 = 0

Solution 11.

Solution 12.

Solution 13.

Solution 14.

Solution 15.

C_{1} → C_{1} + C_{2} + C_{3}

Taking (a + b + c)^{2} common from C_{1} then R_{1} → R_{1} – R_{2}

R_{2} → R_{2} – R_{3} and expand

Solution 16.

Solution 17.

Solution 18.

Solution 19.

Solution 20.

Solution 21.

Solution 22.

P(successful operations performed by doctor) = 80% = \(\frac { 4 }{ 5 }\)

q = \(\frac { 1 }{ 5 }\) , n = 4

Required probability = P(3) + P(4) using binomial distribution = \(\frac { 512 }{ 625 }\)

Like skills: Punctuality, hard work

Solution 23.

Prove R is reflexive, Prove R is symmetric, Prove R is transitive.

Because R is reflexive, symmetric and transitive, so R is an equivalence relation.

Solution 24.

Solution 25.

Let x books of type I and y books of type II are accommodated on a shelf.

Objective function is maximize Z = x + y

Subject to constraints are

6x + 4y ≤ 90

x + 1.5y ≤ 21

x, y ≥ 0

Value of Z is maximum at x = \(\frac { 51 }{ 5 }\) and y = \(\frac { 36 }{ 5 }\), books cannot be in fraction, so 10 books of type I and 7 books of type II can be placed.

Solution 26.

Solution 27.

Solution 28.

E_{1}: Selected student is a boy; E_{2} : Selected student is a girl

A: Selected student having IQ more than 150

Solution 29.

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