RBSE Class 12 Maths Model Paper 2 English Medium are part of RBSE Class 12 Maths Board Model Papers. Here we have given RBSE Class 12 Maths Sample Paper 2 English Medium.

Board |
RBSE |

Textbook |
SIERT, Rajasthan |

Class |
Class 12 |

Subject |
Maths |

Paper Set |
Model Paper 2 |

Category |
RBSE Model Papers |

## RBSE Class 12 Maths Sample Paper 2 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 3 is identity element of the binary operation on Q defined by a * b = \(\frac{a b}{3}\) find a^{-1} for a ∈ Q **[1]**

Question 2.

If sin^{-1} x + 3cos^{-1} x = π Find x. **[1]**

Question 3.

**[1]**

Question 4.

**[1]**

Question 5.

Evaluate \(\int \frac{1-\cos 2 x}{1+\cos 2 x} d x\) **[1]**

Question 6.

Find the position vector of the midpoint of the vector joining the points P(2, 3, 4) and Q(4, 1, -2). **[1]**

Question 7.

If for a vector \(\vec{a},(\vec{x}-\vec{a}) \cdot(\vec{x}+\vec{a})=12\) the find \(\vec|x|\). **[1]**

Question 8.

**[1]**

Question 9.

Find the feasible region for the following constraint **[1]**

x + y ≤ 10, x + 2y ≥ 20, x ≥ 0, y ≥ 0

Question 10.

A pair of dice is thrown 7 times. If getting a total of 7 is a success what is the probability of 6 successes? **[1]**

**Section – B**

Question 11.

**[2]**

Question 12.

**[2]**

Question 13.

Differentiate: log_{e}log_{e}x². **[2]**

Question 14.

Evaluate \(\int \frac{1}{16-9 x^{2}} d x\) **[2]**

Question 15.

Find a vector perpendicular to the vectors \(4 \hat{i}-\hat{j}+3 \hat{k} \text { and }-2 \hat{i}+\hat{j}-2 \hat{k}\) whose magnitude is 9 unit. **[2]**

**Section – C**

Question 16.

If tan^{-1}x + tan^{-1}y + tan^{-1}z = \(\frac{\pi}{2}\) then prove that xy + yz + zx = 1 **[3]**

**OR**

Question 17.

**[3]**

Question 18.

Find k such that the points (k, 2 – 2k), (-k + 1, 2k) and (-4 – k, 6 – 2k) are collinear. **[3]**

Question 19.

Show that of all the rectangles in a circle, the square has the maximum area. **[3]**

Question 20.

Find the minimum value of a such that the function f(x) = x² + 9x + 5 is increasing in [1,2] **[3]**

Question 21.

Find \(\int \frac{d x}{\sqrt{9 x-4 x^{2}}}\) **[3]**

**OR**

Evaluate \(\mathrm{I}=\int \frac{\sin x+\cos x}{9+16 \sin 2 x} d x\)

Question 22.

Find the area enclosed by the lines 2x + y = 4, x = 0, x = 3. **[3]**

Question 23.

Find the area of the ΔABC using calculus where the vertices are A(2,5), B(4, 7) and C(6, 2). **[3]**

Question 24.

By vector method prove that the line joining mid points of two sides of a triangle is parallel to third side. **[3]**

**OR**

Verify the formula \(\vec{a} \times(\vec{b} \times \vec{c})=(\vec{a} \cdot \vec{c}) \vec{b}-(\vec{a} \cdot \vec{b}) \vec{c}\)

where \(\vec{a}=\hat{i}+\hat{j}-2 \hat{k}, \vec{b}=2 \hat{i}-\hat{j}+\hat{k} \text { and } \vec{c}=\hat{i}+3 \hat{j}-\hat{k}\)

Question 25.

A housewife wishes to mix together two kinds of food, X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contain is of one kg of food are given below : **[3]**

Food X |
1 | 2 | 3 |

Food Y |
2 | 2 | 1 |

One Kg. of food X costs Rs. 6/- and one Kg of food Y costs Rs. 10. Find the least cost of the mixture which will produce the diet.

**Section – D**

Question 26.

**[6]**

Question 27.

** [6]**

Question 28.

**OR**

Solve : (e^{y}+ 1)cosx dx + e^{y} sin x dy = 0 **[6]**

Question 29.

**[6]**

Question 30.

A problem in mathematics is given to 3 students whose chances of solving it are a What is the probability that the problem is solved. **[6]**

**OR**

Three coins are tossed together. The random variable X be the number of heads on coins. Find mean X.

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