WEEKLY ASSESSMENT TEST-9

Test (Physics, Chemistry & Mathematics)

TIME: 120 MIN M. M: 180
Instructions:
(i) There are 60 questions
(ii) All questions are single correct MCQs.
(iii) + 3 marks will be awarded for correct answer and  1 for each wrong answer
STUDENT NAME: __________________________________

Physics
1. If a wheel is rolling without slipping on a horizontal surface at a constant linear speed then the point of
contact has
(A) backward acceleration (B) zero acceleration
(C) an upward acceleration (D) a downward acceleration

2. The moment of inertia of a rectangular lamina of mass ‘m’, length ‘’ and width ‘b’ about an axis passing
through its centre of mass, perpendicular to its diagonal and lies in the plane.
 2
 b2  m 4
 b4 
(A) m   (B)  
 12  12  2
 b2 
m 4
 b4 
(C)   (D) none of these
6 2
 b2 

3. A uniform thin rod of mass ‘m’, length ‘’ is hanged with the help of two
identical massless springs of spring constant ‘k’ as shown in figure. Just after
one of the spring is cut, the acceleration of the other end of the rod will be k k
(A) zero (B) g upward
3g m
(C) g downward (D) upward
2 L

4. A thin uniform rod of mass ‘m’ and length ‘’ is standing on a smooth horizontal surface.
A slight disturbance causes the lower end to slip on the smooth surface. The velocity of centre of mass of
the rod at the instant when it makes an angle 60° with vertical will be
9g g
(A) (B)
26 13
3g 3g
(C) (D)
26 13

5. Two small balls A and B, each of mass m, are joined rigidly

at the ends of a light rod of length L. They are placed on a frictionless horizontal
surface. Another ball of mass 2 m moving with speed u towards one of the ball m
and perpendicular to the length of the rod on the horizontal frictionless surface as
shown in the figure. If the coefficient of restitution is 1/2 then the angular speed of
the rod after the collision will be L
4 u u
(A) (B) 2m
3 u m
2 u
(C) (D) None of these
3
6. A person sitting firmly over a rotating stool has his arms folded with two identical balls. If he stretched his
arms along with balls and then the work done by him
(A) zero (B) positive
(C) negative (D) any of these
7. A wheel of mass ‘m’ and radius ‘R’ is rolling on a level road at a linear speed ‘v’. The kinetic energy of the
upper right quarter part of the wheel will be
3 9  16
(A) mV 2 (B) mV 2
8 48
9  16
(C) mV 2 (D) none of these
48

8. A ladder is resting with one end on the vertical wall and other end on a horizontal floor. It is more likely to
slip when a person stands.
(A) near the bottom (B) near the top
(C) at the middle (D) independent of the position of the person

9. A spinning cylinder of mass m and radius R is lowered on a rough


inclined plane of angle 30 with the horizontal and   1 / 3 . The
0
cylinder is released at a height of 3R from horizontal. Find the total
time taken by the cylinder to reach the bottom of the incline.
3R
 R R  R 
(A)  0   (B)  0  30
 g g  g 
 R R
(C)  0  6  (D) None of these
 g g

10. A uniform ring of radius R and mass m is fitted with a massless rod AB along A
its diameter. An ideal horizontal string (whose one end is attached with the
rod at a height r) passes over a smooth pulley and other end of the string is R
attached with a block of mass 2 m, as shown. The co-efficient of friction r
between the ring and the surface is . When the system is released from rest,
the ring moves such that rod AB remains vertical. The value of r is B
 3    
(A) R  1   (B) R  1   2m
 2(1  )   2(1  ) 
 3   3 
(C) R  2   (D) R  1  
 2(1  )   (1   ) 

11. A thin rod of length L is lying along the x-axis with its ends at x = 0 and x = L. Its linear mass density
n
x
varies with x as K   where; n can be zero or any positive number. Then which of the following is
L
correct.
xC.M. xC.M.

L L
(A) (B)
L L
2 2
L L
O n O n
xC.M. xC.M.

