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CBSE Class 12 Physics Previous Year Question Paper Term 1 2021 SSJ-1-Set-4

CBSE Class 12 Physics is important for top performance in your Class 12 Board exams. Your CBSE Class 12 syllabus for Physics includes concepts such as electrostatics matter, magnetism, nuclei, atoms, electric charges, communication systems, and more. On TopperLearning, you can get free access to chapter-wise Class NCERT solutions, which play a crucial role in helping you ace your studies.

Watch our CBSE Class 12 Physics expert videos to clearly understand Physics concepts such as classification of magnetic materials, electrostatic potential energy, capacitors, etc. Whether you are confused about concepts such as integrated circuits or need help with understanding the discovery made by notable Physicists, our chapter-wise CBSE Online Class 12 video lectures can support you with conceptual clarity.

Also, learning every concept prior to final exams can be time-consuming. You can go through our revision notes to quickly revise important concepts from your CBSE Syllabus for Class 12 Science Physics. With better preparation by using TopperLearning e-learning material, you can aim for top marks in your CBSE Class 12 Physics board exams.

Physics is a subject wherein theory is as important as the application of the concepts. Simply learning the theory isn’t going to be useful to get better marks. With the help of solutions by Physics subject experts, you can understand the theory, as well as the practical use of concepts, better. The CBSE solutions on TopperLearning for Physics Class 12 include NCERT textbook solutionssample paper and solutions, and previous year papers and solutions.

CBSE Class 12 solutions on TopperLearning present you with tips on how to write answers accurately so that you score full marks. Use the NCERT solutions for Class 12 Science Physics to learn how to solve numerical questions and answer different types of questions. NCERT solutions will assist you to solve the questions present in your NCERT Physics Class 12 textbook. For further revision and practice, you can solve the CBSE Sample Paper Class 12 on TopperLearning.

Exam fear is quite normal among Class 12 students. You can solve CBSE Online Class 12 previous year question papers and refer to solutions by experts to compare your answers. Also, remember to set a timer when you solve question papers such as CBSE Class 12 Physics Sample Papers 2020-21 and do self-assessments with the help of TopperLearning CBSE solutions. This will help you get familiar with as many accurate answers as you can.

SECTION – A

This section consists of 25 multiple choice questions with over tilt choice to attempt any 20 questions. In case more than desirable number of questions are attempted, only first 20 questions will be considered for evaluation. 

 

Question 1.
An electric dipole placed in a non-uniform electric field will experience: 

  1. Only a force 
  2. Only a torque 
  3. both force and torque 
  4. Neither force nor torque

 

Question 2.
Let NI be the number of electric field lines going out of an imaginary cube of side that encloses an isolated point charge 2q and N2 be the corresponding number for an imaginary sphere of radius that encloses an isolated point charge 3q. Then (N1/N2) is:

  1. begin mathsize 11px style 1 over straight x end style
  2. begin mathsize 11px style 2 over 3 end style
  3. begin mathsize 11px style 9 over 4 end style
  4. begin mathsize 11px style straight pi end style
 

Question 3.
In the circuit given below P ≠ R and the reading of the galvanometer is same with Switch S open or closed. Then: 

  1. IQ = IR
  2. IR =IG
  3. IP = IG
  4. IQ = IG

Question 4.
Two wires A and B, of the same material having length in the ratio 1: 2 and diameter in the ratio 2: 3 are connected in series with a battery. The ratio of the potential differences (VA/ VB) across the two wires respectively is: 
  1. begin mathsize 11px style 1 third end style
  2. begin mathsize 11px style 3 over 4 end style
  3. begin mathsize 11px style 4 over 5 end style
  4. begin mathsize 11px style 9 over 8 end style

Question 5.
Two moving coil galvanometers G1 and G2 have the following particulars respectively: 
N1=30, A1 = 3.6 x 10-3 m2, B1= 0.25 T 
N2= 42, A2 = 1.8 x 10-3, m2, B2 = 0.50 T 
The spring constant is same for both the galvanometers. The ratio of current sensitivities of G1 and G2 is 
  1. 5 : 7 
  2. 7 : 5 
  3. 1:4 
  4. 1 : 1 

Question 6.
A current I is flowing through the loop as shown in the figure (MA = R, MB = 2R). The magnetic field at the centre of the loop is  begin mathsize 11px style fraction numerator straight mu subscript 0 straight I over denominator straight R end fraction end style times: 
  1.  begin mathsize 11px style 5 over 16 comma space into space the space plane space of space the space paper end style
  2.   begin mathsize 11px style 5 over 16 comma space out space of space the space plane space of space the space paper end style
  3.  begin mathsize 11px style 7 over 16 comma space out space of space the space plane space of space the space paper end style
  4. begin mathsize 11px style 7 over 16 comma space into space the space plane space of space the space paper end style

Question 7.
A capacitor and an inductor are connected in two different ac circuits with a glowing in each circuit. The bulb glows more brightly when: 
  1. the number of turns in the inductor is increased
  2. the separation between the plates of the capacitor is increased 
  3. an iron rod is introduced into the inductor  
  4. a dielectric is introduced into the gap between the plates of the capacitor 
 
