METRE
MENTORS EDUSERV TALENT REWARD EXAMINATION
STAGE- II
SAMPLE QUESTION PAPER
(FOR STUDENTS APPEARING FOR CLASS XII BOARD IN 2016)
STREAM: ENGINEERING
Maximum Marks: 198
INSTRUCTIONS
[A]
General
1.
The question paper consists of THREE Parts A to C (Physics, Chemistry and Mathematics). Each part
has THREE sections-Section- I, Section- II and Section- III.
2.
This Question Paper contains 17 pages, other than the coloured cover pages.
3.
This question paper contains total 60 questions. There are 20 questions each in Physics, Chemistry
and Mathematics.
4.
In each part (subject):
Section I contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONLY ONE is correct.
Section II contains 3 paragraphs each describing theory, experiment, data etc. There are 6 multiple
choice questions relating to three paragraphs with 2 questions on each paragraph. Each question of
a particular paragraph has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Section III contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONE or MORE are correct.
5.
The Question Paper has blank spaces at the bottom of each page for rough work. No additional
sheets will be provided for rough work.
6.
[B]
[C]
[D]
Blank papers, clip boards, log tables, slide rule, calculators, cellular phones, pagers and electronic
gadgets, in any form, are NOT allowed.
7.
The OMR ( Optical Mark Recognition) sheet shall be provided separately.
Answering on the OMR
8.
Darken the bubble(s) with Ball Pen (Blue or Black) ONLY corresponding to all the correct option(s).
Filling OMR
9.
On the OMR sheet, fill all the details properly and completely, otherwise your OMR will not be checked.
10. Do not write anything or tamper the barcode in the registration no. box.
Marking Scheme
11. For each question in Section-I and Section-II, you will be awarded +3 marks if you darken the bubble
corresponding to the correct answer ONLY and zero (0) marks if none of the bubbles are darkened. In
all other cases, minus one (–1) mark will be awarded in these sections.
12. For each question in Section-III, you will be awarded +4 marks if you darken ALL the bubble(s)
corresponding to the correct answer(s) ONLY. In all other cases, zero (0) marks will be awarded. No
negative marks will be awarded for incorrect answer(s) in this section.
Name : .......................................................................................................
Registration No.:
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SEAL
DO NOT BREAK THE SEALS ON THIS BOOKLET, AWAIT INSTRUCTIONS FROM THE INVIGILATOR.
Time : 3 hours
For Students appearing for Class XII Board in 2016[E]
METRE [Stage-II ]
[ 1 ]
PART-A: PHYSICS
SECTION – I
This section contains EIGHT questions (Q1 to Q8). Each question has four choices (A), (B), (C) and
(D), out of which ONLY ONE is correct.
1.
A charged particle enters a uniform magnetic field with velocity vector making an angle of 30o with
the magnetic field. The particle describes a helical trajectory of pitch x. The radius of the helix is
(A)
2.
x
2
(B)
x
2 2
(C)
x
2 3
The rate of change of acceleration versus graph of
a particle initially at rest is shown in the graph. If
initial acceleration is zero then velocity of particle at
t = 3s is
(D)
3x
2
da
(rate of change of acceleration)
dt
5
121
m/ s
(A)
4
(C)
3.
81
m/ s
2
81
m/ s
(B)
4
t(s)
(D) 25 m / s
10
What is the amount of power delivered by the ac source in the circuit shown (in watts).
XC= 12
XL= 8
R1= 5
R2= 6
Erms= 130V
(A) 500 watt
(B) 1014 watt
(C) 2013 watt
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(D) 1514 watt
[2]
4.
METRE [Stage-II ]
Sample Question Paper
A triangular prism of glass is located inside water. A ray, incident normally, on one of the faces, is
totally reflected from face BC. Then the minimum refractive index of glass is
3
2
(B) 5/3
(A)
A
C
2 2
45º
5
nw=4/3
4 2
B
(D)
3
In the diagram shown, a time varying non uniform magnetic field passes through a circular region
(C)
5.
of radius R. The magnetic field is directed outwards and it is a function of radial distance ‘r’ and
time ‘t’ according to the relation B = B0rt. What is the induced electric field strength at a radial
distance R/2 from the center?
R
(A) B0R2/12
6.
(B) B0R2/6
(C) 2B0R2/3
(D) B0R2/16
A uniform rod of mass 'M' and length L is hanging from a ceiling. The variation of tensile stress
with distance X from the ceiling is best represented by
(A)
7.
(B)
(C)
(D)
A plane transverse wave is propagating in a direction making an angle of 30° with positive x-axis
in the x-y plane. Find phase difference between points (0, 0, 0) and (1, 1, 1). Wavelength of the
wave is 1 m.
(A) 2rad
(B) ( 3  1)  rad
(C) ( 2  1)  rad
(D) none
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8.
METRE [Stage-II ]
[ 3 ]
The distribution of relative intensity I() of blackbody radiation from a solid body versus the
wavelength  is shown in the figure. If the Wien displacement law constant is 2.9 × 10-3 mK, what
is the approximate temperature of the object?
(A) 50 K
(B) 250 K
(C) 1450 K
(D) 6250 K
SECTION – II
This section contains SIX questions (Q9 to Q14) relating to three paragraphs with TWO questions on
each paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is
correct.
PARAGRAPH 1 (for Q9 & Q10)
A tank having cross sectional area A has a hole at the bottom of area of cross section A1 = A/1000.
Bottom of the tank is a plane mirror. The tank contains water of refractive index 4/3. At the instant,
when height of the water in the tank is 5m, a fish is rising vertically in the tank with a velocity 3 cm/sec
toward the surface.
9.
10.
3cm/s

