MCP-15-10-11th (PQRS) Code-B
REVIEW TEST-5
Class : XI (P,Q,R,S)
PAPER CODE : B
Time : 3 hour Max. Marks : 228
INSTRUCTIONS
1. The question paper contains 20 pages and 2-parts. Part-A contains 54 objective question, Part-B contains
6 "Match the Column" questions. All questions are compulsory.
Please ensure that the Question Paper you have received contains all the QUESTIONS and Pages. If you found some mistake like missing questions or pages then contact immediately to the Invigilator.
PART-A
(i) Q.1 to Q.45 have only one correct alternative and carry 3 marks each.
There is NEGATIVE marking and 1 mark will be deducted for each wrong answer.
(ii) Q.46 to Q.54 have one or more than one is/are correct alternative(s) and carry 5 marks each.
There is NO NEGATIVE marking. Marks will be awarded only if all the correct alternatives are selected.
PART-B
(iii) Q.1 to Q.6 are "Match the Column" type which may have one or more than one matching options and carry 8 marks for each question. 2 marks will be awarded for each correct match within a question. There is NO NEGATIVE marking.
2. Indicate the correct answer for each question by filling appropriate bubble in your OMR answer sheet.
3. Use only HB pencil for darkening the bubble.
4. Use of Calculator, Log Table, Slide Rule and Mobile is not allowed.
5. The answer(s) of the questions must be marked by shading the circles against the question by dark HB pencil only.
USEFUL DATA
Atomic weights: Al = 27, Mg = 24, Cu = 63.5, Mn = 55, Cl = 35.5, O = 16, H = 1, P = 31, Ag = 108, N = 14, Li = 7, I = 127, Cr = 52, K=39, S = 32, Na = 23, C = 12, Br = 80, Fe = 56, Ca = 40, Zn = 65.4, Pt = 195,
Useful constant : g = 9.8 m/sec, h = 6.626 × 10–34 Js
PART-A
For example if only 'B' choice is correct then, the correct method for filling the bubble is
A B C D
For example if only 'B & D' choices are correct then, the correct method for filling the bubble is
A B C D
the wrong method for filling the bubble are
The answer of the questions in wrong or any other manner will be treated as wrong.
PART-B
For example if Correct match for (A) is P, Q; for (B) is P, R; for (C) is P and for (D) is S then the correct method for filling the bubble is
P Q R S (A)
(B)
(C)
(D)
PART-A
Select the correct alternative. (Only one is correct) [45×3 = 135]
There is NEGATIVE marking and 1 mark will be deducted for each wrong answer.
Q.1 The graph of a certain cubic polynomial is as shown. If the polynomial can be written in the form f (x) = x3 + ax2 + bx + c, then
(A) c = 0 (B) c < 0
(C) c > 0 (D) c = – 1
Q.2 In an isosceles triangle ABC, AB = AC, BAC = 108° and
AD trisects BAC and BD > DC. The ratio
BD is
DC
(A)
5 +1
2
3
(B) 2
(C) 1
(D) 2
Q.3 If a function f (x) = ax3 + bx2 + cx + d where a, b, c and d are integers and a > 0 is such that
sin
18 = 0. Then the smallest possible value of f (1) is
(A) 1 (B) 2 (C) 3 (D) 4
Q.4 The sides of a triangle are 6 and 8 and the angle between these sides varies such that 0° < < 90°.
