RBSE Class 12 Maths Model Paper 3 English Medium

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

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

Question 2.
Find the value of tan^-15 + 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) = 3x⁴ – 2x³ – 6x² + 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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