Score Paper 11
Score Paper 11
Important Instructions :
1. Immediately fill in the form number on this page of the Test Booklet with Blue/Black Ball
Point Pen. Use of pencil is strictly prohibited.
: in words ________________________________________________________________
C9Y
T
PART-1 : PHYSICS
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6. A string with a linear mass density of 36 × 10 – 3 kg/m 9. A sound source emits two sinusoidal sound waves,
is under tension of 360 N and is fixed at both ends. both of wavelength λ , along paths A and B as shown
in figure. The sound travelling along path B is
One of its resonance frequencies is 375 Hz. The next
reflected from four surfaces as shown and then
higher resonance frequency is 450 Hz. The mass of merges at point Q, producing minimum intensity at
the string is : that point. The minimum value of d in terms of λ is :
(A) 24 × 10 – 3 kg
(B) 36 × 10 – 3 kg
(C) 12 × 10 – 3 kg
(D) 4 × 10 – 3 kg
7. A point source of sound is kept at origin and a man
is hearing at distance 100 m from the source. (A) λ (B) λ (C) λ (D) λ
8 4 3 6
Calculate the displacement of the man towards the 10. In young's double slit experiment maximum
source so that the loudness heard by man increases intensity is I, then angular position of the point
by 20dB. [Assume that the motion of man is along where the intensity becomes I/4.
the line joining the source and the man] λ λ
(A) sin−1 ( ) (B) sin−1 ( )
3d 2d
(A) 30 m
2λ λ
(C) sin−1 ( ) (D) sin−1 ( )
(B) 90 m d 4d
(C) 20 m 11. The second overtone of an open pipe A and a
(D) 40 m closed pipe B have the same frequencies. The ratio
of fundamental frequency of A to the fundamental
8. The magnetic field in the plane electromagnetic wave frequency of B is:
is given by Bz = 2 × 10 – 7 sin(0.5 × 103x + 1.5 × 1011t)
(A) 3 : 5 (B) 5 : 3 (C) 5 : 6 (D) 6 : 5
tesla. The expression for electric field will be:
12. A ray is incident on the boundary of a medium
3 11
(A) Ez = 30√2 sin(0.5 × 10 x + 1.5 × 10 t)V /m from air at an angle of incidence of 53° such that
(B) Ez = 60 sin(0.5 × 103 x + 1.5 × 1011 t)V /m reflected ray is completely polarised, then
(C) Ey = −30√2 sin(0.5 × 1011 x + 1.5 × 103 t)V /m
refractive index of medium is:
5 5 4 25
(D) Ey = −60 sin(0.5 × 103 x + 1.5 × 1011 t)V /m (A) (B) (C) (D)
3 4 3 9
Enthusiast Course / Score-I / Paper-1 1001CJA101021240034
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13. A sonometer wire of length 2m is made of steel. By 16. The figure shows at time t = 0 second, a rectangular
varying the tension in the wire elastic strain is and triangular pulse on a uniform wire are
varied from 1% to 4%. What is magnitude of approaching each other. The pulse speed of both
change in fundamental frequency of wire if density pulses is 0.5 cm/s. The resultant pulse at t = 2
and young's modulus of steel are 7.7 × 103 kg m – 3 second is :
and 2.2 × 1011 Nm – 2 respectively?
(A) 265 Hz (B) 132.5 Hz
(C) 397.5 Hz (D) 198.75 Hz
14. A uniform rope of length ℓ and mass M hangs
vertically from a rigid support. A block of mass m
is attached to the free end of the rope. A transverse
pulse of wavelength λ is produced at the lower end
(A)
of the rope. The wavelength of the pulse, when it
reaches the top of the rope, is :
(B)
(A) λ √
M −m (B) λ M +m
m m
(C) λ m (D) λ √
M +m
√
M +m m
15. A sound source of frequency 512 Hz approaches a
(C)
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17. The figure shows a string at a certain moment as a 19. Certain plane wavefronts are shown in figure. The
transverse wave passes through it. Three particles A,
refractive index of medium is
B and C of the string are also shown. Match the
physical quantities in the List-I with the description
in the List-II.
List-I List-II
Downwards, if the (A) 2
(P) Velocity of A (1) wave is travelling
(B) 4
towards right.
Downwards, if the (C) 1.5
(Q) Acceleration of A (2) wave is travelling (D) Cannot be determined
towards left.
20. In Young’s double slit experiment, two slits are
Downwards, no matter
(R) Velocity of B (3) which way the illuminated with a light of wavelength 800 nm. The
wave is travelling. line joining A1P is perpendicular to A1A2 as shown
(S) Velocity of C (4) Zero in the figure. If the first minimum is detected at P,
(A) (P) → 2; (Q) → 1,2; (R) → 1; (S) → 4 the value of slits separation a will be: The distance
(B) (P) → 1; (Q) → 1,2; (R) → 4; (S) → 2 of screen from slits is D = 5 cm
(C) (P) → 1; (Q) → 1,2,3; (R) → 2; (S) → 4
(D) (P) → 4; (Q) → 3; (R) → 2; (S) → 1
18. Assertion : In a small segment of string
carrying sinusoidal wave, total energy is conserved.