L L
(C) (D)
L L
2 2
L L
O n O n
12. Co-ordinates of the centre of mass of a sector of uniform circular disc of radius R y
and of mass m and subtends an angle 0 at it’s centre as shown in figure are
 0  0  
 2R sin 2 2R  1  cos 2    2R sin 0 2R  1  cos 0  
(A)  ,   ,0  (B)  ,   ,0
 3 0 3  0    3 0 3  0  
 2  2  
0
 4R sin 0 4R cos 0   4R sin 0 2R  1  cos 0   O x
(C)  , ,0  (D)  ,   ,0
 3 0 3 0   3 0 3  0  

13. Two blocks A and B of masses m and 2m respectively are connected together by a light spring of stiffness
k and then placed on a smooth horizontal surface. The blocks are pushed towards each other such that
spring gets compressed by a length x0 and then released from rest. Find the work done on the block A by
the spring, by the time the spring acquires its natural length, is :
1 2 1 2
(A) kx 0 (B) kx 0
2 4
2 1
(C) kx 02 (D) kx 02
3 3

14. A car C of mass m is initially at rest on the boat A of mass M tied to the C
identical boat B of same, mass M through a massless inextensible string as m
shown in the figure. The car accelerates from rest to velocity v0 with respect
to boat A in time t0 sec. At time t = t0 the car applies brake and comes to M A B M
rest relative to boat in negligible time. Neglect friction between boat and
water, the velocity of boat A just after applying brake is

mMv 0 mMv 0
(A) (B)
m  Mm  2M m  M1  2M
mMv 0 mMv 0
(C) (D)
m  M 2  2M m  M 2m  M
15. 3 blocks of mass 1kg each kept on horizontal smooth ground are
connected by 2 taut strings of length  as shown. B is pulled with constant
acceleration a0 in direction shown. The relative velocity of A & C just after
striking is (if coefficient of restitution of collision between A and C is e)
(A) 2e 2a0 (B) zero
(C) e 2a0 (D) e 4a0

16. Two blocks A & B of mass ‘m’ & 2m respectively are joined to the ends
of an under formed massless spring of spring constant ‘k’. They can m k 2m
move on a horizontal smooth surface. Initially A & B has velocities ‘u’ F 2F
A B
towards left and ‘2u’ towards right respectively. Constant forces of
magnitudes F and 2 F are always acting on A and B respectively in the
directions shown. The maximum extension in the spring during the
motion is
4F  16F2  54mu2k 4F  16F2  54mu2k
(A) xmax  (B) xmax 
3k 3k
4F  16F2  54mu2k 4F  16F2  54mu2k
(C) xmax  (D) xmax 
3k 3k

17. Two balls of equal masses are projected upward simultaneously; one from the ground with speed 50 m/s
and other from a 40 m high tower with initial speed 30 m/s. Then maximum height attained by their centre
of mass is
(A) 50 m (B) 100 m
(C) 200 m (D) None of these
18. In the figure shown, each tiny ball has mass m, and the string has length L.
One of the ball is imparted a velocity u, in the position shown, in which the
L 60°
initial distance between the balls is . The motion of ball occurs on smooth
3 u
horizontal plane. Then the impulse of the tension in the string when it
becomes taut is
mu 3  mu 3 
(A)   (B)  
2L 4L
mu 3  mu 3 
(C)   (D)  
2 4

19. A particle of mass m is projected with a velocity v making on angle  with horizontal. The magnitude of
angular momentum of the projectile about the point of projection when the particle is at its maximum
height ‘H’ is proportional to
3/2 3
(A) V (B) V
3 3
(C) H (D) H

20. A thin uniform rod of mass ‘m’ and length ‘’ is hinged at the x distance from its centre and it receives an
impulse J normal to the rod at its one end which is other side of hinge. For maximum value of angular
speed the x will be

(A) 0 (B)
2
 2   2 
(C)  1   (D)  1  
2 3 2 3
 Chemistry
1. For 3A+2B 2C+D, initial mol of A is double of B. At equilibrium, mole of A and D are equal, Hence
percentage dissociation of A is
(A) 50% (B) 25%
(C) 75% (D) 80%

2.
-
I2+I I 3 . the reaction is set up in aqueous medium we start with 1 mole of I2 and 0.5 mol of I in one
-

litre flask. After equilibrium is reached, excess of AgNO 3 gave 0.25 mole of yellow precipitate.
Equilibrium constant is
(A) 1.33 (B) 2.66
(C) 2.0 (D) 3.0
3. An equilibrium mixture CO(g) + H2O(g) CO2(g) +H2(g) present in a vessel of 2 litre at a temperature
900C was found to contain 0.4 mole CO2, 0.3 mole H2O, 0.2 m-ole CO and 0.5 mole H2. To increase
the concentration of CO to 0.4 mole, CO2 was added to the vessel. How many moles of CO2 must be
added into equilibrium mixture at constant temperature in order to get this change?
(A) 2.022 moles (B) 20.22 moles
(C) 2.22 moles (D) 22.2 moles

