CBSE Sample Papers for Class 12 Maths Paper 5 are part of CBSE Sample Papers for Class 12 Maths. Here we have given CBSE Sample Papers for Class 12 Maths Paper 5.

## CBSE Sample Papers for Class 12 Maths Paper 5

Board |
CBSE |

Class |
XII |

Subject |
Maths |

Sample Paper Set |
Paper 5 |

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 5 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.

Construct a 2 x 2 matrix A = [a_{ij}] whose elements are given by

Question 2.

Find the angle between the line x = y = z and the plane z = 3.

Question 3.

If \(\int _{ 0 }^{ a }{ 3{ x }^{ 2 }dx=8 }\), find the value of a.

Question 4.

Rolle’s theorem for the function f(x) = x^{2} – x – 6 in the interval [-2, 3] is verified. Find the value of c.

**SECTION B**

Question 5.

Question 6.

Question 7.

Using differentials find the approximate value of \(\left( \frac { 17 }{ 81 } \right) ^{ \frac { 1 }{ 4 } }\)

Question 8.

Prove that f(x) = |x – 1|, x ∈ R is not differentiable at x = 1.

Question 9.

Find the vector and cartesian equation of planes that passes through the point (1, 0, -2) and the normal to the plane is \(\hat { i } +\hat { j } -\hat { k }\).

Question 10.

Find the general solution of differential equation sec^{2}x tan y dx + sec^{2}y tan x dy = 0.

Question 11.

Question 12.

Evaluate \(\int _{ 0 }^{ \pi }{ \left| cosx \right| dx }\).

**SECTION C**

Question 13.

Question 14.

Question 15.

Question 16.

Question 17.

Question 18.

Question 19.

Question 20.

Solve the differential equation y dx + x log(\(\frac { y }{ x }\)) dy – 2x dy = 0.

Question 21.

Solve the differential equation \(\frac { dy }{ dx }\) + 2y tan x = sin x.

Question 22.

Rajeev appears for an interview for two posts A and B for which selection is independent. The probability of his selection for the post A is \(\frac { 1 }{ 5 }\) and for post B is \(\frac { 1 }{ 6 }\). What is the probability that he is selected for atleast one of the post? Which values in life he is representing?

Question 23.

**SECTION D**

Question 24.

Question 25.

A fruit grower can use two types of fertilizers in his garden, brand P and brand Q. The amount (in kg) of nitrogen, phosphoric acid. Potash and chlorine in a bag of each mixture are given in the table. Tests indicate that the garden needs atleast 240 kg of phosphoric acid atleast 270 kg of potash and at most 310 kg of chlorine. If the grower wants to minimize the amount of nitrogen added to the garden, how many bags of each mixture should be used. What is the minimum amount of nitrogen added?

Question 26.

Show that the right circular cone of least curved surface and given vo equal to √2 times the radius of base.

**OR**

A window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 m, find the dimensions of the rectangle that will produce the largest area of the window.

Question 27.

Find the area of the region bounded by the curves |x + y| ≤ 1, |x – y| ≤ 1, and 3x^{2} + 3y^{2} ≥ 1 using integration.

Question 28.

There are three coins. One is a two headed coin, another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is choosen at random and tossed, it shows head, what is the probability that it was the two headed coin?

Question 29.

Find the equation of the line through A(5, -3, 2) and through the intersection of the lines

**Solutions**

Solution 1.

Solution 2.

Direction ratio of line = 1, 1, 1

Direction ratio of plane = 0, 0, 1

sin θ = \(\frac { 1 }{ \surd 3 }\)

⇒ θ = sin-1(\(\frac { 1 }{ \surd 3 }\))

Solution 3.

a = 2

Solution 4.

f'(c) = 0

c = \(\frac { 1 }{ 2 }\) ∈ (-2, 3)

Solution 5.

x = 1, y = 2, z = 3, w = 4.

Solution 6.

Solution 7.

Solution 8.

L.H.D. = -1

R.H.D. = 1

L.H.D. ≠ R.H.D.

So f(x) is not differentiable at x = 1

Solution 9.

Solution 10.

Solution 11.

Solution 12.

Solution 13.

Solution 14.

Solution 15.

Solution 16.

Solution 17.

Solution 18.

Solution 19.

Solution 20.

Solution 21.

Solution 22.

Solution 23.

Solution 24.

Solution 25.

Let x bags of brand P and y bags of brand Q fertilizers are used.

Objective function is minimise Z = 3x + 3.5y

Subject to constraints

x + 2y ≥ 240

3x+ 1.5y ≥ 270

1.5x + 2y ≤ 310

x, y ≥ 0

Hence minimum amount of nitrogen added is 470 kg. When 40 bags of brand P and 100 bags of brand Q fertilizers are used.

Solution 26.

Solution 27.

Solution 28.

E_{1}: Two headed coin is selected

E_{2}: biased coin is selected

E_{3}: unbiased coin is selected

A: event getting head.

Solution 29.

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