Reason : Every small part of the string carrying a
sinusoidal wave, moves in SHM.
(A) Assertion is true, Reason is true and Reason is
the correct explanation for Assertion.
(A) 0.5 mm
(B) Assertion is true, Reason is true and Reason is (B) 0.1 mm
NOT the correct explanation for Assertion. (C) 0.4 mm
(C) Assertion is true, Reason is false.
(D) 0.2 mm
(D) Assertion is false, Reason is true.
Enthusiast Course / Score-I / Paper-1 1001CJA101021240034
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SECTION-II : (Maximum Marks: 20) 4. Two identical piano wires have a fundamental
This section contains 05 questions. frequency of 600 vib/sec, when kept under the same
The answer to each question is a Numerical Value. tension. What percentage increase in the tension of
one wire will lead to the occurrence of six beats per
For each question, enter the correct integer value (In
second when both wires vibrate simultaneously.
case of non-integer value, the answer should be
rounded off to the nearest Integer). 5. Two forks A and B when sounded together produce
4 beats/sec. The fork A is in unison with 30 cm
Answer to each question will be evaluated according to
length of a sonometer wire and B is in unison with
the following marking scheme:
25 cm length of the same wire at the same tension
Full Marks : +4 If correct answer is entered.
in same mode. If their frequency are fA and fB and
Zero Marks : 0 If the question is unanswered.
fA + fB = 11 N, then find the value of N.
Negative Marks : –1 If wrong answer is entered.
1. Two wires of different densities but same area of
cross-section are soldered together at one end and
are stretched to a tension T. The velocity of a
transverse wave in the first wire is half of that in
the second wire. Find the ratio of the density of the
first wire to that of the second wire.
2. Three waves of equal frequency having amplitudes
4 μ m, 3 μ m and 3 μ m arrive at a given point with a
successive phase difference of 2 π /3. The amplitude
of the resulting wave in μ m is given by :
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PART-2 : CHEMISTRY
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8. Calculate cell potential of given Galvanic cell. 12. The pair of compounds whose boiling point
difference is less than 20°C are seperated by :-
Pt | H2(1 atm) | H+ (pH = 2) || H+ (pH = 3) | H2 (4 atm) | Pt
(A) Steam distillation
2.303 RT
[Given : = 0.06, log 2 = 0.30] (B) Fractional distillation
F
(A) 0.078 V (C) Distillation under reduced pressure
(B) – 0.078 V (D) Chromatography.
(C) 0.068 V 13.
(D) – 0.068 V
9. Which of the following is incorrect for electrolysis
Configuration across chiral centre is:-
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16. In which of following species hypercongugation 19. Compound (I) & (II) are related as :
take place ?
(A) CH3 – BH2 (B)
(C) (D)
Na
17. ←−−−−−− (P )
Dry ether (A) Enantiomers
Mg ND4 Cl
−−−−−−→ (Q) −−−−→ (R) (B) Diastereomers
Dry ether
(C) Homomers
R is :
(D) Structural isomers
(A)
(C)
(D)
(B)
18.
(C)
(A)
(B)
(D)
(C)
(D)
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SECTION-II : (Maximum Marks: 20) 4. (i)O3 /Zn
−−−−−−−−−⊕−−→ Total nunmber of
This section contains 05 questions. (ii)NH2 −OH/H
The answer to each question is a Numerical Value. localised lone pair in product ?
For each question, enter the correct integer value (In
case of non-integer value, the answer should be 5. How many of below are soluble in NaOH as well as
rounded off to the nearest Integer). release CO2(g) on reaction with sodium bicarbonate?
Answer to each question will be evaluated according to
the following marking scheme: , ,
Full Marks : +4 If correct answer is entered.
Zero Marks : 0 If the question is unanswered.
Negative Marks : –1 If wrong answer is entered. Picric acid, P-nitro phenol, Hydrochloric acid,
1. For a sparingly soluble salt K4[M(CN)6] following
data is given :
,
Solubility product of K4[M(CN)6] = 256 × 10 – 10.
