RBSE Class 12 Maths Model Paper 4 English Medium are part of RBSE Class 12 Maths Board Model Papers. Here we have given RBSE Class 12 Maths Sample Paper 4 English Medium.

Board |
RBSE |

Textbook |
SIERT, Rajasthan |

Class |
Class 12 |

Subject |
Maths |

Paper Set |
Model Paper 4 |

Category |
RBSE Model Papers |

## RBSE Class 12 Maths Sample Paper 4 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 ‘*’ be defined on the set R of all real numbers by a * b = \(\sqrt{a^{2}+b^{2}}\), find the identity element e on R. **[1]**

Question 2.

**[1]**

Question 3.

**[1]**

Question 4.

Find K, if the area of ΔABC is 2 sq. units where A(4, 3), B(-5, 2) and C(k, 0). **[1]**

Question 5.

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

Question 6.

Find unit vector in the direction of \(\vec{a}-\vec{b}\) where \(\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k} \text { and } \vec{b}=2 \hat{i}+\hat{j}+2 \hat{k}\) **[1]**

Question 7.

Find the value of \((2 \hat{i}-3 \hat{j}+4 \hat{k}) \times(3 \hat{i}+4 \hat{j}-4 \hat{k})\) **[1]**

Question 8.

**[1]**

Question 9.

Show the feasible region for the following constraints **[1]**

3x + 2y ≤ 12, x ≥ 0, y ≥ 0

Question 10.

IfA and B are two events such that \(\mathbf{P}(\mathbf{A})=\frac{1}{4}, \mathbf{P}(\mathbf{B})=\frac{1}{2} \text { and } P(A \cap B)=\frac{1}{8}\), then find \(\mathbf{P}(\overline{\mathbf{A}} \cap \overline{\mathbf{B}})\). **[1]**

**Section – B**

Question 11.

If f : R → R be such that f (x) = (1+2x)³, then express f as a composite of two functions from R to R. **[2]**

Question 12.

**[2]**

Question 13.

**[2]**

Question 14.

**[2]**

Question 15.

If A(1, 2, 2), B(2, -1, 1) and C(-1, -2, 3), then find a vector which is perpendicular to the plane of ΔABC. **[2]**

**Section – C**

Question 16.

**[3]**

**OR**

Question 17.

**[3]**

Question 18.

**[3]**

Question 19.

Let x unit and y unit be the length of sides of a square and radius of a circle. **[3]**

Question 20.

Find the values of x for which \(f(x)=\frac{x}{1+x^{2}}\) is increasing or decreasing. **[3]**

Question 21.

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

**OR**

Evaluate \(\int \frac{\sqrt{x}}{\sqrt{a^{3}-x^{3}}} d x\)

Question 22.

Find the area enclosed between the curve x² = 4y and the line x = 4y – 2. **[3]**

Question 23.

Find the area of the region in the first quadrant enclosed by y = 4x², x = 0, x = 1 and y=4. **[3]**

Question 24.

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. **[3]**

**OR**

If four points \(A(\vec{a}), B(\vec{b}), C(\vec{c}) \text { and } D(\vec{d})\) are coplanar, then prove that

\([\vec{a} \vec{b} \vec{c}] = [\vec{b} \vec{c} \vec{d}] + [\vec{c} \vec{a} \vec{d}] + [\vec{a} \vec{b} \vec{d}]\)

Question 25.

Obtain maximum and minimum value where Z = 3x + Oy Subject to constraints **[3]**

x+3y ≤ 60

x+y ≥ 10

x ≥ 0, y ≥ 0

**Section – D**

Question 26.

**[6]**

Question 27.

**[6]**

Question 28.

**[6]**

**OR**

Question 29.

Reduce the equation 3x – 4y + 12z = 5 to normal form and hence find the length of the perpendicular from the origin to the plane. Also, find the direction cosines of the normal to the plane. **[6]**

Question 30.

A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag. **[6]**

**OR**

A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.

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