Question 8.
A pure inductor of 318 mH and a pure resistor of 75 Ω are connected in series to an ac source Of 50 Hz. The voltage across 75 Ω resistor is found to be 150 V. The source voltage is:
  1. 150 V 
  2. 175 V 
  3. 220 V 
  4. 250 V 

Question 9.
The electric potential at a point on the axis of a short electric dipole, at a distance x from the mid -point of dipole is proportional to: 
  1. begin mathsize 11px style 1 over straight x to the power of 4 end style
  2. begin mathsize 11px style 1 over straight x to the power of 3 divided by 2 end exponent end style
  3. begin mathsize 11px style 1 over straight x cubed end style
  4. begin mathsize 11px style 1 over straight x squared end style

Question 10.
Let F1 be the magnitude of the force between two small spheres, charged to a constant potential in free space and F2 be the magnitude of the force between them in a medium of dielectric constant k. Then (F1 / F2) is: 
  1. begin mathsize 11px style 1 over straight k end style
  2. k
  3. k2
  4. begin mathsize 11px style 1 over straight k squared end style

Question 11.
infinity resistance in a resistance box has: 
  1. a resistance of 105 Ω
  2. a resistance of 107 Ω
  3. a resistance of ∞ resistance 
  4. a gap only
 
Question 12.
A battery of 15 V and negligible internal resistance is connected across a 50 Ω resistor. The amount of energy dissipated as heat in the resistor in one minute is: 
  1. 122 J 
  2. 270 J 
  3. 420 J 
  4. 720 J 

Question 13.
Lenz's law is the consequence of the law of conservation of: 
  1. energy 
  2. charge 
  3. mass 
  4. momentum 

Question 14.
The vertical component of earth's magnetic field at a place is begin mathsize 11px style open parentheses fraction numerator 1 over denominator square root of 3 end fraction close parentheses end style, times the horizontal J3 component. The angle of dip at that place is: 
  1. 0° 
  2. 30° 
  3. 45°
  4. 60° 

Question 15.
A long straight wire in the horizontal plane carries a current of 15 A in north to south direction. The magnitude and direction of magnetic field at a point 2.5 m east of the wire respectively are: 
  1. 1.2 μT, vertically upward 
  2. 1.2 μT, vertically downward 
  3. 0.6 μT, vertically upward 
  4. 0.6 μT, vertically downward
 
Question 16
The emf induced in a 10 H inductor in which current changes from 11 A to 2 A in 9x10-1s is: 
  1. 104
  2. 103
  3. 102
  4. 10 v 

Question 17.
A charge Q is placed at the centre of the line joining two charges q and q. The system of the three charges will be in equilibrium if Q is: 
  1. begin mathsize 11px style plus straight q over 3 end style
  2. begin mathsize 11px style negative straight q over 3 end style
  3. begin mathsize 11px style plus straight q over 4 end style
  4. begin mathsize 11px style negative straight q over 3 end style

Question 18.
Electric flux of an electric field  begin mathsize 11px style straight E with rightwards arrow on top end style  g through an area d begin mathsize 11px style straight A with rightwards arrow on top end style  is given by:
  1.  begin mathsize 11px style stack straight E space with rightwards arrow on top cross times straight d stack straight A space with rightwards arrow on top end style
  2. begin mathsize 11px style fraction numerator stack straight E space with rightwards arrow on top cross times straight d stack straight A space with rightwards arrow on top over denominator straight O presuperscript straight s end fraction end style
  3. begin mathsize 11px style stack straight E space with rightwards arrow on top. space straight d stack straight A space with rightwards arrow on top end style
  4. begin mathsize 11px style fraction numerator stack straight E space with rightwards arrow on top. space straight d stack straight A space with rightwards arrow on top over denominator straight O presuperscript straight s end fraction end style

Question 19.
In a potentiometer experiment, the balancing length with a cell is 120 cm. When the cell is shunted by a 1 Ω resistance, the balancing length becomes 40 cm. The internal resistance of the cell is: 
  1. 10 Ω 
  2. 7 Ω
  3. 3 Ω 
  4. 2 Ω 

Question 20.
An electron is projected with velocity  begin mathsize 11px style straight V with rightwards arrow on top end style along the axis of a current carrying long solenoid. Which one of the following statements is true? 
  1. The path of the electron will be circular about the axis. 
  2. The electron will be accelerated along the axis. 
  3. The path of the electron will be helical. 
  4. The electron will continue to move with the same velocity  begin mathsize 11px style straight V with rightwards arrow on top end style along the axis of the solenoid. 

