SAMPLE PAPER -2015 MATHEMATICS CLASS – XII Time allowed: 3 hours Maximum marks: 100 General Instructions: 1. All questions are compulsory. 2. The question paper consists of 26 questions divided into three sections-A, B and C. Section A comprises of 6 questions of one mark each, Section B comprises of 13 questions of four marks each and Section C comprises of 7 questions of six marks each. 3. All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question. 4. There is no overall choice. However, internal choice has been provided in 4 questions of four marks each and 2 questions of six mark each. You have to attempt only one of the alternatives in all such questions. 5. Use of calculators is not permitted. Section A Q1. Evaluate: tan –1 √3 – sec –1 (–2) Q2 Find gof if f(x) =8 x 3 , g(x)= √ 3 . Q3. If [ 3 − 2 5 −2 ] = [ 3 5 −3 −2 ] , find the value of y . Q4. Evaluate: | 30 0 30 0 −60 0 60 0 | Q5. Find p such that p z y x 3 2 1 and 1 4 2 z y x are perpendicular to each other. Q6. Find the projection of on if . =8 and = 2̂ +6̂ + 3
10
Embed
CBSE Mathematics sample question paper with marking scheme
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
SAMPLE PAPER -2015
MATHEMATICS
CLASS – XII
Time allowed: 3 hours Maximum marks: 100
General Instructions:
1. All questions are compulsory.
2. The question paper consists of 26 questions divided into three sections-A, B and C. Section A
comprises of 6 questions of one mark each, Section B comprises of 13 questions of four marks
each and Section C comprises of 7 questions of six marks each.
3. All questions in Section A are to be answered in one word, one sentence or as per the exact
requirement of the question.
4. There is no overall choice. However, internal choice has been provided in 4 questions of four
marks each and 2 questions of six mark each. You have to attempt only one of the alternatives in
all such questions.
5. Use of calculators is not permitted.
Section A
Q1. Evaluate: tan–1√3 – sec
–1 (–2)
Q2 Find gof if f(x) =8 x3
, g(x)= √𝑥3
.
Q3. If [3𝑥 − 2𝑦 5
𝑥 −2] = [
3 5−3 −2
] , find the value of y .
Q4. Evaluate: | 𝑠𝑖𝑛 300 𝑐𝑜𝑠300
−𝑠𝑖𝑛600 𝑐𝑜𝑠600|
Q5. Find p such that p
zyx
321 and
142
zyx
are perpendicular to each other.
Q6. Find the projection of �� on �� if �� . �� =8 and �� = 2𝑖 +6𝑗 + 3��
_____________________________________________________________________ Q20. 4 x + 3 y + 2z = 37000, 5 x + 3 y + 4z = 47000, x + y + z = 1200 1
|A| = - 3 ≠ 0 so A-1 exists. X = A-1 B 1/2
Cofactors of A 2
[−1 −1 2−1 2 16 −6 3
]
Adjoint A 1/2 X = 4000 ,y = 5000, z = 3000 1½ Values ½ _______________________________________________________________ Q21. P = 2tan x, Q = sin x
I.F = 𝑠𝑒𝑐2𝑥 1½
y 𝑠𝑒𝑐2𝑥 = ∫ sin 𝑥 𝑠𝑒𝑐2𝑥 𝑑𝑥 + 𝐶 1
y 𝑠𝑒𝑐2𝑥 = sec x + C 1½
y = 1
sec𝑥 +
𝐶
𝑠𝑒𝑐2𝑥= cos x + C 𝑐𝑜𝑠2𝑥 -------------------(1) 1½
putting x = 𝜋
3 and y = 0 in eqn (1) C = -2 ½
Y= cos x - 2𝑐𝑜𝑠2𝑥 1 __________________________________________________________________________ Q22. Sol: The required plane is (x + 2 y + 3 z ) + k (2 x + y – z +5 )= 0 1
Or (1 + 2 k)x +(2 + k)y +(3 - k)z-4 + 5k = 0 1
5(1+2k) +3 (2+k) -6 (3-k)=0 1
Solving k = 7/19 1
The equation of the plane is : 33 x + 45y +50z = 41 . 2
Q26. Let the mixture contain x kg of food P and y kg of food Q. Minimise Z = 60x + 80y 1/2 subject to the constraints, 3x + 4y ≥ 8 … (2) 5x + 2y ≥ 11 … (3)
x, y ≥ 0 … (4) 2
11
Figure and shading 2
12
The corner points of the feasible region are .A(8/3,0),B(2,1/2),C(0,11/2)
minimum cost Rs 160 at the line segment A(8/3,0) & B(2,1/2) 2
11
Marking scheme can be for any alternative method by the evaluator. Pratima Nayak,KV Teacher