5m
hole
The velocity with which surface is falling down inside container is
(A) 1 cm/s
(B) 2 cm/s
(C) 3 cm/s
(D) 4 cm/s
The velocity of the fish as observed by the observer looking directly at the fish is
(A) 2 cm/s
(B) 3 cm/s
(C) 4 cm/s
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(D) 1 cm/s
[4]
METRE [Stage-II ]
Sample Question Paper
PARAGRAPH 2 (for Q11 & Q12)
Whenever the flux of magnetic field through the area bounded by a closed conducting loop changes,
an emf is induced in the loop. The emf is given by
 
 
d
, where    B  ds is the flux of the magnetic field through the area.
dt
Now consider a loop as shown in the figure. The loop comprises of two parallel rails connected by an
ideal conductor L and a slider of mass m and length l. A uniform external magnetic field B is directed
into the plane of the loop. At t = 0 the slider is imparted a velocity v0 (as shown).
L
B

v0
l
From the given information answer the following questions.
11. The current in the circuit as a function of distance (x) travelled by the slider is
 Bl 
x
 Lm 
(A) i  
12.
 Bl 
x
 L
 Bl  2
(C) i    x
 L
(B) i  
 Bl 
(D) i    x
m
The time period of oscillation of the slider is
(A) T  2
Lm
B 2l 2
(B) T  2
Lm
Bl
(C) T  2
m
B 2l 2
(D) T  2
Lm
Bl 2
PARAGRAPH 3 (for Q13 & Q14)
A solid cylinder of mass m and radius R is kept at rest on a plank of mass 2m lying on a smooth
horizontal surface. Massless and inextensible string connecting cylinder to the plank is passing over a
massless pulley. The friction between the cylinder and the plank is sufficient to prevent slipping. Pulley
A is pulled with a constant horizontal force F.
A
m
R
F
2m
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For Students appearing for Class XII Board in 2016[E]
13.
[ 5 ]
Acceleration of cylinder with respect to earth is
(A)
14.
METRE [Stage-II ]
5F
21m
(B)
5F
21m
(B)
F
7m
(C)
3F
7m
(D)
2F
7m
F
7m
(C)
3F
7m
(D)
2F
7m
Acceleration of plank with respect to earth is
(A)
SECTION – III
This section contains SIX questions (Q15 to Q20). Each question has 4 choices
(A), (B), (C) and (D), out of which ONE OR MORE THAN ONE is correct.
15. In a resonance tube experiment, a closed organ pipe of length 120cm resonates when tuned
with a tuning fork of frequency 340Hz. If water is poured in the pipe then (given v air = 340m/
sec) :
(A) minimum length of water column to have the resonance is 45cm.
(B) the distance between two successive nodes is 50cm.
(C) the maximum length of water column to create the resonance is 95cm.
(D) none of these.
16. Two blocks, of masses M and 2M, are connected to a light spring of spring constant K that has
one end fixed, as shown in figure. The horizontal surface and the pulley are frictionless. The
blocks are released from when the spring is non deformed. The string is light.
K
M
2M
4Mg
.
K
2M 2g 2
(B) Maximum kinetic energy of the system is
K
(A) Maximum extension in the spring is
(C) Maximum energy stored in the spring is four times that of maximum kinetic energy of the
system.
4M 2g 2
(D) When kinetic energy of the system is maximum, energy stored in the spring is
.
K
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[6]
17.
METRE [Stage-II ]
Sample Question Paper
A parallel plate capacitor of capacitance 'C' has charges on its plates
initially as shown in the figure. Now at t = 0, the switch 'S' is closed. Select
