SAMPLEPAPER
12
Engg.
2
13
th
NSO  LevelI  Class 12_Engineering
SetB
MATHEMATICS
1. In a rectangle
ABCD
,
P
,
Q
,
R
and
S
are the midpoints of the sides
AB
,
BC
,
CD
and
DA
respectively and
T
is the point on
RS
such that
RT
= 2
TS
. If the area of
ABCD
is
k
times the area of
D
PQT,
then
k
is ____.
A P B C D R S Q T
(A)
3
(B)
4
(C)
6
(D)
None of these
2. 2
73
– 2
72
– 2
71
is same as ____. (A)
2
72
(B)
2
71
(C)
2
70
(D)
2
73
3. In the following graph for
x
Î
[–1, 1],
f
(
x
) is defined by (A)

x
 – 1
–3 1 –2 2 –1 3 0
y
2 –1 1 –2
x
(B)
–
x
 + 1
(C)
–
x
+ 1
(D)

x

4. Roorkee express normally reaches its destination at 50 km/hr in 30 hours. Find the speed at which it travels to reduce the time by 10 hours? (A)
38 km/hr
(B)
76 km/hr
(C)
75 km/hr
(D)
60 km/hr
5. What is the total number of ways of selecting atleast one object from 2 different sets, each set containing 6 identical objects ? (A)
24
(B)
48
(C)
76
(D)
None of these
6. For every
a
,
b
Î
N a @ b = a
2
when (
a
+
b
) is even =
a
2
–
b
2
when (
a
+
b
) is odd
a
#
b
=
b
2
when
a
×
b
is odd =
a
2
–
b
2
when
a
×
b
is even What is the value of 20 # (21 @ 22)? (A)
0
(B)
2249
(C)
–1849
(D)
Can't be determined
7. The set of values for which
x
3
+ 1
³
x
2
+
x
is _____. (A)
x
³
0
(B)
x
£
0
(C)
x
³
–1
(D)
–1
£
x
£
1
8. A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm
3
/min. When the thickness of ice is 5 cm, then the rate at which the thickness of ice decreases, is ____. (A)
1 cm/min 54
p
(B)
5 cm/min 6
p
(C)
1 cm/min 36
p
(D)
1 cm/min 18
p
3
13
th
NSO  LevelI  Class 12_Engineering
SetB
9. The ratio of the altitude of the cone of greatest volume that can be inscribed in a given sphere to the diameter of the sphere is ____. (A)
2 3
(B)
3 4
(C)
1 3
(D)
1 4
10. The sum of the ages of Anshuman and Armaan is 45 years. Five years ago the product of their ages was 4 times the Anshuman's age at that time. The present ages of Anshuman and Armaan respectively are (A)
25 and 20
(B)
35 and 10
(C)
36 and 9
(D)
40 and 5
11. A virus gives birth to two new viruses in each second and the life span of each virus is 5 seconds. The process of the reproduction is continuous until the death of the virus. Initially there is one newly born virus at time
t
= 0, then find the total number of live viruses just after 10 seconds. (A)
10
3 2
(B)
3
5
(3
5
– 1)
(C)
3
10
– 2
10
(D)
3
10
– 2
5
12. In a class 45% students read English, 30% read French and 20% read both English and French. One student is selected at random. Find the probability that he reads English, if it is known that he reads French. (A)
1 3
(B)
2 3
(C)
5 6
(D)
4 9
13. If
x
= – 0.5, then which of the following has the smallest value ? (A)
2
1/
x
(B)
1
x
(C)
2
1
x
(D)
2
x
14. In a code language if POSE is coded as OQNPRTDF, then the word TYPE will be coded as ____. (A)
SUXZOQFD
(B)
SUXZQOFD
(C)
SUXZOQDF
(D)
SUXZQODE
15. Priti scored more than Rahul. Yash scored as much as Divya. Anusha scored less than Manju. Rahul scored more than Yash. Manju scored less than Divya. Who scored the lowest ? (A)
Manju
(B)
Yash
(C)
Rahul
(D)
Anusha
16. A postman was returning to the post office which was in front of him to the north. When the post office, was 100 m away from him, he turned to the left and moved 50 m to deliver the last letter at the Shanti villa. He, then moved in the same direction for 40 m, turned to his right and moved 100 m. How many metres was he away from the post office ? (A)
0
(B)
150
(C)
90
(D)
100
17. The given below question has a few statements, followed by four conclusions numbered I, II, III and IV. You have to consider every given statements as true, even if it does not confirm to the well known facts. Read the conclusions and then decide which of the conclusions can be logically derived. Statements : 1. Some birds are mangoes. 2. No duck is a parrot. 3. All mangoes are ducks. Conclusions :I. Some birds are ducks. II. Some ducks are mangoes. III. No parrot is duck. IV Some birds are not parrots. (A)
Only I, II and III follow
(B)
Only I and III follow
(C)
Either II or IV follows
(D)
I, II, III & IV follows
4
13
th
NSO  LevelI  Class 12_Engineering
SetB
18. If the following alphabets are arranged in the reverse order, which letter will be 8
th
letter to the left of 7
th
letter counting from the right end ? A B C D E F G H I J K L M N O P Q R S T U V W X Y Z (A)
P
(B)
O
(C)
N
(D)
Q
19. Four ladies A, B, C and D and four gentlemen E, F, G and H are sitting in a circle around a table facing each other. (i) No two ladies or two gentlemen are sitting side by side. (ii) C, who is sitting between G and E, is facing D. (iii) F is between D and A and is facing G. (iv) H is to the right of B. Who is sitting to the left of A ? (A)
E
(B)
F
(C)
G
(D)
H
20. In the given question, a statement followed by two assumptions numbered I and II. An assumption is something supposed or taken for granted. You have to consider the statement and the following assumptions and decide which of the assumptions is implicit in the statement. Statement : Helping the poor is the real service to the humanity. Assumptions : I. Poor people are in need of help from others. II. If we don't help poor, we will not be called human beings. (A)
Only assumption I is implicit.
(B)
Only assumption II is implicit.
(C)
Either I or II is implicit.
(D)
Neither I nor II is implicit.
PHYSICS
21. In the figure shown, a parallel beam of light is incident on the plane of the slits of a Young’s double slit experiment. Light incident on the slit,
S
1
passes through a medium of variable refractive index
m
= 1 +
ax
(where
x
is the distance from the plane of slits as shown), upto a distance
l
before falling on
S
1
. Rest of the space is filled with air. If at
O
a minima is formed, then the minimum value of the positive constant
a
(in terms of
l
and wavelength
in air) is
O
Screen
S
2
S
1
x l S O S O
1 2
=
(A)
l
l
(B)
2
l
l
(C)
2
l
l
(D)
None of these
22. The strings of a violin are tuned to the tones
G
,
D
,
A
and
E
, which are separated by a fifth from one another, that is
F
(
D
) = 1.5
F
(
G
),
F
(
A
) = 1.5
F
(
D
) = 400 Hz and
F
(
E
) = 1.5
F
(
A
). The distance between the two fixed points, the bridge at the scroll and over the body of the instrument is, 0.25 m, the tension on the string
E
is 90 N. The mass per unit length of string
E
is nearly (A)
1 gm/m
(B)
2 gm/m
(C)
3 gm/m
(D)
4 gm/m