The length of 3rd side x is
(A) 2 < x < 14 (B) 0 < x < 10 (C) 2 < x < 10 (D) 0 < x < 14
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Q.5 The sequence a1, a2, a3, satisfies a1 = 19, a9 = 99, and for all n 3, an is the arithmetic mean of
the first n – 1 terms. Then a2 is equal to
(A) 179 (B) 99 (C) 79 (D) 59
Q.6 If b is the arithmetic mean between a and x; b is the geometric mean between 'a' and y; 'b' is the harmonic mean between a and z, (a, b, x, y, z > 0) then the value of xyz is
(A) a3 (B) b3 (C)
b3(2a b) 2b a
(D)
b3(2b a) 2a b
Q.7 Given A(0, 0), ABCD is a rhombus of side 5 units where the slope of AB is 2 and the slope of AD is 1/2. The sum of abscissa and ordinate of the point C is
(A) 4 (B) 5 (C) 6 (D) 8
Q.8 A circle of finite radius with points (–2, –2), (1, 4) and (k, 2006) can exist for
(A) no value of k (B) exactly one value of k
(C) exactly two values of k (D) infinite values of k
Q.9 If a ABC is formed by 3 staright lines
u = 2x + y – 3 = 0; v = x – y = 0 and w = x – 2 = 0 then for k = – 1 the line u + kv = 0 passes through its
(A) incentre (B) centroid (C) orthocentre (D) circumcentre
Q.10 If a, b and c are numbers for which the equation identity, then a + b + c equals
x2 +10x 36 a
x(x 3)2 = x
b
+ x 3 +
c
(x 3)2
is an
(A) 2 (B) 3 (C) 10 (D) 8
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Q.11 Consider the sequence 8A + 2B, 6A + B, 4A, 2A – B, Which term of this sequence will have
a coefficient of A which is twice the coefficient of B?
(A) 10th (B) 14th (C) 17th (D) none
Q.12 Find the sum of the infinite series
1 + 1 + 1 +
9 18 30
1 + 1
45 63
+ .....
1
(A) 3
1
(B) 4
1
(C) 5
2
(D) 3
Q.13 Number of degrees in the smallest positive angle x such that 8 sin x cos5x – 8 sin5x cos x = 1, is
(A) 5° (B) 7.5° (C) 10° (D) 15°
Q.14 There exist positive integers A, B and C with no common factors greater than 1, such that A log2005 + B log2002 = C. The sum A + B + C equals
(A) 5 (B) 6 (C) 7 (D) 8
Q.15 A triangle with sides 5, 12 and 13 has both inscribed and circumscribed circles. The distance between the centres of these circles is
(A) 2 (B)
5
2 (C)
(D) 65 2
Q.16 A large number of oil drop samples in Milikan’s oil drop experiment gave the following values of charges q = 2×10–19 coulomb, 3×10–18 coulomb, 4 ×10–19 coulomb, 5 ×10–18 coulomb & no other values. What could be concluded as the charge of e– from above information.
(A) 2 × 10–18 coulomb (B) 2 × 10–19 coulomb
(C) 1 × 10–19 coulomb (D) 5 × 10–20 coulomb
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Q.17 For a general atom A having three different existance A, A–, A+1, Mark the correct option.
(A) Size order will be A+ > A– > A (B) E A order will be A+ > A > A–
(C) I E order will be A > A– > A+ (D) E N order will be A– > A > A+
Q.18 Assuming Heisenberg Uncertainity Principle to be true what could be the minimum uncertainty in de-broglie wavelength of a moving electron accelerated by Potential Difference of 6 V whose
uncertainty in position is
7 n.m.
22
(A) 6.25 Ã… (B) 6 Ã… (C) 0.625 Ã… (D) 0.3125 Ã…
Q.19 For a closed (not rigid) container containing n = 10 moles of an ideal gas, fitted with movable, frictionless, weightless piston operating such that pressure of gas remains constant at 0.821 atm, which graph represents correct variation of log V vs log T where V is in lit. & T in Kelvin.
(A) (B) (C) (D)
Q.20 A very long rectangular box is divided into n equal compartments with (n–1) fixed SPM (semi permeable membrane) numbered from 1 to (n–1) [n is unknown] as shown. The gases are initially present in only I compartment & can pass through only those SPM whose number is less than or equal to their subscript (like A1 can pass through 1st SPM only, A2 through 1st & 2nd & so on).
If initially all gases have same moles & after substantial time ratio
of P
6
in 3rd compartment to
P
n1
in 1st compartment is 5 then
what would be the value of n (where P
6
& PA
n1
represents partial
pressure of A6 &
An1
respectively) is
(A) 10 (B) 15 (C) 35 (D) 30
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Q.21 Electromagnetic radiations having = 310 Ã… are subjected to a metal sheet having work function = 12.8 eV. What will be the velocity of photoelectrons with maximum Kinetic Energy..