the correct alternative(s) for this circuit diagram.
(A) In steady state the charges on the outer surfaces of plates
'A' and 'B' will be same in magnitude and sign.
(B) In steady state the charges on the outer surfaces of plates 'A' and 'B' will be same in
magnitude and opposite in sign.
(C) In stady state the charges on the inner surfaces of plates 'A' and 'B' will be same in
magnitude and opposite in sign.
(D) The work done by the time steady state is reached is
18.
Assume that entire xz-plane is charged with a uniform surface charge density of 8.85  1012 C/m2.
The potential at origin is assumed to be zero.
(A) the potential at (1, 0, 1) is 2V
(C) the potential at (1, –1, –1) is
19.
20.
5 2 C
2
(B) the potential at (1, –1, –1) is
1
V
2
1
V
2
(D) the potential at (–1, –1, –1) is
1
V
2
A hydrogen like gas atoms absorb radiations of wavelength  0 and consequently emit radiations
of 6 difference wavelengths of which, two wavelengths are shorter than  0 . Choose the correct
alternative (s).
(A) The final excited state of the atoms is n = 3.
(B) The final excited state of the atoms is n = 4
(C) The initial state of the atoms is n = 2
(D) The initial state of the atoms is n = 3.
A thin, symmetric double-convex lens of power P is cut into three parts A, B and C as shown. The
power of:
A
B
(A) A is P
(B) A is 2P
C
(C) B is
P
2
(D) B is
P
4
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METRE [Stage-II ]
[ 7 ]
PART-B: CHEMISTRY
SECTION – I
This section contains EIGHT questions (Q21 to Q28). Each question has four choices (A), (B), (C)
and (D), out of which ONLY ONE is correct.
21.
Calculate the standard potential for the reaction at 298 K
½ O2 + 2H+ + 2e  H2O
If E° for the reaction, ½O2 + H2O + 2e  2OH is + 0.4 V
(A)  1.227 V
22.
(C)  0.828 V
(D) 8.28 V
1
Figure shows a graph of log10 k vs
where k is rate constant and T is temperature. The
T
1
straight line BC has slope, tan  = 
and an intercept of 5 on Yaxis. Thus Ea, the energy
2.303
(B) 1.227 V
of activation is:
B
log10 k
C
A
(A) 2.303  2 cal
23.
24.
(B)
2
cal
2.303
1/T
(C) 2 cal
(D) None of these
Which of the following is arranged in order of increasing dipole moment?
(A) BCl3 < NH3 < H2O < NF3
(B) BCl3 < NF3 < NH3 < H2O
(C) NH3 < NF3 < H2O < BCl3
(D) H2O < NF3 < NH3 < BCl3
–
Calculate the enthalpy of formation of OH ions from the following thermochemical data :
H 2 O (1)  H  (aq )  OH  ( aq ) ;
H 298 K  57.32 kJ
1
H 2 (g )  O 2 (g )  H 2 O ( l ) ;
2
(A) –228.51 kJ
H 298 K  285.83 kJ
(B) –198.51 kJ
(C) + 238.5 kJ
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(D) –238.5 kJ
[8]
25.
26.
27.
METRE [Stage-II ]
Sample Question Paper
Match the method of concentration of the ore in column I with the ore in column II and select the
correct alternate:
Column I
Column II
X. Magnetic separation
A. Ag2S
Y. Froth floatation
B. FeCr2O4
Z. Gravity separation
C. Al2(SiO3)3
X
Y
Z
(A) A
B
C
(B) B
A
C
(C) C
A
B
(D) B
C
A
Which of the following is optically active?
(A)
(B)
(C)
(D)
The rate law for the following intramolecular Cannizzaro reaction will be
O
O
OH
O
OH
Ph — C — C — H 
Ph — CH — C — O
O O
O O
||
||

2
2
(A) rate  k[Ph — C — C — H][O H]
(B) rate = k[Ph—C—C—H] [OH]
O O
||
||

(C) rate  k[Ph — C — C — H ][O H]
O O
||
||

2
2
(D) rate  k[Ph — C — C — H] [O H]
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METRE [Stage-II ]
[ 9 ]
O
28.
i ) OH
(


