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CBSE Sample Papers for Class 12 Maths Paper 3

CBSE Sample Papers for Class 12 Maths Paper 3 are part of CBSE Sample Papers for Class 12 Maths. Here we have given CBSE Sample Papers for Class 12 Maths Paper 3.

CBSE Sample Papers for Class 12 Maths Paper 3

Board CBSE
Class XII
Subject Maths
Sample Paper Set Paper 3
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 3 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.
CBSE Sample Papers for Class 12 Maths Paper 3 1

Question 2.
Evaluate cosec(\(\frac { 1 }{ 2 }\)sec-1\(\frac { 5 }{ 3 }\))

Question 3.
Find the identity element for the binary operation * as a* b = \(\frac { ab }{ 2 }\) ∀ a, b ∈Q – {0}

Question 4.
CBSE Sample Papers for Class 12 Maths Paper 3 2

SECTION B

Question 5.
Find the value of y – x from the following equation
CBSE Sample Papers for Class 12 Maths Paper 3 3

Question 6.
A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/sec. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?

Question 7.
CBSE Sample Papers for Class 12 Maths Paper 3 4

Question 8.
Using differentials find the approximate value of (3.968)3/2 upto 3 places of decimals.

Question 9.
Find the general solution of the following differential equation:
\(\frac { dy }{ dx }\) = 1 + x2 + y2 + x2y2

Question 10.
Write the value of p for which \(\vec { a } =3\hat { i } +4\hat { j } +9\hat { k }\) and \(\vec { b } =\hat { i } +p\hat { j } +3\hat { k }\) are parallel vectors.

Question 11.
In a school there are 1000 students out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. What is the probability that a student choosen randomly studies in class XII, given that the choosen student is a girl.

Question 12.
CBSE Sample Papers for Class 12 Maths Paper 3 5

SECTION C

Question 13.
CBSE Sample Papers for Class 12 Maths Paper 3 6

Question 14.
CBSE Sample Papers for Class 12 Maths Paper 3 7

Question 15.
A given quantity of metal is to be cast into a half cylinder with a rectangular base and semicircular ends. Show that the total surface area is minimum when the ratio of the length of the cylinder to the diameter of its semicircular ends is π : (π + 2).

Question 16.
Find the intervals in which the function f(x) = sin x + cos x, 0 ≤ x ≤ 2π is strictly increasing or strictly decreasing.

Question 17.
Find the value of k if f(x) is continuous at x = 2
CBSE Sample Papers for Class 12 Maths Paper 3 8

Question 18.
CBSE Sample Papers for Class 12 Maths Paper 3 9

Question 19.
CBSE Sample Papers for Class 12 Maths Paper 3 10

Question 20.
CBSE Sample Papers for Class 12 Maths Paper 3 11

Question 21.
Find the equation of the perpendicular drawn from the point P(2, 4, -1) to the line \(\frac { x+5 }{ 1 } =\frac { y+3 }{ 4 } =\frac { z-6 }{ -9 }\). Also write the coordinates of the foot of the perpendicular from P to the line.

Question 22.
A drunk man takes a step forward with probability 0.4 and backwards with probability 0.6. Find the probability that at the end of 11 steps, he is just one step away from the starting point. Is drinking alcohol a good habit? Why?

Question 23.
For three persons A, B, C the chances of being selected as a manager of a firm are in the ratio 4 : 1 : 2 respectively. The respective probabilities for them to introduce a radical change in marketing strategies are 0.3, 0.8 and 0.5. If the change take place, find the probability that it is due to the appointment of B.

SECTION D

Question 24.
Using matrices solve the following system of equations
x + y + z = 1, x – 2y + 3z = 2, x – 3y + 5z = 3
OR
CBSE Sample Papers for Class 12 Maths Paper 3 12

Question 25.
Let * be a binary operation on Q defined by a * b = \(\frac { 3ab }{ 5 }\). Show that * is commutative, associative. Also find its identity element if exist.

