9.combined Test 1 ( Paper 1) English
COMBINED TEST - 1 (CT-1)
PAPER-1
Duration : 3 Hours Max. Marks : 180
GENERAL INSTRUCTIONS
1. The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of three sections and total number of questions are 60.
Marking Scheme
2. In Section 1 (Total Marks: 20), for each question you will be awarded 2 marks if you give the correct answer and zero mark otherwise. There are no negative marks in this section.
3. In Section 2 (Total Marks: 20), for each question you will be awarded 4 marks if you give the correct answer and zero mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded.
4. In Section 3 (Total Marks: 20), for each question you will be awarded 4 marks if you give the correct answer and zero mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded.
SECTION-1 : (Only One option correct type)
This section contains 10 multiple choice qustions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. The diagram shows a solenoid and a loop such that the solenoid’s axis lies in the plane of the loop. Both the solenoid and the loop carry constant currents in the directions as shown in the diagram. If the system is released from rest, the loop
(A) move towards the solenoid, rotates clockwise
(B) move towards the solenoid, rotates anticlockwise
(C) move away the solenoid, rotates clockwise
(D) move away the solenoid, rotates anticlockwise
2. A massless rod connecting two particles each of mass m at the ends is hinged at its centre, such that it can rotate in horizontal plane. A wire of linear charge density is placed at a distance r parallel to rod in same horizontal plane. If one particle is slightly displaced, then angular frequency of small oscillations will be
(A) (B)
(C) (D) no oscillation
3. Two hollow-core solenoids, A and B, are connected by a wire and separated by a large distance, as shown in the diagram. Two bar magnets, 1 and 2, are suspended just above the solenoids. If the magnet 1 is dropped through
solenoid A as shown, then the magnet 2 will simultaneously be
(A) Attracted by a magnetic force towards solenoid B
(B) Repelled by a magnetic force away from solenoid B
(C) Repelled by an electric force away from solenoid B
(D) Unaffected by solenoid B.
4. Figure shows two large cylindrical shells having uniform linear charge densities + and – . Radius of inner cylinder is ‘a’ and that of outer cylinder is ‘b’. A charged particle of mass m, charge q revolves in a circle of radius r. Then its speed ‘v’ is : (Neglect gravity and assume the radii of both the cylinders to be very small in comparison to their length.)
(A) (B)
(C) (D)
5. The voltage applied to an X-ray tube is 18 kV. The maximum mass of photon emitted by the X-ray tube will be: (A) 2 × 10–13 kg (B) 3.2 × 10–36 kg (C) 3.2 × 10–32 kg (D) 9.1 × 10–31 kg
6. A current source sends a current i = i0 cos t). When connected across an unknown load gives a voltage output of, V = V0 sin (t + /4) across that load. Then voltage across the current source may be brought in phase with the current through it by :
(A) connecting an inductor in series with the load
(B) connecting a capacitor in series with the load
(C) connecting an inductor in parallel with the load
(D) connecting a capacitor in parallel with the load.
7. A uniform electric field exists in xy plane. The potential of points A (2,2), B(–2, 2) and C(2, 4) are 4V, 16V, 12V, respectively. The electric field is
(A) (4ˆi 5ˆj)V / m
(B) (3ˆi 4ˆj)V / m
(C) – (3ˆi 4ˆj)V / m
(D) (3ˆi – 4ˆj)V / m
8. Two identical samples (same material and same amount) P and Q of a radioactive substance having mean life T are observed to have activities AP & AQ respectively at the time of observation. If P is older than Q, then the difference in their ages is:
AP
AQ
1 AP
AP
(A) T 𝑙n
(B) T 𝑙n
(C)
𝑙n
(D) T
AQ
A
T AQ
AQ
P
9. Half lives of two isotopes X and Y of a material are known to be 2 × 109 years and 4 × 109 years respectively. If a planet was formed with equal number of these isotopes, then the current age of planet, given that currently the material has 20% of X and 80% of Y by number, will be
(A) 2 × 109 years (B) 4 × 109 years (C) 6 × 109 years (D) 8 × 109 years
10. AB and CD are uniform line charges of infinite length having charge density
and
and lying along the z
axis and y–axis respectively. The force between them depends on the perpendicular distance between
them, 'r' as, F 1.2 , then the value of n is :
20rn
(A) 0 (B) 1/2 (C) 1 (D) 2
SECTION-2 : (One or more option correct type)
This section contains 5 multiple choice qustions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
11. Two capacitor of 2 F and 3 F are charged to 150 volt and 120 volt respectively. The plates of a capacitor are connected as shown in the figure. A discharged capacitor of capacity 1.5 F falls to the free ends of
the wire. Then after the system comes in steady state :
(A) Charge on the 1.5 F capacitor will become 180 C.