(A) 0, no emission will occur (B) 2.18 × 106 m/s
(C) 2.18 × 106 m/s (D) 8.72 × 106 m/s
Q.22 If in Bohr’s model, for unielectronic atom, time period of revolution is represented as Tn,z where
n represents shell no. and z represents atomic number then the value of T1,2 : T2,1 will be
(A) 8 : 1 (B) 1 : 8 (C) 1 : 1 (D) None of these
Q.23 Certain amount of phosphorus (P4) was made to react with certain amount of oxygen to give a mixture of P4O6 & P4O10 in the molar ratio of 2 : 1 (P4O6 : P4O10). If none of the reactants remained after the reaction(s) then what was the ratio of mass of P4 : O2 taken initially. (A) 93 : 88 (B) 88 : 93 (C) 3 : 11 (D) 11 : 3
Q.24 Consider the following nuclear reactions involving X & Y.
X Y + 4 He
Y 8O18 + 1H1
If both neutrons as well as protons in both the sides are conserved in nuclear reaction then identify
period number of X & moles of neutrons in 4.6 gm of X
(A) 3, 2.4 NA (B) 3, 2.4 (C) 2, 4.6 (D) 3, 0.2 NA
Q.25 40 miligram diatomic volatile substance (X2) is converted to vapour that displaced 4.92 ml of air at 1 atm & 300 K. Atomic weight of element X is
(A) 400 (B) 40 (C) 200 (D) 100
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Q.26 An U tube containing ideal gas closed at both ends having infinite long columns consists of mercury having initial height difference of 76 cm as shown. Both left column & right column have a hole from which gas is coming out according to rate law as given. [Assume outside the U-tube to be a perfect vaccum at all the instant] Given: ln2 = 0.69
Left Column
dP
= K P ; K
= 0.693 × 10–2 sec–1
dt 1 1
Right Column
dP
= K P ; K
= 1.386 × 10–2 sec–1
dt 2 2
where P = Pressure in the respective column
If at t = 0 pressure in Left Column = 1atm then what will be the height difference in the two levels after 200 sec.
(A) 0 (B) 76 (C) 38 (D) 19
Q.27 Calculate total maximum mass (kg) which can be lifted by 10 identical balloon (each having volume 82.1 lit. and mass of material = 3 kg) at a height 83.14 m at Mars where g = 5 m/ s2 & atmosphere contains only Ar (At. wt.40). At Mars temperature is 10 K and density of
atmosphere at ground level is to be applicable).
2 k gm/lit. [Given : e–0.1 = 0.9] (Assume d
0.821 H
= d0
eMgh RT
(A) 2000 × 0.81–30 (B) 1970 (C) 2000 × 0.9 –30 (D) 2000 × 0.81 – 3
Q.28 A mixture of CH4 (15 ml), CO (10 ml) is mixed with sufficient O2 gas in an eudiometry tube(operating at 1 atm & 500 K) is subjected to sparking and then cooled back to the original temperature of 500K. If Vc1 be volume contraction due to the above process and Vc2 be the contraction after passing the resultant gas(es) through CuSO4 (anhydrous), then Vc1,Vc2 will be (A) 30, 0 (B) 30, 30 (C) 5, 30 (D) 5, 0
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Questions No. 29 to 30 (2 questions)
Read the following comprehension and answer the question that follow.
One of the concerns of various chemists is of selecting an appropriate equation of state which can relate the four parameters (P, V, T and n) & give results close to experimental values at critical conditions. Although Vander Waal equation is easy to use, the experimental value of 'Z' (compressibility factor) at critical condition does not match with the predicted value [Experimental : 0.27, Predicted (Vander Waal) 0.375] For this reason, another equation of state is being used known as
RT a V RT
Dieterici Equation P =
e m
V b
m
where a, b are dieterici constant, Vm = Molar volume, P = Pressure & T = Temperature which gives better results at Critical Condition. ( ZCritical Condition = 2/e2).
dP
d2P
Also at Critical condition = 0 &
2 = 0.
dV T
T
If PC, VC, TC are critical pressure, volume & temperature and
V & T are related as 2a × (V –b)2 = V3RT .
