COMMON TEST # 5 – C-XII-1

FIITJEE COMMON TEST – V

MONTHLY
PHYSICS, CHEMISTRY & MATHEMATICS
BATCHES – NWCM820X1R-X4R, NWTR820C01, D01,CAMP820, NWCM820G1W, NWCM820X1W - X11W,

ASSESSMENT

CODE: 124096
NWTW820D01-D02, PANINI820-XII G1, PANINI820-XII1 - XII7, PIN820-XII B

Time Allotted: 3 Hours Maximum Marks: 186

▪ Please read the instructions carefully. You are allotted 5 minutes specifically for
this purpose.
▪ You are not allowed to leave the Examinat ion Hall before the end of the test.

INSTRUCTIONS
Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR
sheet before attempting the paper. Wrong CODE or no CODE will give wrong results.

A. General Instructions
1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.
2. This question paper contains Three Section.
3. Section-I is Physics, Section-II is Chemistry and Section-III is Mathematics.
4. Each section is further divided into two parts: Part-A & Part-C
5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided
for rough work.
6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in
any form, are not allowed.

B. Filling of OMR Sheet

1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR
sheet.
2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No.
and write in ink your Name, Test Centre and other details at the designated places.
3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Three Parts.

(i) Part-A (01 – 05) contains 5 multiple choice questions which have only one correct answer. Each question
carries +3 marks for correct answer and – 1 mark for wrong answer.
PART – A (06 – 13) contains 8 Multiple Choice Questions which have One or More Correct answer.
For each question in the group Q. 6 – 13 of PART – A you will be awarded
Full Marks: +4 If only the bubble(s) corresponding to all the correct options(s) is (are) darkened.
Partial Marks: +1 For darkening a bubble corresponding to each correct option, provided NO incorrect
option is darkened.
Zero Marks: 0 If none of the bubbles is darkened.
Negative Marks: −2 In all other cases.
For example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will result
in +4 marks; darkening only (A) and (D) will result in +2 marks; and darkening (A) and (B) will result in −2
marks, as a wrong option is also darkened.

(iii) Part-C (01 – 05) contains 5 Numerical based questions with single digit integer as answer, ranging from 0
to 9 and each question carries +3 marks for correct answer. There is no negative marking.

Name of the Candidate: __________________________________________

Batch: ___________________ Date of Examination: __________________

Enrolment Number: _____________________________________________

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COMMON TEST # 5 – C-XII-2

S
SEEC
CTTIIO
ONN –– II:: P
PHHY
YSSIIC
CSS
PART – A
(Single Correct Choice Type)
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.

1. An object is placed at a distance of 3f from a convex lens of focal length f. A slab of refractive index 
is placed in between lens and object. The image of the object will be formed nearest to the object if
thickness of the slab is
f f
(A) f (B) 2f (C) (D)
 −1  −1

2. An observer can see through a pinhole the top end of a thin rod of
height h, placed as shown in the figure. The beaker height is 3h
and its radius h. When the beaker is filled with a liquid upto a
height 2h, he can see the lower end of the rod. Then the
refractive index of the liquid is 3h
(A) 5/2 (B) 5/2 h
(C) 3/2 (D) 3/2 2h
3. If an object is placed unsymmetrically between two plane mirrors inclined at an angle of 72°, then the
total number of images formed is
(A) 5 (B) 4 (C) 2 (D) infinite

4. An object of length 1 cm is placed on the principle axis of an

equiconvex lens of radius 5 cm. Distance between the lens and
object is 20 cm. Space between the lens and object is filled with =2 =1 =1
medium of two different refractive indices 2 and 1 as shown in the 1.5
figure. Refractive index is 1 on the left of the object and on the right
side of the lens. Boundary of both medium is mid-way between the 10cm 10cm
object and lens.
(A) The image will be formed at distance of 7.5 cm from the optical centre of lens
(B) The image will be formed at distance of 10 cm from the optical centre of lens
(C) The image will be formed at distance of 15.0 cm from the optical centre of lens
(D) The image will be formed at distance of 12.5 cm from the optical centre of lens

5. Mark the incorrect option.

(A) The speed of light of different colour are same in free space (vacuum).
(B) The speed of light of different colour are different in a medium (other than vacuum).
(C) The speed of light of different colour are same in a medium (other than vacuum).
(D) None of these
Space for rough work

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COMMON TEST # 5 – C-XII-3

(Multi Correct Choice Type)

This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONE OR MORE may be correct.

