CBSE Sample Papers for Class 12 Maths Paper 8 are part of CBSE Sample Papers for Class 12 Maths. Here we have given CBSE Sample Papers for Class 12 Maths Paper 8.

## CBSE Sample Papers for Class 12 Maths Paper 8

Board |
CBSE |

Class |
XII |

Subject |
Maths |

Sample Paper Set |
Paper 8 |

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 8 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 the 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 line makes angles 90° and 60° respectively with the positive directions of x and y-axes, find the angle which it makes with the positive direction of the z-axis.

Question 2.

Evaluate: \(\int _{ 2 }^{ 3 }{ { 3 }^{ x }dx }\)

Question 3.

If A is a 3 x 3 invertible matrix, then what will be the value of k if det (A^{-1}) = (det A) k?

Question 4.

**SECTION B**

Question 5.

Prove that if E and F are independent events, then the events E and F’ are also independent.

Question 6.

A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is ₹ 100 and that on a bracelet is ₹ 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced.

Question 7.

Find \(\int { \frac { dx }{ { x }^{ 2 }+4x+8 } }\)

Question 8.

Show that all the diagonal elements of a skew-symmetric matrix are zero.

Question 9.

Question 10.

Show that the function f(x) = 4x^{3} – 18x^{2} + 27x – 7 is always increasing on R.

Question 11.

Find the vector equation of the line passing through the point A(1, 2, -1) and parallel to the line 5x – 25 = 14 – 7y = 35z.

Question 12.

For the curve y = 5x – 2x^{3}, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when x = 3.

**SECTION C**

Question 13.

Question 14.

Prove that x^{2} – y^{2} = c (x^{2} + y^{2})^{2} is the general solution of the differential equation (x^{3} – 3xy^{2}) dx = (y^{3} – 3x^{2}y) dy, where C is a parameter.

Question 15.

Question 16.

Often it is taken that a truthful person commands more respect in society. A man is known to speak the truth 4 out of 5 times. He throws a dice and reports that it is a six. Find the probability that it is actually a six. Do you also agree that the value of truthfulness leads to more respect in society?

Question 17.

Question 18.

Question 19.

Question 20.

Question 21.

Using vectors find the area of triangle ABC with vertices A (1, 2, 3), B (2, -1, 4) and C (4, 5, -1).

Question 22.

Solve the following L.P.P. graphically

Maximise z = 4x + y

Subject to following constraints

x + y ≤ 50

3x + y ≤ 90

x ≥ 10

x, y ≥ 0

Question 23.

**SECTION D**

Question 24.

Using integration, find the area of a region bounded by the triangle whose vertices are (-2, 1), (0, 4) and (2, 3)

**OR**

Find the area bounded by the circle x^{2} + y^{2} = 16, the line √3 y = x and x-axis in the first quadrant, using integration.

Question 25.

Solve the differential equation x \(\frac { dy }{ dx }\) + y = x cos x + sin x, given that y = 1 when x = \(\frac { \pi }{ 2 }\)

Question 26.

Question 27.

Question 28.

A metal box with a square base and vertical sides is to contain 1024 cm^{3}. The material for the top and bottom costs ₹ 5 per cm^{2} and the material for the sides costs ₹ 2.50 per cm^{2}. Find the least cost of the box.

Question 29.

**Solutions**

Solution 1.

Let lines make an angle α, β, γ with +ve directions of x, y, and z-axis

Solution 2.

Solution 3.

Solution 4.

Solution 5.

Solution 6.

Number of necklaces produced per day = x

Number of bracelets produced per day = y

Objective function is maximise profit z = ₹ (100 x + 300 y)

Subject to constraints are

Solution 7.

Solution 8.

Let A is a square matrix.

A = [a_{ij}]

A is skew symmetric matrix, so

A’ = -A

a_{ij} = -a_{ij} for all possible values of i and j

If i = j then a_{ii} = -a_{ii}

2 a_{ii} = 0

a_{ii} = 0 for all values of i’s

means all the diagonal elements of a skew symmetric matrix are zero.

Solution 9.

Solution 10.

Solution 11.

Solution 12.

Solution 13.

Solution 14.

Solution 15.

Solution 16.

Let E_{1} is the event: six appears on a dice

E_{2} is the event: six does not appear on a dice

A is the event: man reports six appears on a dice

Solution 17.

Solution 18.

Solution 19.

Solution 20.

Solution 21.

Solution 22.

Solution 23.

Solution 24.

Solution 25.

Solution 26.

Solution 27.

Solution 28.

Solution 29.

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