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KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION
SAMPLE PAPER – 03 (2017-18)
SUBJECT: MATHEMATICS(041)
BLUE PRINT : CLASS XII
Chapter
VSA
(1 mark)
Short answer
(2 marks)
Long answer
- I (4 marks)
Long answer
- II (6 marks)
Total
Relations and Functions 1(1) -- -- 6(1) 7(2)
Inverse Trigonometric
Functions
Matrices -- 2(1) -- -- 2(1)
Determinants 1(1) -- 4(1) 6(1) 11(3)
Continuity &
Differentiability
Applications of
Derivatives
Integrals - - 2(1) 4(1) 6(1) 12(3)
Applications of the
Integrals
Differential Equations -- 2(1) 4(1) -- 6(2)
Vector Algebra
Three-Dimensional
Geometry
Linear Programming -- -- -- 6(1) 6(1)
Probability -- 2(1) 8(2) -- 10(3)
Total 4(4) 16(8) 44(11) 36(6) 100(29)
KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION
SAMPLE PAPER – 03 (2017-18)
SUBJECT: MATHEMATICS MAX. MARKS : 100
CLASS : XII DURATION : 3 HRS
General Instruction:
(i) All questions are compulsory.
(ii) This question paper contains 29 questions.
(iii) Question 1 - 4 in Section A are very short-answer type questions carrying 1 mark each.
(iv) Question 5 - 12 in Section B are short-answer type questions carrying 2 marks each.
(v) Question 13 - 23 in Section C are long-answer-I type questions carrying 4 marks each.
(vi) Question 24 - 29 in Section D are long-answer-II type questions carrying 6 marks each.
SECTION – A
Questions 1 to 4 carry 1 mark each.
1. Evaluate :
1
sin sin
2. Let * be a binary operation, on the set of all non-zero real numbers, given by *
ab
a b for all
a b , R {0}. Find the value of x , given that 2 * ( x * 5) = 10.
3. If A is a square matrix and | A| = 2, then write the value of | AA ' | , where A ' is the transpose of
matrix A.
4. If a line has direction ratios 2, – 1, – 2, determine its direction cosines.
SECTION – B
Questions 5 to 12 carry 2 marks each.
5. Simplify :
1
cos sin
tan , 0
cos sin
x x
x
x x
6. Find the value of a if
a b a c
a b c d
7. If
1
tan
a x
y
ax
, find
dy
dx
8. Evaluate:
1
2
sin
x
e x dx
x
9. Use differential to approximate 36..
10. If a
and b
are two unit vectors such that a b
is also a unit vector, then find the angle between
a
and b
11. Assume that each born child is equally likely to be a boy or a girl. If a family has two children,
what is the conditional probability that both are girls given that atleast one is a girl?
12. Form the differential equation representing the family of parabolas having vertex at origin and
axis along positive direction of x - axis.
22. Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is
of
the volume of the sphere.
23. Find points on the curve
2 2
x y
at which the tangents are (i) parallel to x - axis (ii) parallel to y - axis.
OR
Find the intervals in which the function f given by f ( x ) = 2 x
3
2
increasing (b) strictly decreasing
SECTION – D
Questions 24 to 29 carry 6 marks each.
24. Show that the function f : R → { x R : −1 < x <1} defined by f( x) = ,
x
x R
x
is one-one and
onto function.
OR
Consider f : R
→ [−5, ∞) given by f ( x ) = 9 x
2
- 6 x − 5. Show that f is invertible with
1
y
f y
25. If a , b and c are real numbers, and 0
b c c a a b
c a a b b c
a b b c c a
. Show that either a + b + c = 0 or
a = b = c.
OR
If A
and B =
, find ( AB )
26. Evaluate:
2 2 2 2
0
cos sin
x
dx
a x b x
OR
Find
3
2
1
( x 5 ) x dx
as the limit of a sum.
27. Find the area of the region {( x , y ) :
2
0 y x 1, 0 y x 1, 0 x 2 }
28. Find the equation of the plane passing through the point (– 1, 3, 2) and perpendicular to each of
the planes x + 2 y + 3 z = 5 and 3 x + 3 y + z = 0.
29. A merchant plans to sell two types of personal computers — a desktop model and a portable
model that will cost Rs. 25,000 and Rs. 40,000 respectively. He estimates that the total monthly
demand of computers will not exceed 250 units. Determine the number of units of each type of
computers which the merchant should stock to get maximum profit if he does not want to invest
more than Rs. 70 lakhs and his profit on the desktop model is Rs. 4,500 and on the portable
model is Rs. 5,000. Make an L.P.P. and solve it graphically.