6. One fourth part of an equiconvex lens of focal length 100 cm is removed

as shown in the figure. An object of height 1 cm is placed in front of the O
lens. It is observed that all the images are of equal height. Then

400
(A) Object is at a distance of cm from the lens.
3
(B) The magnitude of magnification produced by upper and lower part is equal.
(C) The no. of images formed is two.
(D) The product of magnification of both the lenses is negative.

7. Laws of reflection are valid for

(A) plane surface (B) curved surface (C) zigzag surface (D) none of these

8. A ray of light from a denser medium strike a rarer medium at an

angle of incidence i. The reflected and refracted rays make an angle
i r
of 900 with each other. The angle of reflection and refraction are r
and r. The critical angle is (are)
(A) sin–1 (tan r) (B) sin–1 (tan i)
r
(C) sin–1 (tan r) (D) tan–1 (sin i)

9. A ray of light travelling in a transparent medium falls on a surface separating the medium from air at
an angle of incidence 450. The ray undergoes total internal reflection. If n is the refractive index of the
medium with respect to air, select the possible value(s) of n from the following
(A) 1.3 (B) 1.4 (C) 1.5 (D) 1.6

10. A flat mirror M is arranged parallel to a wall and light from a point s p
source S on the wall is reflected back to the wall. With what velocity 45 0

will be spot move along the wall if the mirror is brought up to the wall
with a velocity v?
(A) v
(B) 2v
(C) the spot will move to right M
(D) the spot will move to left

11. A converging lens is used to form an image on a screen. When the upper half of the lens is covered
by an opaque screen,
(A) half the image will disappear. (B) complete image will be formed.
(C) intensity of the image will increase (D) intensity of the image will decrease.
Space for rough work

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COMMON TEST # 5 – C-XII-4

12. A diverging beam of light from a point source S having divergence angle  , •S
falls symmetrically on a glass slab as shown. The angles of incidence of the 
two extreme rays are equal. If the thickness of the glass slab is t and the
refractive index n, then the emergent rays are i i
(A) converging
(B) diverging n

(C) making angle  with each other

(D) making angle 2 with each other

13. The distance d between two identical concave mirrors of radius

of curvature R. So, as to coincide the image I on the object O
itself, which is placed at the mid point can be O
(A) R (B) 2R
(C) 3R (D) R/2
d

PART – C
(Integer Type)
This section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to
9. The correct digit below the question number in the ORS is to be bubbled.

1. A spherical surface of radius of curvature R separates air (refractive index 1.0) from glass (refractive
index 1.5). The centre of curvature is in the glass. A point object P placed in air is found to have a real
PO
image Q in the glass. The line PQ cuts the surface at a point O, and PO = OQ. Find the value of .
R

2. Focal length of an equiconvex lens is 2 cm. If we cut it once perpendicular to principle axis, and then
along principle axis. Find the focal length (in cm) of each part.

3. A bulb is placed at a depth of 2 7 m in water and a floating opaque disc is placed over the bulb so
that the bulb is not visible from the surface. Find the radius (in meter) of the disc should be at least
(water = 4/3)

4. A ray of light falls normally on a refracting face of a prism of refractive index 1.5. If the ray just fails to
−1 k
emerge from the prism. If the angle of prism is sin then find the value of k.
3

5. For a concave mirror of focal length 20 cm, if the object is at a distance of 30 cm from the pole, find
magnitude of magnification.
Space for rough work

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COMMON TEST # 5 – C-XII-5

S
SEEC
CTTIIO
ONN –– IIII:: C
CHHE
EMMIIS
STTR
RYY
PART – A
(Single Correct Choice Type)
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.

