RBSE Class 12 Maths Model Paper 1 English Medium

RBSE Class 12 Maths Model Paper 1 English Medium are part of RBSE Class 12 Maths Board Model Papers. Here we have given RBSE Class 12 Maths Sample Paper 1 English Medium.

Board	RBSE
Textbook	SIERT, Rajasthan
Class	Class 12
Subject	Maths
Paper Set	Model Paper 1
Category	RBSE Model Papers

RBSE Class 12 Maths Sample Paper 1 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.
5. If there is any error/difference/contradiction in Hindi & English versions of the question paper, the question of Hindi version should be treated valid.

6. Section	Q.No	Marks for question
   A	1-10	1
   B	11-15	2
   C	16-25	3
   D	26-30	6

7. There are internal choices in Q. No. 16. 21. 24. 28 and 30. You have to attempt only one of the alternatives in these questions.
8. Draw the graph of Q.No. 25 on the graph paper.

Section – A

Question 1.
Write composition table for addition S = {(0, 1, 2); +₃}. [1]

Question 2.
If \(\cot ^{-1} x+\tan ^{-1}\left(\frac{1}{3}\right)=\frac{\pi}{2}\) then find the value of x. [1]

Question 3.
[1]

Question 4.
If points (x, -2), (5, 2), (8, 8) are collinear, then find the value of x. [1]

Question 5.
Find \(\int \log x d x\) [1]

Question 6.
Find the unit vector along the sum of vectors \(a=2 \hat{i}+2 \hat{j}-5 \hat{k}, b=2 \hat{i}+\hat{j}+3 \hat{k}\) [1]

Question 7.
Find the value of \(\left[ \begin{array}{lll}{2 \hat{i}} & {\hat{j}} & {\hat{k}}\end{array}\right]+\left[ \begin{array}{lll}{\hat{i}} & {\hat{j}} & {\hat{k}}\end{array}\right]+\left[ \begin{array}{lll}{\hat{k}} & {\hat{j}} & {2 \hat{i}}\end{array}\right]\) [1]

Question 8.
[1]

Question 9.
Show the region of feasible solution under the following constraints x + 2y ≤ 8, .x ≥ 0, y ≥ 0 in answer book. [1]

Question 10.
[1]

Section – B

Question 11.
If function f: R → R, f (x) = 2x + 1 then show that \(\left(f^{-1}\right)^{-1}=f\) [2]

Question 12.
[2]

Question 13.
Examine Continuity at x = 1 of function f(x) = |x – 1| [2]

Question 14.
Find \(\int \frac{1}{1+\sin x} d x\) [2]

Question 15.
If a vector makes angles α, β, and γ respectively with axes OX, OY, OZ, then prove that sin²α + sin²β + sin²γ = 2. [2]

Section – C

Question 16.
[3]
OR

Question 17.
[3]

Question 18.
[3]

Question 19.
Find equation of normal to the curve 2x² – y² = 14 which is parallel to line x + 3y = 6. [3]

Question 20.
Find two positive numbers x and y, sum of them is 60 and xy³ is maximum. [3]

Question 21.
Find \(\int \sqrt{x^{2}+a^{2}} d x\)  [3]
OR
Find \(\int \frac{1}{1-6 x-9 x^{2}} d x\)

Question 22.
Find area of region bounded by curve \(y=2 \sqrt{1-x^{2}}\) and above x-axis. [3]

Question 23.
Find area of region bounded by curve [(x,y)/x² ≤ y ≤ x]  [3]

Question 24.
If \(\overline{a}=3 \hat{i}+\hat{j}+2 \hat{k} \text { and } \overline{b}=2 \hat{i}-2 \hat{j}+2 \hat{k}\) then find unit vector \(\hat{n} \) perpendicular both \(\overline{a} \text { and } \overline{b}\) [3]
OR

Question 25.
By graphical method solve the following linear programming problem for [3]
Maximum z = 2x + 3y
Constraints 4x + 6y ≤ 60,  2x + y ≤ 20 and x ≥ 0, y ≥ 0.

Section-D

Question 26.
[6]

Question 27.
Show that \(\int_{0}^{\frac{\pi}{2}} \log \sin x d x=\frac{\pi}{2} \log \frac{1}{2}\) [6]

Question 28.

OR
Find the perticular solution of the differential equation \(\frac{d y}{d x}\) + 2xy = xsin x² If x = 0 and y = 1. [6]

Question 29.
Find the angle between the two lines. These direction-cosines are given by the following relations. l- 5m + 3n = 0 and 7l² + 5m² – 3n² = 0 [6]

Question 30.
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six. [6]
OR
Two coins are tossed at the same time. Find the variance of “number of heads”.

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