C C C C C
Q.29 PC, VC, TC in terms of dieterici constant will be respectively
(A)
a 4b2e2
, 2b,
a 4bR
(B)
a 27b2
, 3b,
8a 27 Rb
(C)
a 4b2e2
, 3b,
a 4bR
(D)
a b2e2
, 2b,
a 4bR
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Q.30 If Vr =
V
(reduced volume), Tr =
C
T P
(reduced temperature) & Pr =
C C
(reduced pressure)
then which of the following represents reduced equation of state for dieterici equation. [All equation dimensionally correct]
2 2
VrTr
1 e Tr
V T e2T
(A)
Pr e
Vr =
2
(B)
Pr e
r r (Vr
– b) = r
2
2a
1 e2T
2
1
e2T T
(C)
P e VrTr V
= r
(D)
P e VrTr V
= r C
r r 2 2 r r 2 2
Question No. 31 & 32 (2 questions)
A motorcycle moves around a vertical circle with a constant speed under the influence of the
force of gravity W , the force of friction between the wheels and the track f , and the normal force between the wheels and the track N .
Q.31 Which of the following vectors has a constant magnitude?
(A) N (B) N + f
(C) f + W
(D)
N + W + f
Q.32 Which of the following vectors, when nonzero, is always directed toward the center of the circle or away from the centre of the circle?
(A) f (B) W (C) f + W
(D)
N + f
Q.33 A ball is released from position A and travels 5m before striking the smooth fixed inclined plane as shown. If the coefficient of restitution in the impact is e = 1/2, the time taken by the ball to strike the plane again is
(A) 1s (B) 2 s (C) 2.5 s (D) 3 s
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Q.34 At t = 0 a particle leaves the origin with a velocity of 6 m/s in the positive y direction. Its acceleration
is given by a =
2ˆi 3ˆj m/s2. The x and y coordinates of the particle at the instant the particle
reaches maximum y coordinate are
(A) 2m, 3m (B) 4m, 6m (C) 1m, 3m (D) 2m, 6m
Q.35 Figure shows a pendulum of length L suspended form the top of a flat beam of height L/2. The bob is pulled away from the beam so it makes an angle with the vertical. Now, it is released from rest. If
is themaximum angular deflection to the right, then
(A) = (B) <
(C) < 2 (D) > 2
Q.36 In the figure, block 'A' of mass 'm' is attached to one end of a light spring and the other end of the spring is connected to another block 'B' of mass 2m through a light string. 'A' is held and B is at rest in equilibrium. Now A is released. The acceleration of A just after that instant is 'a'. The same thing is repeated for 'B'. In that case the acceleration of 'B' is 'b', then value of a/b is:
(A) 0 (B) (C) 2 (D) 1/2
Q.37 In the following figure, what is the minimum coefficient of friction needed between the block & fixed incline so that the system does not move.
(A)
(C) 1 2
(B) 1 3
(D)
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Q.38 A square plate has three circular holes of same radius so that centre of each hole is equidistant from the centre of the square plate. A ABC can be formed by joining the centres of the holes as shown in the figure. The plate is placed on a frictionless horizontal surface. If we increase the temperature, then
(A) each side of the triangle will increase and the angle will remain same
(B) each side of the triangle will remain same and the angle will increase
(C) sides of the triangle as well as will increase
(D) sides of the triangle as well as will remain same
Q.39 10 gm of ice at –20°C is dropped into a calorimeter containing 10 gm of water at 10°C. The specific heat of water is twice that of ice. Neglect heat capacity of the calorimeter. When equilibrium is reached, the calorimeter will contain
(A) 10 gm ice and 10 gm of water (B) 20 gm of water
(C) 5 gm ice and 15 gm of water (D) 20 gm ice
Q.40 A wire having cross-sectional area S is attached to wall on one side and a block of mass M on the other side which placed on a horizontal surface having coefficient of friction as shown. Material of wire has coefficient of thermal expansion and Young's modulus Y. At initial temperature there is no stress in the wire. Now the wire is cooled. At what decrease in temperature the block will begin to move.