1. Mixture of volatile components A and B has total vapour pressure (in torr) PTotal = 254 – 119 XA.
Where XA is mole fraction of A in the mixture. Hence PA0 and PB0 are in torr
(A) 254, 119 (B) 119, 254 (C) 135, 254 (D) 154, 119

2. What should be the boiling point of 1.0 molal aqueous KCl solution(assuming complete dissociation of
KCl) if Kb H2O is 0.52 K m –1.
(A) 100.52oC (B) 101.04oC (C) 99.48oC (D) 98.96oC

3. Which of the following complex compound(s) is/are paramagnetic and low spin?
(i) K3[Fe(CN)6] (ii) [Ni(CO)4]
(iii) [Cr(NH3)6]3+ (iv) [Mn(CN)6]4–

(A) (i) only (B) (ii) & (iii) (C) (i) & (iv) (D) (iv) only

4. Gold dissolves in aqua-regia forming

(A) AuCl3 (B) AuCl2 (C) [AuCl4]– (D) Au(NO3)2

5. Which of the following acts as oxidising agent in acidic medium only?

(A) KMnO4 (B) H2O2 (C) K2Cr2O7 (D) None of these

(Multi Correct Choice Type)

This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONE OR MORE may be correct.

6. Solution of phenol and aniline showing deviation from Raoult’s law will show
(A) Hmix < 0 (B) Vmix < 0
(C) PT > PA A + PB B
o o
(D) Smix < 0

7. In which of the following pairs of solutions will the values of Van’t Hoff factor be the same?
(A) 0.05 M K4[Fe(CN)6] and 0.1 M FeSO4
(B) 0.10 M K4[Fe(CN)6] and 0.05 M FeSO4.(NH4)2SO4.6H2O
(C) 0.2 M NaCl and 0.1 M BaCl2
(D) 0.05 M FeSO4(NH4)2SO4.6H2O and 0.02 M KCl.MgCl2.6H2O

8. EM0 2+ /M for first row transition metals are

EM0 2+ /M V Cr Mn Fe Co Ni Cu
-1.18 -0.91 -1.18 -0.44 -0.28 -0.5 +0.34
Which of the following statements is/are correct?
0
(A) EM2 + /Mn is unusually more negative due to greater stability of Mn2+
(B) Cr2+ is better reducing agent than Mn2+
(C) Copper does not displace hydrogen from dilute acids
(D) Reducing character decreases along the given row
Space for rough work

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COMMON TEST # 5 – C-XII-6

9. Which of the following gases are soluble in water due to formation of their ions?
(A) NH3 (B) CH4 (C) SO2 (D) HCl

10. Consider the following solutions:

I. 1 M aq. glucose solution II. 1 M aq. NaCl solution
III. 1 M aq (NH4)3PO4 solution IV. 1 M benzoic acid in benzene
Select the correct statement for above solution
(A) All are isotonic solution (B) III is hypertonic of I, II and IV
(C) IV is hypotonic of I, II and III (D) II is hypotonic of III but hypertonic of I & IV

11. Which of the following is the correct match?

Catalyst Application
(A) Ziegler-Natta catalyst Polymerisation of ethane
(B) [C2H4PdCl2] Wacker’s process
(C) V2O5 Haber’s process
(D) Fe34+ 2I− + S2O82− ⎯⎯
→I2 + 2SO24−

12. Which of the following are coloured due to charge transfer?

(A) MnO−4 (B) [Fe(H2O)5NO]2+ (C) FeSO4.7H2O (D) Cr2O72−

13. Identify the correct statements

(A) 0 increasing order is [CrCl6]3– < [Cr(NH3)6]3+ < [Cr(CN)6]3–
(B) CFSE for [Ti(H2O)6]3+ is -0.4 0
(C) [NiCl4]2– as well as [Ni(CO)4] are diamagnetic
(D) The halide ions are arranged as I– < Br– < Cl– < F– in the spectrochemical series

PART – C
(Integer Type)
This section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to
9. The correct digit below the question number in the ORS is to be bubbled.

1. The spin only magnetic moment of [MnBr4]2– is 5.9 B.M. The number of unpaired electrons in Mn is

2. If K4[Fe(CN)6] is 50% dissociated in aq. Solution, then Van’t Hoff factor will be

3. The number of ions which will be coloured in aq. solution will be

Ti3+, V3+, Cu3+, Sc3+, Mn2+, Fe3+, Co2+

4. Number of -bonds in a molecule of Ferrocene are

5. 620 g of glycol is added to 4 kg of water in the radiator of a car. What amount of ice will separate out
at -6oC(Kf = 1.86 K Kg mol–1) is n  10–1 Kg, then n is
Space for rough work

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COMMON TEST # 5 – C-XII-7

S
SEEC
CTTIIO
ONN –– IIIIII:: M
MAAT
THHE
EMMA
ATTIIC
CSS
PART – A
(Single Correct Choice Type)
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.