Question 26.
Find the area of the region bounded by the curve y2 = 2y – x and the y-axis.
OR
Find the area of the region given by {(x, y) : x2 ≤ y ≤ |x|)

Question 27.
CBSE Sample Papers for Class 12 Maths Paper 3 13

Question 28.
Find the equation of the plane passing through the point P(1, 1, 1) and containing the line \(\vec { r } =\left( 3\hat { i } +\hat { j } +5\hat { k } \right) +\lambda \left( 3\hat { i } -\hat { j } -5\hat { k } \right)\). Also show that the plane contains the line \(\vec { r } =\left( -\hat { i } +2\hat { j } +5\hat { k } \right) +\mu \left( \hat { i } -2\hat { j } -5\hat { k } \right)\)

Question 29.
A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts while it takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of ₹ 2.50 per package of nuts and ₹ 1.00 per package of bolt. How many package of each type should be produced each day so as to maximise his profit if he operates his machines for at most 12 hours a day? Formulate this as LPP and solve it.

Solutions

Solution 1.
2 sin2x – 3 sinx + 1 = 0
x = \(\frac { \pi }{ 2 }\) , \(\frac { \pi }{ 6 }\)

Solution 2.
√5

Solution 3.
a * e = e * a = a
\(\frac { ea }{ 2 }\) = a ⇒ e = 2

Solution 4.
CBSE Sample Papers for Class 12 Maths Paper 3 14

Solution 5.
CBSE Sample Papers for Class 12 Maths Paper 3 15

Solution 6.
CBSE Sample Papers for Class 12 Maths Paper 3 16

Solution 7.
CBSE Sample Papers for Class 12 Maths Paper 3 17

Solution 8.
CBSE Sample Papers for Class 12 Maths Paper 3 18

Solution 9.
CBSE Sample Papers for Class 12 Maths Paper 3 19

Solution 10.
CBSE Sample Papers for Class 12 Maths Paper 3 20

Solution 11.
E1: Student choosen randomly studies in class XII
E2: Student choosen randomly is a girl.
CBSE Sample Papers for Class 12 Maths Paper 3 21

Solution 12.
CBSE Sample Papers for Class 12 Maths Paper 3 22

Solution 13.
CBSE Sample Papers for Class 12 Maths Paper 3 23
CBSE Sample Papers for Class 12 Maths Paper 3 24

Solution 14.
CBSE Sample Papers for Class 12 Maths Paper 3 25

Solution 15.
Let radius of half cylinder is r and its height = h
CBSE Sample Papers for Class 12 Maths Paper 3 26

Solution 16.
CBSE Sample Papers for Class 12 Maths Paper 3 27

Solution 17.
CBSE Sample Papers for Class 12 Maths Paper 3 28

Solution 18.
CBSE Sample Papers for Class 12 Maths Paper 3 29

Solution 19.
CBSE Sample Papers for Class 12 Maths Paper 3 30

Solution 20.
CBSE Sample Papers for Class 12 Maths Paper 3 31
CBSE Sample Papers for Class 12 Maths Paper 3 32

Solution 21.
CBSE Sample Papers for Class 12 Maths Paper 3 33

Solution 22.
CBSE Sample Papers for Class 12 Maths Paper 3 33.1

Solution 23.
E1: Person A is selected as manager
E2: Person B is selected as manager
E3: Person C is selected as manager
A: Selected person introduce radical change in marketing strategy
CBSE Sample Papers for Class 12 Maths Paper 3 34

Solution 24.
CBSE Sample Papers for Class 12 Maths Paper 3 35
CBSE Sample Papers for Class 12 Maths Paper 3 36

Solution 25.
* is commutative because a * b = b * a
* is associative because a * (b * c) = (a * b) * c
Let identity element is e.
a * e = e * a = a
e = \(\frac { 5 }{ 3 }\)

Solution 26.
CBSE Sample Papers for Class 12 Maths Paper 3 37

Solution 27.
CBSE Sample Papers for Class 12 Maths Paper 3 38

Solution 28.
CBSE Sample Papers for Class 12 Maths Paper 3 39

Solution 29.
Let manufacturer produces x package of nuts and y package of bolts.
Objective function is maximise profit Z = ₹ 2.50x + 1y
Subject to constraints are
x + 3y ≤ 12
3x + y ≤ 12
x, y ≥ 0
CBSE Sample Papers for Class 12 Maths Paper 3 40
Hence maximum profit is ₹ 10.50 when 3 package of nuts and 3 package of bolts manufacture.

We hope the CBSE Sample Papers for Class 12 Maths Paper 3 help you. If you have any query regarding CBSE Sample Papers for Class 12 Maths Paper 3, drop a comment below and we will get back to you at the earliest.

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