CBSE Sample Papers for Class 12 Maths Paper 7 are part of CBSE Sample Papers for Class 12 Maths. Here we have given CBSE Sample Papers for Class 12 Maths Paper 7.

## CBSE Sample Papers for Class 12 Maths Paper 7

Board |
CBSE |

Class |
XII |

Subject |
Maths |

Sample Paper Set |
Paper 7 |

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 7 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 of order 3 and |adj A| = 144, then find the value of |3A| ?

Question 2.

Question 3.

Evaluate \(\int { \frac { { sec }^{ 2 }\left( logx \right) }{ x } } dx\)

Question 4.

Differentiate log (x + \(\sqrt { { x }^{ 2 }+{ a }^{ 2 } }\)) with respect to x.

**SECTION B**

Question 5.

Using elementary transformation find the inverse of the matrix \(\begin{pmatrix} 5 & 4 \\ 3 & 2 \end{pmatrix}\)

Question 6.

Using differentials find the approximate value of f(5.001) where f(x) = x^{3} – 7x^{2} + 15.

Question 7.

Find the equations of tangents to the curve 3x^{2} – y^{2} = 8 which passes through the point (\(\frac { 4 }{ 3 }\) , 0)

Question 8.

If cos y = x cos (a + y) prove that \(\frac { dy }{ dx } =\frac { { cos }^{ 2 }\left( a+y \right) }{ sina }\)

Question 9.

Find the coordinate of the point where the line \(\frac { x+1 }{ 2 } =\frac { y+2 }{ 3 } =\frac { z+3 }{ 4 }\) meets the plane x + y + 4z = 6.

Question 10.

Let A and B are two events such that P (\(\bar { A\cup B }\)) = \(\frac { 1 }{ 6 }\), P(A ∩ B) = \(\frac { 1 }{ 4 }\) and P(\(\bar { A }\)) = \(\frac { 1 }{ 4 }\) .Prove that A and B are independent events.

Question 11.

Solve for x, tan^{-1}2x + tan^{-1}3x = \(\frac { \pi }{ 4 }\)

Question 12.

Evaluate \(\int { \frac { x-4 }{ \left( x-2 \right) ^{ 3 } } } { e }^{ x }dx\)

**SECTION C**

Question 13.

Question 14.

Question 15.

Question 16.

Question 17.

Question 18.

Form the differential equation of the family of circles in the first quadrant which touches the coordinate axes.

Question 19.

Question 20.

Question 21.

An instructor has a question bank consisting of 300 easy True/False questions, 200 difficult True/False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question.

Question 22.

An insurance company insured 2000 scooters and 3000 motorcycles. The probability of an accident involving a scooter is 0.01 and that of a motorcycle is 0.02. An insured vehicle met with an accident. Find the probability that the accidented vehicle was a motorcycle. How we can avoid accidents?

Question 23.

**SECTION D**

Question 24.

If the sum of the lengths of the hypotenuse and a side of a right angled triangle is given, show that the area of the triangle is maximum when the angle between them is \(\frac { \pi }{ 3 }\).

**OR**

A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8m^{3}. If building of tank cost ₹ 70 per square metre for the base and ₹ 45 per square metre for the sides, what is the cost of least expensive tank?

Question 25.

Find the area of the region included between the parabola y^{2} = x and the line x + y = 2 using integration.

**OR**

Find the area of the smaller region bounded by the ellipse \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\) and the line \(\frac { x }{ 3 } +\frac { y }{ 2 } =1\) using integration.

Question 26.

If \(A=\left( \begin{matrix} 3 & 2 & -1 \\ -2 & 1 & 2 \\ 1 & -3 & 1 \end{matrix} \right)\) , find A^{-1}. Hence solve the system of linear equations

3x – 2y + z = 2

2x + y – 3z = – 5

-x + 2y + z = 6

Question 27.

A company manufactures two types of toys. Toys of Type A require 5 minutes each for cutting and 10 minutes each for assembling. Toys of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours available for assembling. The profit is ₹ 0.50 each for type A and ₹ 0.60 each for type B toys. How many toys of each type should be manufactured in order to maximize the profit?

Question 28.

The points A (4, 5, 10), B(2, 3, 4) and C(1, 2, -1) are three vertices of a parallelogram ABCD. Find the vector and cartesian equation of the sides AB and BC and find coordinates of D.

**OR**

Find the angle between lines whose direction cosines are given by the relations 3l + m + 5n = 0 and 6mn – 2nl + 5lm = 0

Question 29.

Solve the differential equation \(\frac { dy }{ dx }\) = sin (x + y) + cos (x + y)

**Solutions**

Solution 1.

Solution 2.

Solution 3.

Solution 4.

Solution 5.

Solution 6.

Solution 7.

Solution 8.

Solution 9.

Solution 10.

Solution 11.

Solution 12.

Solution 13.

Solution 14.

Solution 15.

Solution 16.

Solution 17.

Solution 18.

Equation of family of circle in the first quadrant which touches both the coordinate axes is

Solution 19.

Solution 20.

Solution 21.

Let E_{1} is the event: it is an easy question

E_{2} is the event: it is an M.C.Q (Multiple Choice Question)

True/False Easy Question = 300

True/False Difficult Question = 200

MCQ easy question = 500

Difficult MCQ = 400

Total Questions = 300 + 200 + 500 + 400 = 1400

Total easy questions = 300 + 500 = 800

Total difficult questions = 200 + 400 = 600

E_{1} ∩ E_{2} = easy M.C.Q = 500

E_{2} = 500 + 400 = 900

Solution 22.

E_{1} : Total insured scooters = 2000

E_{2} : Total insured motorcycles = 3000

Total vehicles = 5000

A is the event insured vehicle meets with an accident.

Solution 23.

Solution 24.

Solution 25.

Solution 26.

Solution 27.

Let x type A and y type B toys manufactured.

Hence profit is maximum at the point (8, 20) means 8 toys of type A and 20 toys of type B should be manufactured.

Solution 28.

In parallelogram diagonal bisect to each other, so mid point of BD = Mid point of AC

Solution 29.

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