ASSESSMENT TEST

Test (Physics, Chemistry & Mathematics)

Physics
1. Two infinitely long conductors ABC and DEF are placed as
shown. Each of them carry current of 100A as shown. Then A
magnetic induction at ‘O’ (mid point of BE) will be
C B =45°
(A) 4  104 T
(B) 2  10 4 T 10cm
D O
(C) 1 104 T
45°= E
(D) 0 T
F

2. An infinite collection of current carrying infinite conductors each carrying a current I outwards
perpendicular to papers are placed at x = 0, 20, 30, 40 … at infinite on the x-axis. Another
infinite collection of current carrying conductors each carrying a current I inwards perpendicular
to the papers are placed at x =  0, 20, 30, 40 … at infinite here 0 is a positive constant.
Then the magnetic field at the origin due to the above collection of current carrying conductor is
0I 0In2
(A) zero (B) (C) (D) infinite
 0 n2  0

3. A wire carrying a current I is bent into the shape of an y

exponential spiral, r = e, from  = 0 to  = 2 as shown in

I
figure. To complete a loop, the ends of the spiral are connected I
by a straight wire along the x axis. Find the magnitude at B at  x
r
the origin.
I

0I  0I  0I  0I
(A) 1  e2   (B) 2 1  e 2   (C) 1  e 2   (D) 1  e 2  
2 2  4 2  4 

4. The figure shown the cross section of a long cylindrical conductor A r

through which an axial hole of radius r is drilled with its centre at
point A. O is the centre of the conductor. 120
If an identical hole were to be drilled centred at point B while 30 O
maintaining the same current density the magnitude of magnetic field
B
at O
(A) will increase
(B) will decrease
(C) will remains the same
(D) May increase of decrease depending on the value of r.
                     I
5. A long solenoid of radius 2R contains another coaxial solenoid of
radius R. The coils have the same number of turns per unit length                     2I
2R
and initially both carry zero current. At time, t = 0, current start R
increasing linearly with time in both solenoids. At any moment the r
current flowing in the inner coil is twice as large as that in the outer               
2I
one and their directions are same. A charged particle, initially at                I
rest between the two solenoids, start moving along a circular
trajectory due to increasing current in the solenoid as shown in the
figure What is the radius of the circle? (Assume magnetic field due
to each solenoid remains uniform over its cross-section.)
3
(A) 2R (B) 3R (C) R (D) none of these
2

6. A charge particle of charge ‘q’ and mass ‘m’ enters in a given 30 v
    
magnetic field ‘B’ and perpendicular to the magnetic field as shown in     
the figure. It enters at an angle of 60 with the boundary surface of 
‘B’
   
magnetic field and comes out at an angle of 30 with the boundary     
surface of the magnetic field as shown in the figure. Find width ‘d’ in     
which magnetic field exist. v     
(m, q)
60
   d 
( 3  1)mv ( 3  1)mv
(A) (B)
4qB qB
( 3  1)mv ( 3  1)mv
(C) (D)
3qB 2qB

7. A particle of specific charge q/m is projected from the origin of coordinates with initial velocity
v1ˆi  v 2 ˆj in space having uniform electric field and magnetic field as E ĵ and B ĵ respectively.
The particle will definitely return to the origin once if
v1B v 2B
(A) is an integer (B) is an integer
E E
v12  v 22 B q v1  v 2 B
2 2

(C) is an integer (D) is an integer

E m E

8. A electron is projected normally from the surface of a sphere with

v0
speed v0 in a uniform magnetic field perpendicular to the plane of the wall
paper such that its strikes symmetrically opposite on the sphere with
a x
respect to the x-axis. Radius of the sphere is ‘a’ and the distance of its b

centre from the wall is ‘b’. What should be magnetic field such that
B
the charge particle just escapes the wall
2bmv 0 2bmv 0
(A) B  (B) B 
(b 2  a2 )e (a2  b2 )e
(a2  b2 ) me(b 2  a2 )
(C) B (D) B
2bmv 0 2bmv 0

9. In a certain region, a uniform electric field E and magnetic field B are x

present in the opposite directions. At the instant t = 0, a particle of mass
m carrying a charge q is given velocity vo at an angle  with y-axis, in
the yz plane. The time after which the speed of the particle would be E z
B
minimum is equal to  vo
mv o mv o sin 
(A) (B)
qE qE
y
mv o cos  2m
(C) (D)
qE qB
 10. A positively charged particle of charge ‘q’ enters in a uniform magnetic          
field ‘B’ directed inward and is deflected a distance y0 after traveling a  y       
         
distance x0 as shown in the figure. Then the magnitude of linear          y0 
momentum of the particle is          
qBx 0 qB  x 02  q    x0     x
(A) (B)   x0          
2 2  y0           
qB 2 qB 2
(C) (x 0  y 02 ) (D) (x 0  y 02 )
2y 0 2y 0