4. Phosgene, COCl2, a poisonous gas decomposes according to the equation

COCl2(g) CO(g) + Cl2(g)
If Kc=0.083 at 900C, what is the value of Kp
(A) 0.125 (B) 8.0
(C) 6.1 (D) 0.16

5. Consider the following equilibria

-7
2SO3(g) 2SO2 (g) + O2 (g); KC= 2.310
-3
2NO2(g) 2NO (g) + O2(g) ; KC=1.410
What is the equilibrium constant value for the reaction?
SO2(g)+NO2(g) SO3(g) + NO(g)
-2
(A) 77 (B) 1.310
-4 -10
(C) 1.610 (D) 3.210
-3
6. The equilibrium constant, Kp for sublimation of solid iodine at 298 K is 4.05610 atm. The vapour
pressure of iodine at this temperature is
-3
(A) 4.05610 torr. (B) 0.308 torr.
4
(C) 3.08 torr. (D) 2.510 torr

7. For an equilibrium
A+B C+D Kc=60
Starting with 7 moles of A, 8 moles of B and 14 moles of D, how may moles of C would be present at
equilibrium
(A) 5 (B) 6
(C) 4 (D) 3
8. XY2 dissociates as XY2 (g) XY(g) + Y (g), When the initial pressure of XY2 is 600 mm of Hg. The
total pressure developed is 800 mm of Hg. KP for the reaction is
(A) 200 (B) 50
(C) 100 (D) 150
9. 25 mol of H2 and 18 mol of I2 vapour were heated in a sealed glass tube at 465C, 30.8 mole of HI was
formed at equilibrium. The percentage degree of dissociation of HI at 465C is
(A) 35% (B) 40%
(C) 24.5 % (D) 28 %

10. In terms of mole fraction, equilibrium constant is written as K x. The relationship between Kc and Kx is
N
 RT 
(A) Kc=Kx  KC  K X
 (B) N
 P   P 
 
 RT 
n  n
KC  RT   P 
(C)   (D) KX=KC  
KX  P   RT 
11. In the reaction
CH3COCH3 CH3CH3(g) + CO(g)
1
The initial pressure of CH3COCH3 is 100 mm Hg. At equilibrium mole fraction of CO (g) is the valve of
3
Kp is
(A) 20 mm Hg (B) 40 mm Hg
(C) 50 mm Hg (D) 100 mm Hg

12. The equilibrium that is not affected by increase in pressure is

(A) 2SO2(g) + O2(g) 2SO3(g) (B) PCl3(g) + Cl2(g) PCl5(g)
(C) N2(g) + 3H2(g) 2NH3(g) (D) N2(g) + O2(g) 2NO(g)

13. What are the most favorable conditions for the reaction?
1
SO2 + O2 SO3, to occur?
2
(A) low T, High P (B) low T, low P
(C) high T, P low (D) high T, high P

14. The equilibrium constant of the reaction H2(g) + I2(g) 2HI(g) is 32 at a given temperature. The
-3 -3
equilibrium concentration of I2 and HI are 0.510 and 810 M respectively. The equilibrium
concentration of H2 is
(A) 1  10 M (B) 0.5  10 M
-3 -3

(C) 2  10 M (D) 4  10 M
-3 -3

15. The equilibrium constant of the reaction

H2O(g) + CO(g) H2(g) + CO2(g) is 0.44 at 1260 K. The equilibrium constant for the reaction
2H2(g) + 2CO2(g) 2CO(g) + 2H2O(g) at 1260 K is equal to
(A) 0.44 (B) 0.88
(C) 5.16 (D) 126

16. 
K1
In reversible reaction A  B, the initial concentration of A and B are 2 and 3 in moles per litre and
K2
–2
the equilibrium concentrations are (2 – x) and (3 + x) respectively. Calculate value of x(k 1 = 2 × 10 , k2 =
–3
4 × 10 )
(A) 0.8 (B) 1.2 (C) 2.4 (D) 0.5

17. In a reaction A  s 
3B  g  3C  g . If the conc. Of B at equilibrium is increased by a factor of 3, it

will cause the equilibrium concentration of C to change to
(A) 4 times the original value (B) 1/2 of its original value
(C) 1/3 of its original value (D) 3 times the original value
18. At a certain temperature the vapour density of N2O4 is 30.2. The percent dissociation at this
temperature is
(A) 52.31 % (B) 26.06 % (C) 78.2 % (D) 39.1 %