Predict the product in the following reaction
( ii ) H / H 2O
product.
O
OH
OH
OH
(A)
(B)
COOH
(C)
(D)
O
COOH
SECTION – II
This section contains SIX questions (Q29 to Q34) relating to three paragraphs with TWO questions
on each paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is
correct.
PARAGRAPH 1 (for Q29 & Q30)
Consider the following energy level diagram :
6C(s) + 6H2(g) + 9O2(g)
C6H12O6 + 6O2(g)
x
y
Energy
z
6CO2(g) + 6H2O (l)
Answer the following questions on the basis of the given diagram :
29. The heat of formation of glucose is
(A) –x
(B) –y
(C) x – y
30. In the given diagram ‘z’ refers to

0
(A) 6  Hf of CO2

(C) H0c of C6H12O6
(D) –x + z
(B) H0f of C6H12O6
(D) H0c of C(s)  H0f of H2O
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[ 10 ]
METRE [Stage-II ]
Sample Question Paper
PARAGRAPH 2 (for Q31 & Q32)
Ortho boric acid is a white crystalline solid. It is soluble in water. It can be prepared by acidifying
aqueous solution of borax on heating. Borax first loses water molecules and swells up. On furthest
heating it turns into a transparent liquid, which solidifies into glass like material known as borax bead.
31. Boric acid crystallizes in a layer structure in which H3BO3 are bonded together by
(A) Dative bond
(B) Hydrogen bond
(C) van der Waal’s force
(D) Ionic and Dative bonds
32.
375K
 375 K
Re dheat
H3BO3 
 X 
 Y  Z
acid
acid
X, Y and Z are
(A) B2O3, HBO2 and H2B2O4
(C) HBO2, B2O3, H2B4O7
(B) HBO2, H2B2O7, B2O3
(D) B2O3, H2B4O7, B(OH)3
PARAGRAPH 3 (for Q33 & Q34)
A chemist performs the following reactions:
(i) K2[PtCl4] + 2NH3 
 A + 2KCl
(ii) [Pt(NH3)4](NO3)2 + 2KCl 
 B + 2NH3 + 2KNO3
She finds both A and B are white, diamagnetic, crystalline compounds that give elemental analyses for
the formula PtCl2(NH3)2. However A is more soluble in polar solvents, such as ethanol, while B is
soluble in petroleum ether and CCl4.
Another chemist who reads a report of this experiment and immediately identifies A and B. Since nickel
is in the same group of the periodic table as platinum, he decides to perform the same experiment with
Ni(II) but is unsuccessful. He obtains some K2NiCl4, but when he attempts to run reaction (i), the only
products he is able to isolate are Ni(NH3)6Cl2 and KCl. When triphenyl phosphine, Ph3P, is used in place
of ammonia as one of the ligands (chloride ion is still the second ligand), compound C is isolated. This
compound analyses for the empirical formula NiCl2(Ph3P)2, and is greenish, paramagnetic, and soluble
in organic polar solvents. Regardless of the reaction conditions or concentrations chosen, only C is
found; no other isomers are observed.
33. The structure of A is
NH3
Cl
Pt
(A)
NH3
NH3
Pt
(B)
Cl
Cl
Cl
NH3
Cl
(C)
NH3
Pt
NH3
Cl
Cl (D) NH3
Pt
NH3
Cl
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34.
METRE [Stage-II ]
[ 11 ]
Compound C is
Ph3P
Cl
Ph3P
Ni
(A)
Ni
(B)
Ph3P
Cl
Cl
PPh3
Ni
(C) Ph P
3
Cl
PPh3
P Ph3
PPh 3
Ni
Ni
(D) Cl
Cl
Cl
Cl
Cl
Cl
SECTION – III
This section contains SIX questions (Q35 to Q40). Each question has 4 choices (A), (B), (C) and (D),
out of which ONE OR MORE THAN ONE is correct.
35. Consider the following statements and pick up the correct statements:
CH2– Br will react more readily than O N
2
(A) MeO
reaction
Br
(B)
Br
for SN1 reaction
will react more readily than
Cl
(C)
Cl
for SN1 reaction
will react more readily than
N
N
H
(D) SN1 reaction occurs in polar protic solvent
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CH2Br for SN1
[ 12 ]
36.
METRE [Stage-II ]
Sample Question Paper
In which of the following cases, the major product has been correctly shown?
Br
 
H2O
(A)
Me3CO K
(B)

