RBSE Class 12 Maths Model Paper 2 English Medium

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.

RBSE Class 12 Maths Sample Paper 2 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 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_elog_ex². [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^-1x + tan^-1y + tan^-1z = \(\frac{\pi}{2}\) 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]

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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