(A)
Mg
YS
(B)
2Mg
YS
(C)
Mg 2YS
(D) none
Q.41 Two trains, which are moving along different tracks in opposite directions towards each other, are put on the same track by mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trains are 300 m apart. Graphs given below show their velocities as function of time as the trains slow down. The separation between the trains after both have stopped, is:
(A) 120 m (B) 280 m (C) 60 m (D) 20 m
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Q.42 One end of a thin uniform rod of length L and mass M is riveted to the centre of a uniform circular disc of radius r and mass 2 M so that the rod is normal to the disc. The centre of mass of the combination from the centre of the disc is at distance of
L
(A) zero (B) 2
L
(C) 3
L
(D) 6
Q.43 In an electron gun, emission current from the cathode is given by the equation,
I = AT2 e(B (KT))
[K = Boltzmann constant, A = constant]
The dimensional formula for AB2 is same as
(A) KT (B) IT2 (C) IK2 (D)
IK2 T
Q.44 Two long motor boats are moving in the same direction in still water, the boat A with speed of 10km/h and other with a speed of 20km/h. While they are passing each other coal is shoveled from the slower boat to the faster one at a rate 1000kg/min. Assume that the shoveling is always normal relative to the boat A and resistance offered by water is negligible.
How much approximate additional force must be provided by driving engine of faster boat (B) if its velocity is to be maintained sconstant
(A) 46N (B) 32N (C) 20N (D) 167 N
Q.45 In a one-dimensional collision, a particle of mass 2m collides with a particle of mass m at rest. If the particles stick together after the collision, what fraction of the initial kinetic energy is lost in the collision?
1
(A) 0 (B) 3
1
(C) 2
2
(D) 3
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Select the correct alternatives. (one or more than one is/are correct) [9 × 5 = 45]
There is NO NEGATIVE marking.
Q.46 The equation
| x 2 |10x2 1 = | x 2 |3x
has
(A) 3 integral solutions (B) 4 real solutions
(C) 1 prime solution (D) no irrational solution
Q.47 Which of the following statements hold good?
(A) If M is the maximum and m is the minimum value of y = 3 sin2x + 3 sin x · cos x + 7 cos2x then the mean of M and m is 5.
(B) The value of cosec 18 –
sec 18 is a rational which is not integral.
(C) If x lies in the third quadrant, then the expression
+ 4 cos2 x is
independent of x.
(D) There are exactly 2 values of in [0, 2] which satisfy 4 cos2 2
cos 1 = 0.
Q.48 If the quadratic equation ax2 + bx + c = 0 (a > 0) has sec2 and cosec2 as its roots then which of the following must hold good?
(A) b + c = 0 (B) b2 – 4ac 0 (C) c 4a (D) 4a + b 0
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Q.49 In the following six electronic configuration (remaining inner orbitals are completely filled). Mark the correct option(s).
C–I C–II
C–III C–IV
C–V C–VI
(A) Stability order : C–II > C–I & C–IV > C–III
(B) Order of spin multiplicity : C–IV > C–III = C–I > C–II
(C) C–V violates all the three rules of electronic configuration
(D) If C–VI represents A then A2+ when kept near a magnet faces weak repulsions (acts as dimagnetic).
Q.50 Following represents the Maxwell distribution curve for an ideal gas at two temperatures T1 & T2. Which of the following option(s) are true?
(A) Total area under the two curves is independent of moles of gas
(B) If dU1= f Umps1 & dU2 = f Umps2 then A1 = A2
(C) T1 > T2 and hence higher the temperature, sharper the curve.
(D) The fraction of molecules having speed = Umps decreases as temperature increases.