Br
(C)
EtO
Br

Br
(D)
C2H5OH

EtOH
37.
38.
39.
When ZnS and PbS minerals are present together, then NaCN is added to separate them in the
froth floatation process as a depressant, because
(A) Pb (CN)2 is precipitated while no effect on ZnS
(B) ZnS forms soluble complex by adding NaCN
(C)PbS forms soluble complex Na2 [Pb (CN)4]
(D)They cannot be separated by adding NaCN.
Which of the following arrangement will produce oxygen at anode during electrolysis ?
(A) Dilute H2SO4 solution with Cu electrodes.
(B) Dilute H2SO4 solution with inert electrodes.
(C) Fused NaOH with inert electrodes.
(D) Dilute NaCl solution with inert electrodes.
Which statements are correct for the following compounds?
CHO
H
HO
40.
CHO
OH
H
HO
H
H
OH
C6H5
C 6H 5
(I)
(II)
(A) Both are in threo form.
(B) Both are enantiomers.
(C) Both are diastereomers.
(D) Both are in erythro form.
Which of the following compound/species is/are aromatic species?
O
(A)
(B)
O

(C)
(D)
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METRE [Stage-II ]
[ 13 ]
PART-C: MATHEMATICS
SECTION – I
This section contains EIGHT questions (Q41 to Q48). Each question has 4 choices (A), (B), (C) and
(D), out of which ONLY ONE is correct.
41.
n
n
n
If each critical point of f(x) = (x  ) 1 (x  ) 2 (x   ) 3 , where n1 , n 2 , n 3 I+ is either local maximum
or local minimum then
(A) n1, n2, n3 are even integer
(B) n1 is odd , n2 is even , and n3 is even
(C) n1, n2 , n3 prime numbers
(D) n1, n2, n3 are odd integers
42.
If A1, A2, ..., A8 are independent events such that P  Ai  
1
, 1  i  8 , then the probability that
i 1
none of the events occurs is
(A)
43.
2
9
(B)
1
3
(C)
1
2
(D)
1
9



  



If a , b , c are unit vectors such that | a + b + 3 c | = 4. Angle between a and b is 1 , between b
  2 



and c is 2 and between a and c varies in  ,  , then maximum value of cos1 + 3cos2 is
6 3 
44.
(A) 3
(B) 4
(C) 2 2
(D) 6
Let f : R  R and g : R  R be two one–one and onto functions such that they are the mirror
images of each other about the line y = a. If h : R  R such that h(x) = f(x) + g(x), then h(x) is
(A) one–one onto
45.
(B) one–one into
(C) many-one onto
(D) many-one into
dy
x (2log x  1)
The solution of the equation dx  sin y  y cos y is
(A) y sin y  x 2 log x 
x2
c
2
(C) y cos y  x 2 log x 
x2
c
2
(B) y cos y  x 2 (log x  1)  c
(D) y sin y  x 2 log x  c
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[ 14 ]
46.
47.
METRE [Stage-II ]
Sample Question Paper
If the graph of f ( x )  2 x 3  ax 2  bx, a, b  N cuts the x axis at three distinct points, then the
minimum possible value of a  b is
(A) 2
(B) 4
(C)6
(D) 8
Let P(x) be a polynomial of least degree whose graph has three points of inflexion (–1, –1), (1,
1) and a point with abscissa 0 at which the curve is inclined to the axis of abscissas at an angle
1
of 60°. Then
 P( x)dx equal to
0
(A)
3 3 2

14 7
(B)
(C) 2 2  1
2 1
(D)
3 3 2

14
7
(D)
1
3e
1
I1
x 2 dx
ex
I

dx
and
2
0 e x3 2  x3 . Then I 2 is
0 1  x
1
48.
Let I1 
(A)
3
e

(B)

e
3
(C) 3e
SECTION – II
This section contains SIX questions (Q49 to Q54) relating to three paragraphs with TWO questions
on each paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is
correct.
PARAGRAPH 1 (for Q49 & Q50)
In a tournament, there are sixteen players S1, S2, …, S16 and divided into eight pairs at random. From
each game a winner is decided on the basis of a game played between the two players of the pair.
Assuming that all the players are of equal strength
49. The probability that exactly one of S1 or S2 is a winner
(A)
50.
8
15
(B)
1
2
(C)
1
3
(D)
7
30
(C)
1
3
(D)
7
30
Both S1 and S2 are among eight Winners
(A)
8
15
(B)
1
2
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For Students appearing for Class XII Board in 2016[E]
METRE [Stage-II ]
[ 15 ]
PARAGRAPH 2 (for Q51 & Q52)
Integration plays a vital role in proving identities involving binomial coefficients whose algebraic method
of proving is, in general, cumbersome and requires the help of Mathematical Induction. If we apply both
integration and induction/recursion techniques, several elegant binomial identities are proved. For
instance
C0 
C1 C2
( 1)n Cn 1
1

