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.

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.

**SECTION B**

Question 5.

Find the value of y – x from the following equation

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.

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 + x^{2} + y^{2} + x^{2}y^{2}

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.

**SECTION C**

Question 13.

Question 14.

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

Question 18.

Question 19.

Question 20.

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**

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 y^{2} = 2y – x and the y-axis.

**OR**

Find the area of the region given by {(x, y) : x^{2} ≤ y ≤ |x|)

Question 27.

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 sin^{2}x – 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.

Solution 5.

Solution 6.

Solution 7.

Solution 8.

Solution 9.

Solution 10.

Solution 11.

E_{1}: Student choosen randomly studies in class XII

E_{2}: Student choosen randomly is a girl.

Solution 12.

Solution 13.

Solution 14.

Solution 15.

Let radius of half cylinder is r and its height = h

Solution 16.

Solution 17.

Solution 18.

Solution 19.

Solution 20.

Solution 21.

Solution 22.

Solution 23.

E_{1}: Person A is selected as manager

E_{2}: Person B is selected as manager

E_{3}: Person C is selected as manager

A: Selected person introduce radical change in marketing strategy

Solution 24.

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.

Solution 27.

Solution 28.

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

Hence maximum profit is ₹ 10.50 when 3 package of nuts and 3 package of bolts manufacture.

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