(B) Charge on the 2 F capacitor will become 120 C.
(C) Positive charge flows through A from left to right.
(D) Positive charge flows through A from right to left.
12. Two metallic bodies separated by a distance 20 cm, are given equal and opposite charges of magnitude 0.88 C . The component of electric field along the line AB, between the plates, varies as E = (3 x2 + 0.4) N/C, where
x
x (in meters) is the distance from one body towards the other body as shown.
(A) The capacitance of the system is 10F
(B) The capacitance of the system is 20F
(C) The potential difference between A and C is 0.088 Volt.
(D) The potential difference between A and C cannot be determined from the given data.
13. The figure above shows an energy level diagram for the hydrogen atom.
Several transitions are marked as , . The diagram is only
4
indicative and not to scale. 3
(A) The transition in which a Balmer series photon absorbed is VI.
(B) The wavelength of the radiation involved in transition is 486 nm. 2
(C) IV transition will occur when a hydrogen atom is irradiated with radiation of wavelength 103nm.
(D) IV transition will emit the longest wavelength line in the visible portion 1
of the hydrogen spectrum.
14. An ideal inductor, (having initial current zero) a resistor and an ideal battery are connected in series at time t = 0. At any time t, the battery supplies energy at the rate PB, the resistor dissipates energy at the rate PR and the inductor stores energy at the rate PL.
(A) PB = PR + PL for all times t.
(B) PR < PL for all times t.
(C) PR < PL only near the starting of the circuit.
(D) PR > PL only near the starting of the circuit. a
15. A wire having a positive uniform linear charge density , is bent in the form of a ring of radius R. Point A as shown in the figure, is in the plane of the ring but not at the centre. Two elements of the ring of lengths a1 and a2 subtend very small same angle at the point A. They
are at distances r1 and r2 from the point A respectively.
(A) The ratio of charge of elements a1 and a2 is r1/r2.
(B) The element a1 produced greater magnitude of electric field at A than
element a2.
(C) The elements a1 and a2 produce same potential at A.
(D) The direction of net electric field at A is towards element a2.
SECTION-3 : (Integer value correct Type)
This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive)
16. An infinitely long string uniformly charged with a linear charge density
= 1C and a segment of length 𝑙 uniformly charged with linear charge
1
density =
𝑙n4
C lie in a plane at right angles to each other and
separated by a distance 𝑙 (as shown in figure). Determine the
force with which these two interact. (in mili newton).
17. A cavity of radius r =
9.1
2
× 10–2 m is present inside a solid dielectric sphere of
radius R = 20 cm, having a volume charge density of = 1.5 × 10–9 C/m3. The distance between the centres of the sphere and the cavity is a = 8.85 × 10–2 m. An electron e is kept inside the cavity at an angle = 450 as shown. If the speed of the electron when it strikes the sphere again is 'V' × 105 m/sec . Then
calculate 'V'.
Neglect gravity. (me = 9.1 × 10–31 kg, e = 1.6 × 10–19 C and 0 = 8.85 ×10–12 C2/Nm2)
18. A thin planoconvex, lens of focal length F is split into two halves, one of the halves is shifted along the optical axis. The separation between object and image planes is 1.8 m. The magnification of the image formed by one of the half lenses is 2. If the focal length of the lens is 10x cm then value of x is :
19. A charge particle moves with constant velocity (ˆi ˆj) m/s in a uniform magnetic field
→ (2ˆi 3kˆ)T and
→ ˆ ˆ ˆ
electric field E (3i Ey j 2k)N/ m . Calculate Ey (in N/C).
20. Determine the magnitude of potential difference (in volts) between X and Y in the circuit shown in Figure.
A nswers
1. (B) 2. (B) 3. (A) 4. (A) 5. (C)
6.
(A)
7.
(D)
8.
(B)
9.
(D)
10.
(A)
11.
(A,C)
12.
(A,B,C)
13.
(A,C)
14.
(A,B,D)
15.
(A,B,C,D)
16.
9
17.
4
18.
4
19.
3
20.
4
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