 ... 
  (1  x)n dx 
2
3
n 1
n 1
0
where Cr  n Cr ,r  0,1,2,....,n
m
( 1)k n
( 1)k m
 Ck ,S 2  
 Ck , where m > n then,
k 0 k  m  1
k 0 k  n  1
n
51.
If S1  
(A) S 2 
mn
S1
mn
(B) S 2   S1
(C) S 2  S1
52.
(D) S1  S 2  0 , for all m and n
The compact value of series C 0 
2 2n (2n  1)!
(A)
(n!) 2
C1 C 2 C 3
(1) n C n


 ....... 
must be equal to
3
5
7
2n  1
2 2 n (n!) 2
(B)
(2n  1)!
(C) 2 2 n (n!) 2
(D)
2n
2n  1
PARAGRAPH 3 (for Q53 & Q54)
A continuous function f (x ) satisfying x 4  4 x 2  f ( x )  2 x 2  x3 for all x  [0, 2]. Such that the area
bounded by y  f ( x ), y  x 4  4 x 2 , the y-axis and the line x  t ( 0  t  2) is k times the area bounded
by y  f ( x ), y  2 x 2  x 3 , y-axis and the line x = t (0  t  2). Then
53.
The function f (x ) , is given by :
(A)
1
[ x 4  kx 3  2(k  2) x 2 ]
k 1
(B)
1
[ x 4  ( k  2) x 3  2( k  2) x 2 ]
k 1
(C)
1
[ x 4  ( k  2) x 3  2( k  2) x ]
k 1
(D)
1
[ x 4  kx 3  2(k  2) x ]
k 1
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[ 16 ]
54.
METRE [Stage-II ]
Sample Question Paper
If k = 0; then f (x ) is symmetric about :
(A) origin
(B) y-axis
(C)x-axis
(D) y = x
SECTION – III
This section contains SIX questions (Q55 to Q60). Each question has 4 choices
(A), (B), (C) and (D), out of which ONE OR MORE THAN ONE is correct.
55.
Which of the following statements is/are true ?
(A) sin1
1
 1 
 tan1 

e
 
(B) sin1
1
 1 
 tan1 

e
 
(C) sin1 x  tan1 x has 3 solutions
(D) If x, y  (0,1), then x  y  sin1 x  tan1 y
56.
2 | x |  | x  2 |  || x  2 | 2 | x || 

The function f(x) = min | x  2 |,
 has a local maximum or a local
2


minimum at x =
(A) 
57.
2
3
(B) 0
(C)
2
3
(D) 2
If points A and B are represented by the non-zero complex numbers z1 and z2 on the argand
plane such that |z1 + z2| = |z1 – z2| and ‘O’ is the origin, then
(A) ortho-centre of AOB lies at O
(B) circum-centre of OAB is
z 

(C) arg  1   
2
 z2 
(D) AOB is isosceles
z1  z2
2
Space for rough work
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For Students appearing for Class XII Board in 2016[E]
58.
METRE [Stage-II ]
[ 17 ]
3 5 
 8 11 14 
Let Sn (n  1) be a sequence of sets defined by S1  {0},S2   ,  ,S3   , , 
2 2
3 3 3 
15 19 23 27 
S4   , , ,  ,..., then
4 4 4 4
(A) smallest element in S 20 is
399
20
(B) smallest element in S20 is
(C) sum of elements in S20 is 589
59.
401
20
(D) sum of elements in S20 is 609
Let points F1, F2 are foci of ellipse
x 2 y2

 1 and P is a point on ellipse such that
9
4
| PF1 | : | PF2 |  2 : 1 , then
(A) equation of circumcircle of PF1F2 is x 2  y 2  5
(B) equation of circumcircle of PF1F2 is x 2  y 2  6
(C) area of PF1F2 is equal to 4
(D) area of PF1F2 is equal to 6.
60.
Let three chords of lengths 2, 3 and 4 of a circle subtend angles x, y and x + y respectively at the
centre of the circle, then
(A)
cos x 
17
32
(B) cos x 
7
8
(C) cos y 
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11
18
(D) cos y 
7
128