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Q.51 A sample of H2O2 solution labelled as 33.6 volume has density of 264 gm/lit. Mark the correct option(s) representing concentration of same solution in other units.[Solution contains only H2O & H2O2]
(A) Mole fraction of H2O2 in the solution = 0.25 (B) % w/v = 102%
(C)
MH O = 6 M
(D)
m = 1000 m
2 2 54
Q.52 Two smooth spheres A and B of equal radii but of masses 1 kg and 2 kg move with speeds 21 m/s and 4 m/s respectively in opposite directions and collide. The velocity of A is reduced to 1 m/s in the same direction. Then, which of the following statements is incorrect?
(A) The velocity of B becomes 6 m/s and its direction is reversed
(B) The coefficient of restitution is 0.2
(C) The loss of kinetic energy of the system due to the collision is 200 J
(D) The magnitude of impulse applied by the two spheres on each other is 10 Ns
Q.53 A box is accelerating with acceleration = 20 m/s2. A block of mass 10 kg placed inside the box and is in contact with the vertical wall as shown. The friction coefficient between the block and the wall is = 0.6 and take g = 10 m/s2
(A) The acceleration of the block will be 20 m/s2
(B) The friction force acting on the block will be 100 N
(C) The contact force between the vertical wall and the block will be 100 N
(D) The contact force between the vertical wall and the block is only electromagnetic in nature
Q.54 When the resultant force on a system of particles is zero,
(A) The centre of mass of the system must be at rest
(B) Acceleration of each particle may be in the same direction
(C) Velocity of each particle may be in the same direction
(D) If only one particle has initially non-zero velocity then it is possible that all the particles simultaneously have zero velocity after some time
PART-B
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MATCH THE COLUMN [6 × 8 = 48]
INSTRUCTIONS:
Column-I and column-II contains four entries each. Entries of column-I are to be matched with some entries of column-II. One or more than one entries of column-I may have the matching with the same entries of column-II and one entry of column-I may have one or more than one matching with entries of column-II.
Column-I Column-II
Q.1 (A) Area of the triangle formed by the straight lines (P) 1 x + 2y – 5 = 0, 2x + y – 7 = 0 and x – y + 1 = 0
in square units is equal to (Q) 3/4
(B) Abscissa of the orthocentre of the triangle whose
vertices are the points (–2, –1); (6, – 1) and (2, 5) (R) 2
(C) Variable line 3x( + 1) + 4y( – 1) – 3( – 1) = 0
for different values of are concurrent at the (S) 3/2 point (a, b). The sum (a + b) is
(D) The equation ax2 + 3xy – 2y2 – 5x + 5y + c = 0 represents two straight lines perpendicular to each other, then | a + c | equals
Column-I Column-II
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If the perimeter of the parallelogram is 2( a + b )
where a, b N then (a + b) equals
Q.3 Column I & column II contain data on Schrondinger Wave–Mechanical model, where symbols have
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their usual meanings.Match the columns.
Column I Column II (Type of orbital)
(A) (P) 4s
(B) (Q) 5px
(C) (, ) = K (independent of & ) (R) 3s
(D) atleast one angular node is present (S) 6dxy
Q.4 For any chemical reaction Reactants products; the net energy change involved in the process is
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Eproducts – Ereactants . Using this & the following ENERGY diagram representing energy of each collection. Match column I with column II.
Column I (Process) Column II | Energy change |
(A) EA1 of Mg+(g) (P) 25
(B) IE1of Cl– (g) (Q) 100
(C) H.E. of Mg+2 (g) (R) 350
(D) L.E. of MgCl2(s) (S) 400
Q.5 Quantity Unit
(A) Energy density (Energy per unit volume) (P) Dyne/cm2
(B) Force constant of a spring (Q) kg-m/s
(C) Pressure (R) Erg/cm2
(D) Area under force-time graph (S) Pascal
Q.6 Ablock is placed on a rough horizontal surface having coefficient of friction .A
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mg
variable force F = kt, 0 t < acts on it at an angle to the
k sin
horizontal.
Quantities Variation as a function of time
(A) Normal reaction (P)
(B) Friction (Q)
(C) Acceleration (R)
(D) Velocity (S)
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