• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer

CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

  • NCERT Solutions
    • NCERT Solutions for Class 12 English Flamingo and Vistas
    • NCERT Solutions for Class 11 English
    • NCERT Solutions for Class 11 Hindi
    • NCERT Solutions for Class 12 Hindi
    • NCERT Books Free Download
  • TS Grewal
    • TS Grewal Class 12 Accountancy Solutions
    • TS Grewal Class 11 Accountancy Solutions
  • CBSE Sample Papers
  • NCERT Exemplar Problems
  • English Grammar
    • Wordfeud Cheat
  • MCQ Questions

CBSE Sample Papers for Class 12 Maths Paper 2

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.
CBSE Sample Papers for Class 12 Maths Paper 2 1

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.
CBSE Sample Papers for Class 12 Maths Paper 2 2

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
CBSE Sample Papers for Class 12 Maths Paper 2 3

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-1y is a solution of the differential equation y2y’ + y2 + 1 = 0.

Question 11.
CBSE Sample Papers for Class 12 Maths Paper 2 4

Question 12.
CBSE Sample Papers for Class 12 Maths Paper 2 5

SECTION C

Question 13.
CBSE Sample Papers for Class 12 Maths Paper 2 6

Question 14.
CBSE Sample Papers for Class 12 Maths Paper 2 7

Question 15.
CBSE Sample Papers for Class 12 Maths Paper 2 8

Question 16.
CBSE Sample Papers for Class 12 Maths Paper 2 9
CBSE Sample Papers for Class 12 Maths Paper 2 10

Question 17.
CBSE Sample Papers for Class 12 Maths Paper 2 11

Question 18.
CBSE Sample Papers for Class 12 Maths Paper 2 12

Question 19.
CBSE Sample Papers for Class 12 Maths Paper 2 13

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
CBSE Sample Papers for Class 12 Maths Paper 2 14

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
CBSE Sample Papers for Class 12 Maths Paper 2 15

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
CBSE Sample Papers for Class 12 Maths Paper 2 16

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.
CBSE Sample Papers for Class 12 Maths Paper 2 17

Solution 6.
CBSE Sample Papers for Class 12 Maths Paper 2 18

Solution 7.
CBSE Sample Papers for Class 12 Maths Paper 2 19
Volume is increased by 3%.

Solution 8.
CBSE Sample Papers for Class 12 Maths Paper 2 20

Solution 9.
CBSE Sample Papers for Class 12 Maths Paper 2 21

Solution 10.
Differentiate x + y = tan-1y and get y2y’ + y2 + 1 = 0

Solution 11.
CBSE Sample Papers for Class 12 Maths Paper 2 22

Solution 12.
CBSE Sample Papers for Class 12 Maths Paper 2 23

Solution 13.
CBSE Sample Papers for Class 12 Maths Paper 2 24

Solution 14.
CBSE Sample Papers for Class 12 Maths Paper 2 25

Solution 15.
C1 → C1 + C2 + C3
Taking (a + b + c)2 common from C1 then R1 → R1 – R2
R2 → R2 – R3 and expand

Solution 16.
CBSE Sample Papers for Class 12 Maths Paper 2 26

Solution 17.
CBSE Sample Papers for Class 12 Maths Paper 2 27

Solution 18.
CBSE Sample Papers for Class 12 Maths Paper 2 28

Solution 19.
CBSE Sample Papers for Class 12 Maths Paper 2 29

Solution 20.
CBSE Sample Papers for Class 12 Maths Paper 2 30

Solution 21.
CBSE Sample Papers for Class 12 Maths Paper 2 31

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.
CBSE Sample Papers for Class 12 Maths Paper 2 32
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.
CBSE Sample Papers for Class 12 Maths Paper 2 33
CBSE Sample Papers for Class 12 Maths Paper 2 34

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
CBSE Sample Papers for Class 12 Maths Paper 2 35
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.
CBSE Sample Papers for Class 12 Maths Paper 2 36
CBSE Sample Papers for Class 12 Maths Paper 2 37

Solution 27.
CBSE Sample Papers for Class 12 Maths Paper 2 38

Solution 28.
E1: Selected student is a boy; E2 : Selected student is a girl
A: Selected student having IQ more than 150
CBSE Sample Papers for Class 12 Maths Paper 2 39

Solution 29.
CBSE Sample Papers for Class 12 Maths Paper 2 40

We hope the CBSE Sample Papers for Class 12 Maths Paper 2 help you. If you have any query regarding CBSE Sample Papers for Class 12 Maths Paper 2, drop a comment below and we will get back to you at the earliest.

Primary Sidebar

NCERT Exemplar problems With Solutions CBSE Previous Year Questions with Solutoins CBSE Sample Papers
  • The Summer Of The Beautiful White Horse Answers
  • Job Application Letter class 12 Samples
  • Science Lab Manual Class 9
  • Letter to The Editor Class 12 Samples
  • Unseen Passage For Class 6 Answers
  • NCERT Solutions for Class 12 Hindi Core
  • Invitation and Replies Class 12 Examples
  • Advertisement Writing Class 11 Examples
  • Lab Manual Class 10 Science

Recent Posts

  • Understanding Diversity Question Answer Class 6 Social Science Civics Chapter 1 NCERT Solutions
  • Our Changing Earth Question Answer Class 7 Social Science Geography Chapter 3 NCERT Solutions
  • Inside Our Earth Question Answer Class 7 Social Science Geography Chapter 2 NCERT Solutions
  • Rulers and Buildings Question Answer Class 7 Social Science History Chapter 5 NCERT Solutions
  • On Equality Question Answer Class 7 Social Science Civics Chapter 1 NCERT Solutions
  • Role of the Government in Health Question Answer Class 7 Social Science Civics Chapter 2 NCERT Solutions
  • Vital Villages, Thriving Towns Question Answer Class 6 Social Science History Chapter 9 NCERT Solutions
  • New Empires and Kingdoms Question Answer Class 6 Social Science History Chapter 11 NCERT Solutions
  • The Delhi Sultans Question Answer Class 7 Social Science History Chapter 3 NCERT Solutions
  • The Mughal Empire Question Answer Class 7 Social Science History Chapter 4 NCERT Solutions
  • India: Climate Vegetation and Wildlife Question Answer Class 6 Social Science Geography Chapter 8 NCERT Solutions
  • Traders, Kings and Pilgrims Question Answer Class 6 Social Science History Chapter 10 NCERT Solutions
  • Environment Question Answer Class 7 Social Science Geography Chapter 1 NCERT Solutions
  • Understanding Advertising Question Answer Class 7 Social Science Civics Chapter 7 NCERT Solutions
  • The Making of Regional Cultures Question Answer Class 7 Social Science History Chapter 9 NCERT Solutions

Footer

Maths NCERT Solutions

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 11 Maths
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 8 Maths
NCERT Solutions for Class 7 Maths
NCERT Solutions for Class 6 Maths

SCIENCE NCERT SOLUTIONS

NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Chemistry
NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 9 Science
NCERT Solutions for Class 7 Science
MCQ Questions NCERT Solutions
CBSE Sample Papers
NCERT Exemplar Solutions LCM and GCF Calculator
TS Grewal Accountancy Class 12 Solutions
TS Grewal Accountancy Class 11 Solutions