11. A current i flows in a long straight wire with cross-section having the 
  
i y
form of a thin half ring of radius R. a charge particle of charge q is  
x
projected with speed v from the centre O of ring in a direction  R 
perpendicular to diameter PR as shown in the figure. The force acting  O 
on the charge is P q v R
qv 0i
(A) zero (B)
4R
qv 0 i qv0 i
(C) (D)
2 R 2R

12. An electron gun T emits electrons accelerated by a potential difference V Electron gun
T A
in a vacuum. The emitted electrons move in the direction of line TA as 

shown in figure. The target M is placed at a distance d from the electron d

gun in such a way that the line segment connecting the point T and M and M

the line TA subtend the angle  as shown in figure. Find the magnetic
induction B of the uniform magnetic field (perpendicular to the plane
determined by the line TA and the point M) in order that the electrons hit
the target M.
2mV sin  mv sin 
(A) 2 (B) 2
e d e d
2mv sin  mv sin 2
(C) (D) 2
e d e d

13. N turns of wire having cross sectional diameter D are tightly wound completely
on a conical core having a semi vertex angle  as shown in the figure. The 
winding starts at the vertex and there is no space left between the turns. If the
current through this coil is I, what will be the magnetic moment of the coil?
ID2 N2 sin2  ID2N2 sin 
(A) (B)
3 3
ID2N3 sin3  ID2N3 sin 
(C) (D)
3 3
14. The magnetic dipole moment of a 
uniformly charged triangular lamina of 

side a, rotating about axis AB (see A

figure) and having charge per unit area

 is M. Find the magnetic dipole
moment of uniformly charged
hexagonal lamina of side a, having
charge per unit area  and rotating
about axis of the frame.
(A) 30 M (B) 28 M B
M

(C) 32 M (D) 26 M
axis is lying on the plane of the lamina in each
case
15. In a certain region of space a uniform and constant electric field and a magnetic field parallel to
each other are present. A proton is fired from a point ‘A’ in the field with speed v = 4  104 m/s
at an angle of  with the field direction. The proton reaches a point B in the field where its
sin 
velocity makes an angle  with the field direction. If  3 . Find the electric potential
sin 
difference between the points A and B. Take mp (mass of proton) = 1.6  10-27 kg and e
(magnitude of electronic charge) = 1.6  10-19 C.
(A) 16 V (B) 16/3 V (C) 90 V (D) 30 V
 
16. The space has electromagnetic field which is given as B  B0kˆ and E  E0kˆ . A charged particle
having mass m and positive charge q is given velocity v 0 ˆi at origin at t = 0 sec. The z-coordinate
of the particle when it passes through the z-axis is (neglect gravity through motion)
22mE0 42mE0 mE0 4 2mE0
(A) (B) (C) (D)
qB02 qB02 qB02 qB20

17. A circular conducting loop of radius R carries a current I. Another straight infinite
conductor carrying current I passes through the diameter of this loop as shown in I
I
the figure. The magnitude of force exerted by the straight conductor on the loop is
(A) 0I2 (B) 0I2
R
 0I2  0I2 O
(C) (D)
2 

18. A conducting wire is bent in the form of a parabola y2 = 2x carrying a y

current i = 2A as shown in the figure. The wire is placed in a uniform
 (2m, 0)
magnetic field B  –4Kˆ . The magnetic force on the wire is
x
(A) –16iˆ (B) 32iˆ
ˆ
(C) –32i (D) 16iˆ


19. A particle with charge q and mass m starts its motion from origin with a velocity v = a î . A
 b 3b ˆ
uniform magnetic field B  ˆi  j exists everywhere in space. The component of velocity
4 4
vector in y-direction when the value of z-coordinate becomes maximum is
3 3
(A) a (B) a (C) 2 3a (D) 4 3a
4 2

Y
20. A particle with positive charge Q and mass m enters a magnetic
×
field of magnitude B, existing only to the right of boundary YZ. m
Q
×
The direction of the motion of the particle is perpendicular to the ×

direction of B. Let T  2 
m  × B
. The time spent by the particle in 
 QB  ×
×
the field will be
×
(A) T (B) 2T ×
   2    2 
(C) T  (D) T   ×
 2   2  Z
 Chemistry
R

O 
   
HCN
2 H , Pt2 NaNO
dil. HCl
1.