 2 
A=  and A = 125 , then  =
3
1. If
 2  
(A) 3 (B) 2 (C) 5 (D) 0

 1 2
If A =   , then A is equal to (n  N)
n
2.
 0 1 
 1 2n  2 n  1 2n   1 n
(A)   (B)   (C)   (D)  
0 1  0 1 0 −1 0 1

3. Number of real values of  for equations (  + 3) x + (  + 2) y + z = 0 , 3x + (  + 3) y + z = 0 and

2x + 3y + z = 0 has a non-trivial solutions is
(A) 0 (B) 1 (C) 2 (D) infinite

 0 0 1
4.
 
If A = 0 1 0 , then A −1 is
 
 1 0 0 
(A) –A (B) A (C) 1 (D) None of these

 1 −1 x 
5.
 
If 1 x 1 has no inverse, then the real value of x is
 
 x −1 1
(A) 2 (B) 3 (C) 0 (D) 1

(Multi Correct Choice Type)

This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONE OR MORE may be correct.

6. If A and B are square matrices of same order such that AB = A and BA = B, then
B = A2 A =B (C) ABA = A BAB = B
2 2
(A) A (B) B (D)

7. If A is an invertible matrix, then which of the following are true?

(A) A O (B) Adj. A  O (C) A 0 (D) A −1 = A Adj.A

Space for rough work

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COMMON TEST # 5 – C-XII-8

8. The system of equation (1 +  ) x1 + x2 + x3 = 1 x1 + (1 +  ) x2 + x3 =  x1 + x2 + (1 +  ) x3 = 2

(A) is in consistent if =0 (B) has a unique solution if (  + 3)  0
(C) has infinite number of solution for  = −3 (D) has no solution for  = −3

a b c   q −b y 
9.
   
If A = x y z , B = −p a − x , then:
   
p q r   r −c z 
(A) A = B (B) A = − B

(C) A =2B (D) A is invertible if and only if B is invertible

10. If A and B are symmetric and commute, then which of the following is/are symmetric?
−1 −1
(A) A B (B) AB (C) A −1 B−1 (D) None of these

 1 3 2   1
11. 1 x 1  2 5 1  2 = 0 if x =
15 3 2  x 
(A) -7 (B) -11 (C) -2 (D) -14

12. Which of the following statment is always true for square matrix
(A) Adjoint of a symetic matrix is symmetric (B) Adjoint of unit matrix is unit matrix
(C) A(adj A) =(adj A)A (D)Adjoint of diagonal matrix is diagonal matrix

ex sin x 1
13. If  = cos x log e (1 + x 2 ) 1 = a + bx + cx 2 , then
x x2 1
(A) a=0 (B) a =1 (C) b = −1 (D) b = −2

PART – C
(Integer Type)
This section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to
9. The correct digit below the question number in the ORS is to be bubbled.

a1 a2 a3
1. If a1,a2 ,a3 ,5,4,a6 ,a7 ,a8 ,a9 are H.P., then the value of the determinant 5 4 a6 can be
a7 a8 a9
p
expressed in the lowest form as , find (p − 2q) .
q

Space for rough work

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COMMON TEST # 5 – C-XII-9

sin  cos  sin 

2. Consider f() = cos  sin  cos  , then number of solutions of f() = 0 in [0,  ] is
cos  sin  sin 

1 n n
n
3. If k = 2k n + n+1
2
n +n 2
and  k = 56 , then n is equal to
k =1
2k − 1 n2
n + n +1
2

1
f ( x) f   + f ( x)
 x
4. If = = 0 , f ( x ) = a + bx n and f ( 2 ) = 17, then f ( 5) / 313 is equal to
 
1
1 f 
 x
2
x cos x ex
 /2
5. If f ( x ) = sin x x2 sec x , then the value of  f ( x ) dx is equal to
− /2
tan x 1 2

Space for rough work

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