Given : λ m∞ ( K + ) = 150 Ohm−1 mol−1 cm2
λ m∞ ([M(CN)6 ]
4Θ
) = 400 Ohm−1 mol−1 cm2
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PART-3 : MATHEMATICS
−π
and f π
b
(
4
) = 0, g (
4
) = 0 then
6. Let I = ∫ (x3 − x2 − 2x) dx. If I is minimum then
a
5π 3π
f( ) + g( ) is equal to :
4 4 (a, b) is : (where b > a > – 1)
(A) 0 (A) ( – 1, 2)
(B) π (B) ( – 1, 0)
(C) ℓ n2 + π (C) (0, 2)
(D) ℓ n2 + 2 π (D) ( – 1, 1)
Enthusiast Course / Score-I / Paper-1 1001CJA101021240034
C9Y
7. The value of
6π
π 1+e
(A) e8 + 1
(B) x + y = 2 or x + y = 0
π
(B) √ 2e + 18 2
(C) x + y − 2 = yex
π
e8
(C) +1 (D) Both A & B are correct
√ 2
(D)
π
e8 − 1 12. If n→∞
lim
xn − x−n
xn + x−n
= f(x) (0 < x < 1) then value of
9. Let a differentiable function 1
sgn(−f(x))ℓn (x + √1 + x2 ) dx
1 ∫ is :
⎛ ⎞
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13. ∫
1 + sin x
dx is equal to :
17. An inverted conical tank of 3m radius and 9m
⎷
cos(
3π
+ x) height is initially full of water has an outlet at
2
bottom. The outlet is opened at some instant. The
(A) 2cot – 1(cosec x) + c 1
rate of flow through the outlet at anytime t is 4h 2
(B) 2cot−1 (√cos ec x − 1) + c where h is height of water level above the outlet at
(C) tan – 1 (cosec x – 1) + c time t, then time it takes to empty the tank, is :
2π 27π
(D) −2tan−1 (√cos ec x) + c (A) unit (B) unit
7 10
14. The value of (C) π
unit (D) π
unit
1 2 3 6 7 6
lim((
n→∞ 1 + n2
) +
4+n 2
+
9+n 2
+. . . +
37n
)
18. Assertion : If f satisfies the equation
is : 8
(C) 1
ℓn37 (D) ℓ n37 Reason : If f is an odd function then ∫ f(x) dx = 0
2
15.
−a
Orthogonal trajectories of the family of curves (A) Both Assertion & Reason are true and the
xy = k + x is : reason is the correct explanation of the
(A) family of circles assertion
(B) family of straight lines (B) Both Assertion & Reason are true but the
reason is not the correct explanation of the
(C) family of parabola
assertion
(D) family of hyperbola
(C) Assertion is true statement but Reason is false
16. Statement - I : The general solution of dydx + xy = x (D) Both Assertion and Reason are false statements
−x2
is y = 1 + ce . 4απ
Statement - II : The number of arbitrary constants 19. If Iα = ∫ |sin x| [sin x]dx ∀ α ∈ N (where [·]
in the general solution of the differential equation −4απ
is equal to order of differential equation. denotes greatest integer function) then value of
(A) Statement - I is true and Statement - II is false ∑
20
Iα is :
(B) Statement - I is false and Statement - II is true α=1
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20. 1. If f(x) is an even function such that f(12 – x) = f(x)
List-I List-II 6 12
Equation) differential 0 0
x(xy – 1) dy 3
value of K is : (where C is integration constant)
(B) (Q) 3Ay = 2(Ax + B) 2 +C 1
+ y (xy+2) dx = 0
2y
3. The value of ∫ ((
1
1 − x5 ) 2 − (1 − x2 ) 5 ) dx is :
1
1 √
3
d y 2
2 tan−1 ( ) 0
dy d y
(C)
(
dx dx3
) + (
dx2
)
(R)
√ 2
1
x
2y 2
4. If f : R+ → R be a differentiable function satisfying
dy − ℓ n (1 + ) x
= 0( > 0) 2 x2 f(t)
dx f(x) = x ℓ nx – x – ∫ dt ∀ x ∈ R+ then value
= ℓ nx + c t ℓ nt
1
(D) (x − 2y)
dy
=x+y (S) xy = ℓ nxy – 3 ℓ nx + c of [f(e)] is :
dx (where [·] represents greatest integer function)
(A) A → P ; B → S ; C → Q ; D → R 1
ex
dx
(B) A → Q ; B → S ; C → R ; D → P
5.
∫
1+x
0
Find the value of 1
is :
(C) A → P ; B → R ; C → S ; D → Q ∫
x3 dx
4 −1
0 ex ( 2−x4 )
(D) A → S ; B → Q ; C → P ; D → Q
SECTION-II : (Maximum Marks: 20)
This section contains 05 questions.
The answer to each question is a Numerical Value.
For each question, enter the correct integer value (In
case of non-integer value, the answer should be
rounded off to the nearest Integer).
Answer to each question will be evaluated according to
the following marking scheme:
Full Marks : +4 If correct answer is entered.
Zero Marks : 0 If the question is unanswered.
Negative Marks : –1 If wrong answer is entered.
Enthusiast Course / Score-I / Paper-1 1001CJA101021240034
C9Y
Space for Rough Work
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