Final product is
R R

CH2OH
(A) (B)
OH
OH
R
R

O
(C) (D)
O
OH

2. The major final product formed in the reaction

 2 i NH OH  i EtMgBr
CHO 
 ii P2 O5  ? 
 ii  H O
?
3

(A) PhCHO (B) PhCOCH2CH3

CH3 CN

(C) Ph NH2 (D)

CH3

i  O3 SeO2  i HO
3. 2  Butene   X    Y    Z
 ii Me2S  ii H / H2O
The end product [Z] is
O
O
C
(A) C (B) O
O C
O
O
O
O
(C) (D) O O
O
O
O
4. O
Formaldehyde
Me

H  cat.
  X
C7H12 O3
Me
The major compound [X] is
O
O
Me Me
Me
(A) (B) Me
O O
O O
H3C
H3C C O
C O
CH3 CH2
(C) (D)
O
O
O
O
5.
O
1) H C C Cl AlCl 3 CH3 OH  Solvent 
Br
3
[ U ]          V 
H 2 SO 4 Cat

Mg / ether

P2O
Y W

The compound [X] is

D
O O

(A) H3C C D (B) H3C C D

D
OD OCH 3

(C) H3C C D (D) H3C C D

H OCH 3

6. O O

OEt 1) dil. HCl

   X
2) Heat
The compound [X] is
O O O

(A) (B) Cl

O O O O

(C) OEt (D) EtO

7. The major product formed in the reaction given below is

 i ozonolysis

ii aq. NaOH,   ?

O O

(A) (B)

O
(C) (D)

8. Which of the following molecules can not be reduced by using LiAlH 4?

O CHO

C H H OH

(A) CH2 (B) H OH

C H HO H

O CH2OH
O O
O O
(C) (D)
H3C C CH2 C OC2H5

9. CH3CHO+H2NOH  CH3CH=NOH
the above reaction occurs at
(A) pH=1 (B) pH=4.5
(C) any value of pH (D) pH=12

10. Formaldehyde & Formic acid can be disting used by

(A) Tollen’s reagent (B) Fehling’s solution
(C) Ferric chloride (D) NaHCO3

11.
O
10 % NaOH, H 2 O
? Product of the reaction is:

OH OH

O
(A) (B)

OH

HO
(C) O (D)

O
 O

HCl, H 2O
? Production of the rection is
12.
O O

(A) (B)

OH
O O
OH O

(C) (D)

13. What is the starting material used in the following reaction?

O Ph
OH

10 % NaOH, H 2O
?

O
OH
(A) 2 (B) 2

(C) 2 (D) 2
O

14. Which of the following compounds in the product of an aldol condensation reaction?
O

O
(B)

(A) HO
OH

O O
OH
OH
(C) (D)

15.
O
NaOH, H 2O
O
100C ? Pdoduction of the reaction is:
 HO O
O

(A) (B)

O O

(C) (D)

16.

NaOH
? product of the reaction is
Heat
O
O

(A) O (B)
O

(D)
(C)

O O

17. Which of the following is not the product of an intermolecular aldol condensation?
O O

(A) (B)

O O
CH2

(C) (D)

18. Which product(s) should be formed in the following reaction?

O

NaOH, H 2 O

(a) CH3 (b)

O O
O O

(c)
(d)

(A) (a) and (b) (B) (a), (b), and (c)

(C) c and (d) (D) (c) only
19. Which is the major product of the following reaction?
O O
EtO Na , EtOH, Heat

H3C H

O
O

(a) CH3
(b)

O O

H CH3
(c) (d)

(A) (a) (B) (b)

(C) (c) (D) (d)

dil. KOH
(A); Product (A) is:
20.
O

O
(A)

(B)
O

OH
OH
(C)

OH (D)
 Mathematics
1. Let f(x) and g(x) be differentiable for  x  2 such that f(0) = 2, g(0) = 1 and f(2) = 8. Let there exists a real
number c in (0, 2) such that f(c) = 3. g(c), then g (2) equals
(A) 2 (B) 3
(C) 4 (D) 5

2. The equation of the tangent to the curve y = e–|x| at the point where the curve cuts the line x = 1 is
(A) x + y = e (B) e(x + y) = 1
(C) y + ex = 1 (D) (x + ey = 2)

 x 3  log 2 b, 0  x  1
3. Let f(x) =  . Then the set of values of b for which f(x) has least value at x = 1 is
 3x, x 1
(A) (–, 2) (B) [16, )
(C) (2, 16) (D) none of these