19. The vapour density of PCl5 is 104.16 but when heated to 230C, the vapour density is reduced to 62.
The degree of dissociation of PCl5 at the temperature will be
(A) 6.8% (B) 68% (C) 46% (D) 64%

20. A mixture of N2 and H2 in the molar ratio 1 : 3 attains equilibiurm when 50% of mixture has reacted. If P
is the total pressure of the mixture, the partial pressure of NH3 formed is P/y. The value of y is:
(A) 3 (B) 2 (C) 5 (D) None of these
 Mathematics
2 2
1. If Normal at the point (am ,-2am) of the parabola y = 4ax, subtends a right angle at the vertex if
(A) m = 1 (B) m = 2
1
(C) m =  3 (D) m = 
2
2
2. The mid-point of the chord y -2x + 3 = 0 of the parabola y = 4x is
(A) (2, 1) (B) (5/2, 2)
(C) (1, -1) (D) none of these
2
3. Length of latus-rectum of parabola y + 2ax + 2by + c = 0 is
(A) a (B) 2a
(C) 3a (D) 4a
2
4. If PSQ in the focal chord of the parabola y = 8x such that SP = 6. Then the length of SQ is
(A) 6 (B) 4
(C) 3 (D) none of these

If the normal to the parabola y = 4ax, (focus  S) at a point P on it meets the x-axis at G, then
2
5.
(A) SP > SG (B) SP = SG
(C) SP < SG (D) none of these
2
6. The angle between the tangents at the ends of the latus rectum of the parabola y = 4x is
 
(A) (B)
4 3

(C) (D) none of these
2
2 3
7. If the tangents drawn from the point (0, 2) to the parabola y = 4ax are inclined at an angle , then |a|
4
equals
(A) 1 (B) 2
(C) 4 (D) 6

The circle x + y + 2x = 0,   R, and  < 0 and the parabola y = 4x

2 2 2
8.
(A) touch externally (B) touch internally
(C) intersect each other (D) none of these
2
9. If a chord AB of the parabola x = 4by whose equation is y = mx + c subtends a right angle at the vertex of
the parabola, then
(A) c = 4bm (B) b = 4cm
(C) c = 4b (D) b + 4cm = 0
1 1
10.
2
If a chord of the parabola y = 8x passing through its focus F meets it in P and Q, then  is
| FP | | FQ |
equal to
1
(A) (B) 1
2
(C) 2 (D) none of these
2
11. The straight line lx + my + n = 0 will touch the parabola y = 4x if
(A) l, m, n are in G.P (B) l, n, m are in G.P.
(C) l, m, n are in H.P. (D) l, n, m are in H.P.
2
12. The number of focal chord(s) of length 4/7 in the parabola 7y = 8x is
(A) 1 (B) zero
C) infinite (D) None of these .
2
13. Three normal are drawn from point (5, 0) to parabola y = 4x. The centriod of the triangle formed by feet
of these three normals is
 1 1
(A)  ,  (B) (5, 0)
2 2
(C) (2, 0) (D) (0, 2)
 2
14. The focus of the parabola x – 8x + 2y + 7 = 0 is
 1  9
(A)  0,   (B)  4, 
 2  2
 9
(C) (4, 4) (D)   4,  
 2
2 2 2
15. The normal drawn at a point (at1 , 2at1) of the parabola y = 4ax meets it again in the point (at2 , 2at2) then
2
(A) t1 = 2t2 (B) t1 = 2t2
(C) t1t2 = –1 (D) none of these

16. The coordinates of the point on the parabola y = x2 + 7x +2, which is nearest to the
straight line y = 3x – 3 are
(A) ( -2, -8) (B) ( 1, 10)
(C) ( 2, 20) (D) ( -1, -4)

17. If the normal to y2 = 12 x at P (3, 6) meets the parabola again in point Q then the circle
with PQ as diameter is
(A) x2 + y2 + 30x + 12y  27 = 0 (B) x2 + y2 + 30x + 12y + 27 = 0
(C) x2 + y2  30x  12y  27 = 0 (D) x2 + y2  30x + 12y  27 = 0

18. The angle between the tangents drawn from the origin to the parabola y2 = 4a (x  a) is
(A) 900 (B) 300
 1
(C) tan1  2  (D) 450

19. The coordinates of an end point of the latus rectum of the parabola (y -1)2 = 4(x + 1) are
(A) (0, 1) (D) (4, -3)
(C) 0, -1) (D) (2, 3)

20. The graph represented by the equations x = asin2t and y = 2a sint is

(A) a portion of a parabola (B) a parabola
(C) a part of a hyperbola (D) none of these.