RBSE Class 12 Maths Model Paper 3 English Medium are part of RBSE Class 12 Maths Board Model Papers. Here we have given RBSE Class 12 Maths Sample Paper 3 English Medium.

Board |
RBSE |

Textbook |
SIERT, Rajasthan |

Class |
Class 12 |

Subject |
Maths |

Paper Set |
Model Paper 3 |

Category |
RBSE Model Papers |

## RBSE Class 12 Maths Sample Paper 3 English Medium

**Time – 3 ¼ Hours**

**Maximum Marks: 80**

**General instructions to the examines**

- Candidate must write first his/her Roll No. on the question paper compulsorily.
- All the questions are compulsory.
- Write the answer to each question in the given answer book only.
- For questions having more than one part, the answers to those parts are to be written together in continuity.

**Section – A**

Question 1.

If ‘*’ is addition modulo 5 on z, find (2 * 3) * 4. **[1]**

Question 2.

Find the value of tan^{-1}5 + tan^{-1}\(\frac{1}{5}\) **[1]**

Question 3.

**[1]**

Question 4.

**[1]**

Question 5.

Evaluate \(\int \frac{1-\tan x}{1+\tan x} d x\) **[1]**

Question 6.

Find the sum of vector \(\vec{a}=\hat{i}-2 \hat{j}+\hat{k}, \vec{b}=-2 \hat{i}+4 \hat{j}+5 \hat{k} \text { and } \vec{c}=\hat{i}-6 \hat{j}-7 \hat{k}\) **[1]**

Question 7.

Find the volume of parallelepiped whose coterminous edges are given by the vectors \(\vec{a}=4 \hat{i}-3 \hat{j}+\hat{k}, \vec{b}=3 \hat{i}+2 \hat{j}-\hat{k} \text { and } \vec{c}=3 \hat{i}-\hat{j}+2 \hat{k}\) **[1]**

Question 8.

Find the equation of a line in vector form which passes through the origin and (5, -2, 3) **[1]**

Question 9.

Construct feasible region of the following constraint : 2x + y ≤ 500, x, y ≥ 0 **[1]**

Question 10.

A bag contains 5 white, 7 red and 8 black balls. If 4 balls are drawn without replacement find the probability of getting all white balls. **[1]**

**Section – B**

Question 11.

**[2]**

Question 12.

**[2]**

Question 13.

**[2]**

Question 14.

**[2]**

Question 15.

Find the value of \(|\vec{a} \times \vec{b}| \text { of }|\vec{a}|=10,|\vec{b}|=2 \text { and } \vec{a} \cdot \vec{b}=12\) **[2]**

**Section – C**

Question 16.

**[3]**

**OR**

Question 17.

**[3]**

Question 18.

**[3]**

Question 19.

Find the interval in which the function f(x) = sinx – cosx is increasing or decreasing when x ∈ [0, π] **[3]**

Question 20.

Find the maximum and minimum value of the function **[3]**

f(x) = 3x^{4 }– 2x^{3} – 6x^{2} + 6x + 1, x ∈ (0, 2]

Question 21.

Evaluate \(\int \frac{x^{2}}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)} d x\) **[3]**

**OR**

Find \(\int \frac{\sin (\log x)}{x^{3}} d x\)

Question 22.

Find the area enclosed by the lines x + 2y = 8, x = 2, x = 4 and x-axis. **[3]**

Question 23.

Find the area enclosed between the curve x² + y² = 9 and the line x = \(\sqrt{2} y\). **[3]**

Question 24.

Find the volume of the parallelopiped with co-terminous sides given by the vectors \(\vec{a}=2 \hat{i}-3 \hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+2 \hat{k} \text { and } \vec{c}=2 \hat{i}+\hat{j}-\hat{k}\) **[3]**

**OR**

Find the position vector of the centroid of a triangle, given the position vectors of its vertices

\(\vec{a}, \vec{b} \text { and } \vec{c}\) respectively.

Question 25.

Solve the following problems by graphical method **[3]**

Maximum Z = -x + 2y

Subject to x ≥ 3, x + y ≥ 5, x + 2y ≥ 6,

x ≥ 0, y ≥ 0

**Section – D**

Question 26.

**[6]**

Question 27.

**[6]**

Question 28.

**[6]**

**OR**

Question 29.

Show that the points A(1, -1, 3) and B(3, 3, 3) are at equal distance from the plane \(\vec{r} \cdot(5 \hat{i}+2 \hat{j}-7 \hat{k})+9=0\) **[6]**

Question 30.

In a factory which manufactures bolts, machines A, B and C manufacture respectively 25%, 35% and 40% of the bolts, of their outputs 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product and it found to be defective. What is the probability that it is manufactured by machine B? **[6]**

**OR**

A man is known to speak truth 3 out of 4-times. He throws a die and reports that it is a 6. Find the probability that it is actually 6.

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