4. The number of solutions of the equation x3 +2x2 +4x + 2cosx = 0 in [0, 2] is
(A) 0 (B) 1
(C) 2 (D) 3

5. Let (x) = (f(x))3 –3(f(x))2 + 4f(x) + 5x + 3 sinx + 4 cosx  x  R, then

(A)  is increasing whenever f is increasing (B)  is increasing whenever f is decreasing
(C)  is decreasing whenever f is increasing (D) Nothing can be said

6. If the equation x4 + 4x3 – 8x2 + p = 0 has all the roots real and distinct then
(A) p < 0 (B) 0 < p < 3
(C) p > 128 (D) 3 < p < 128

  sin t  cos t   e  2   t  1  t  2  dt (0 < x  4). Number of points where f(x) assumes

x 3 5
t
7. Let f(x) =
0
local maximum value is
(A) 0 (B) 2
(C) 3 (D) none of these

8. Let f: [2, 7]  [0, ) be a continuous and differentiable function. Then the value of
 f  7     f  2   f 2. f 7
2 2

(f(7) – f(2)) is (where c  (2, 7))

3
(A) 3. f2 (c) .f(c) (B) 5 f2 (c) .f (c)
(C) 5 f2 (c) .f(c) (D) none of these

9. The maximum value of cos (cos(sinx)) is

(A) cos (cos 1) (B) cos 1
(C) 1 (D) 0

2/3
10. The point at which y = x is the normal to the curve x  y 2 / 3  a2 / 3 is
 1 1   a a 
(A)  ,  (B)  ,
2 2 2 2  2 2
 a a  a a 
(C)  ,  (D)  , 
 2 2 2 2 2 2 
11. If a < 0 and f(x) = eax + e−ax in monotonically decreasing, then x belongs to
(A) (0, ) (B) (3, )
(C) (− , 0) (D) none of these

 
2
  x  5  , where 1  x  3 is
2
12. The maximum value of 3  4 x  x 2  4
(A) 34 (B) 36
(C) 32 (D) 20

13. The equation of the tangent to the curve y = b e-x/a, where it crosses the y –axis, is
x y
(A)  1 (B) x + y = a + b
b a
x y
(C)   1 (D) x + y = a – b
a b

14. If f; [1, 10]  [1, 10] is a non-decreasing function and g: [1, 10]  [1, 10] is a non-increasing function
Let h(x) = f (g(x)) with h(1) = 1, then h(2)
(A) lies in (1, 2) (B) is more than 2
(C) is equal to 1 (D) is not defined

sin(x 2  3x), x  0
15. Let f(x) =  . Then f(x)
 5x  6x, x0
2

(A) has a local maximum at x = 0

(B) has a local minimum at x = 0
(C) neither local maximum nor local minimum at x=0
(D) none of these

16. Slope of the normal to the curve x = t2 + 3t – 8, y = 2t2 –2t –5, at the point P (2, –1) is given by
(A) 7/6 (B) –7/6
(C) 6/7 (D) none of these
2
17. Least value of the function f (x) = esin x  2 sin x
is
1 1
(A) (B)
3
e e6
1
(C) e3 (D) 3
e
1
If f  x   e dt  0  x  1 , t is a parameter, then the maximum value of f  x  is
|t  x|
18.
0

(A) e 1 (B) 2 (e  1)
(C) e  1 (D) 2  e 1
19. f(x) = x /logex, x  1, is decreasing in interval
(A) (0, e) (B) (1, e)
(C) (e, ) (D) none of these

20. If a, b, c, d are four positive real numbers such that abcd =1, then minimum value of
(1 + a) (1 + b) (1 + c) (1 + d) is
(A) 8 (B) 12
(C) 16 (D) 20
 ASSESSMENT TEST
(Answer key)
Physics

1. A 2. C 3. D 4. C
5. A 6. D 7. B 8. A
9. B 10. C 11. C 12. A
13. C 14. A 15. A 16. A
17. B 18. B 19. B 20. C

Chemistry
1. C 2. B 3. C 4. A
5. D 6. B 7. A 8. B
9. B 10. D 11. A 12. B
13. D 14. C 15. C 16. D
17. B 18. D 19. B 20. B

Mathematics
1. B 2. D 3. B 4. A
5. A 6. B 7. C 8. C
9. A 10. D 11. C 12. B
13. C 14. C 15. B 16. B
17 D 18. C 19. B 20. C