In pursuit of excellence, the CBSE board conducts a thorough research on emerging educational requirements. While designing the syllabus, the board ensures that every topic meets the learning needs of students in the best possible manner. CBSE Class 12 Maths - http://cbse.edurite.com/cbse-maths/cbse-class-12-maths.html
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Cbse 12 Class Maths Sample Paper
1. MATHEMATICS
SAMPLE TEST PAPER
CLASS XII
Class:12
Time 3hrs
Max Mks:100
No of pages: 3
General Instructions:
rit
e.
co
m
Ò All questions are compulsory.
Ò The question paper consists of 29 questions divided into three sections - A, B and C.
Ò Section - A comprises of 10 questions of one mark each, Section B is of 12 questions of four
marks each, Section C comprises of 7 questions of six marks each.
Ò Internal choice has been provided in four marks question and six marks question. You have to
attempt any one of the alternatives in all such questions
Ò use of calculator not permitted.
1. Find the value of x , if
w
w
sin2x
2. Evaluate: ∫ ( 3+ secx )dx
.e
du
SECTION A
Question number 1 to 10 carry 1 mark each
w
3. If A is irreversible matrix or order 5 and ∣ A∣ = 5, then find [adj,A]
a
a b
b
b
i
k
4. Find the projection of ⃗ on ⃗ , if ⃗ . ⃗ = 6 and ⃗ =4 ⃗ + ⃗j +8 ⃗
2
2x
5. Evaluate: ∫ ( 1+ 3x ) dx
3π
6. what is the value of tan-1 4
7. write the order of the matrix
8. write the position vector of the mid point of the vector join g the points p(2,3,4 and q (4,-1,2))
9. write the distance from following plane from the origin2x-y+2z+1 = 0
0
i
k
i
k
10. Find λ if (2 ⃗ +6 ⃗j +14 ⃗ )*( ⃗ -λ ⃗j +7 ⃗ ) = ⃗
2. SECTION B
Question numbers 11 to 22 carry 4 marks each.
11. State whether the function is one -one, onto or objective. Justify your answer
a) f:R→R defined by f (x) = 4+5x
b) f:R→R defined by f (x) = 4x+5x2
dy
12. use mathematical induction prove that dx (xn)=nx(n-1)for all n belongs N for all positive
integers n.
13.
rit
e.
co
m
1+
1−
√ x− √ x π
14. prove that tan-1( √ x+ √ x )= 2
1+
1−
15. Find the derivative of the function given by f(x) = (1+x) (1+x2) (1+x4)(1+x8) and hence find
f(3)
16. using properties of determinants, prove that
w
prove that
w
w
.e
du
or
17. solve the differential equation
2
2
x dy - y dx= √x + y
or
dy
2
dx = log(x+2)
18. A speaks truth 10 times out of 15 times. A dice is tossed. He reports that it was 6. What is the
probability it was actually 6.'
sin− 1( x)
d2y
dy
19. If y =
, show that (1-x2) dx2 -3x dx -y = 0
2
√1− x
20. Express the following matrix as the sum of symmetric and skew symmetric matrix, and verify
your answer.
3. rit
e.
co
m
21. On multiplying choice examination with three possible answers for each of the five questions,
what is the probability that a candidate would get four or more correct answer just by guessing?
22. Finds the shortest between the following lines:
r
⃗ = (1+λ) ⃗ +(2-λ) ⃗j + (λ+1)7 ⃗ ; ⃗ = (2 ⃗ - ⃗j + - ⃗ )+μ(2 ⃗ + ⃗j +2 ⃗ )
i
i
i
k r
k
k
SECTION C
Question numbers 23 to 29 carry 6 marks each.
23. solve using matrices:
2x-y+3z = 5
3x+2y-z = 7
4x+5y-5z = 9
or
using matrix method solve the following system of equations:
2x+y+z = 3
3x-y+z = 0
x-2y+3z = -6
du
24. Find the area of the region bounded by y2 = 4x, x = 1, x = 4 and x -a xis in the first quadrant
.e
or
Evaluate lim 0− 2 ∫
as limit of a sum.
25. Show that the height of the cylinder of maximum volume that can be inscribed in a cone of
1
height h is 3 h.
w
w
w
x 2 + x+ 1 dx
26. Find the equation of the plane passing through the (-1,-1,2) are perpendicular to each of the
following planes 2x+3y-3z = 2 and 5x-4y+z = 6
or
Find the point on the curve y2 = 4x which is nearest to the point (-,-8)
27. Sketch the graph of y = Ix + 5I and evaluate the area under the curve y = x + 5 above x-axis
and between x = -7 to x = O.
28. Using the method of integration, find the area of region bounded by the lines 2x+y = 4, 3x-2y =
6, x-3y+5 = 0
29. A can hit a target 4 times in 5 shots,B 3 times in 4 shots and C, 2 times in 3 shots. Calculate the
probability that:
a)A,B,C all may hit b) none of them ii hit the target