RBSE Class 12 Maths Model Paper 4 English Medium

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

1. Candidate must write first his/her Roll No. on the question paper compulsorily.
2. All the questions are compulsory.
3. Write the answer to each question in the given answer book only.
4. 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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