Question 21.
If the speed v of a charged particle moving in a magnetic field begin mathsize 11px style straight B with rightwards arrow on top end style  ( begin mathsize 11px style straight V with rightwards arrow on top end style is perpendicular to begin mathsize 11px style straight B with rightwards arrow on top end style ) is halved, then the radius of its path will:
  1. not change
  2. become two times  
  3. become one- fourth  
  4. become half  
 
Question 22.
A metal plate is getting heated. Which one of following statements is incorrect?
  1. It is placed in a space varying magnetic field that does not vary with time. 
  2. A direct current is passing through the plate.
  3. An alternating current is passing through the plate.
  4. It is placed in a time varying magnetic field.

Question 23.
In an ac circuit the applied voltage and resultant current are E = E0 sin ⍵t and  begin mathsize 11px style straight I equals straight I subscript 0 space sin space open parentheses ωt plus straight pi over 2 close parentheses end style  respectively. The average power consumed in the circuit is:
 
  1. E0I0
  2.  begin mathsize 11px style fraction numerator straight E subscript 0 straight I subscript 0 over denominator 2 end fraction end style
  3. begin mathsize 11px style fraction numerator straight E subscript 0 straight I subscript 0 over denominator square root of 2 end fraction end style
  4. Zero


Question 24.
The speed acquired by a free electron when accelerated from rest through a potential difference of 100 V is : 
  1. 6 × 106 ms-1
  2. 3 × 106 ms-1
  3. 4 × 105 ms-1
  4. 2 × 103 ms-1
 
Question 25.
Which one of the following is not affected by the presence of a magnetic field?  
  1. A current carrying conductor 
  2. A moving charge 
  3. A stationary charge 
  4. A rectangular current loop with its parallel to the felid
SECTION B

This section consists of 24 multiple choice questions with over all choice to attempt any 20 questions. In case more than desirable number of questions are attempted, only first 20 questions will be considered for evaluation.
 
 
Question 26.
Two point charges + 16q and – 4q are located at x = 0 and x = L. The location of the point on x-axis at which the resultant electric field due to these charges is zero, is:
  1. 8 L
  2. 6 L
  3. 4 L
  4. 2 L
 
Question 27.
An electric dipole of dipole moment 4 × 10-5 C-m, kept in  a uniform electric field  of 10-3 NC-1, experience  a torque of 2 × 10-8 Nm. The angle which the dipole makes with the electric field is :
  1. 30°
  2. 45°
  3. 60°  
  4. 90° 
 
Question 28.
Three identical charges are placed on x-axis from left to right with adjacent charges separated by a distance d. The magnitude of the force on a charge from its nearest neighbour charge is F. Le begin mathsize 11px style 1 with logical and on top end style  be the unit vector along + x axis, then the net force on each charge from left to right is :  
  1.  begin mathsize 11px style left parenthesis 2 space straight E space stack 1 comma with logical and on top space minus 2 space straight F space stack 1 comma with logical and on top 2 space straight F space 1 with logical and on top right parenthesis space end style 
  2. begin mathsize 11px style left parenthesis straight F space stack 1 comma with logical and on top space 0 comma space straight F space 1 with logical and on top right parenthesis space end style
  3.  begin mathsize 11px style left parenthesis space space minus 5 over 4 straight F space stack 1 comma with logical and on top space 0 comma space plus 5 over 4 straight F space 1 with logical and on top right parenthesis space end style 
  4.  begin mathsize 11px style left parenthesis 2 space straight F space stack 1 comma with logical and on top space 0 comma 2 space straight F space 1 with logical and on top right parenthesis space end style 

Question 29.
Two students A and B calculate the charge flowing through a circuit. A concludes that 300 C of charges flows in 1 minute. B concludes that 3.125 × 1019 electrons flow in 1 second. IF the current measured in the circuit is 5A, then the correct calculation is done by :
  1. B
  2. both A and B
  3. neither A nor B

Question 30.
The resistance of two wires having same length and same area of cross-section are 2Ω and 8Ω respectively. If the resistivity of 2Ω wire is 2.65 × 10-8 Ω–m then the resistivity of 8Ω wire is :
  1. 10.60 × 10-8 Ω-m
  2. 8.32 × 10-8 Ω-m
  3. 7.61 × 10-8 Ωm
  4. 5.45 × 10-8 Ωm


Question 31.
In a certain region field  begin mathsize 11px style straight E with rightwards arrow on top end style  and magnetic field  begin mathsize 11px style straight B with rightwards arrow on top end style  are perpendicular to each other. An electron enters the region perpendicular to the direction of both  begin mathsize 11px style straight E with rightwards arrow on top end style and  begin mathsize 11px style straight B with rightwards arrow on top end style  moves undeflected. The speed of the electron is :  
  1. begin mathsize 11px style straight E with rightwards arrow on top space. straight B with rightwards arrow on top end style  
  2. begin mathsize 11px style open vertical bar straight E with rightwards arrow on top space cross times straight B with rightwards arrow on top close vertical bar end style
  3. begin mathsize 11px style fraction numerator open vertical bar straight E with rightwards arrow on top space close vertical bar over denominator open vertical bar straight B with rightwards arrow on top close vertical bar end fraction end style
  4. begin mathsize 11px style fraction numerator open vertical bar straight B with rightwards arrow on top close vertical bar over denominator open vertical bar straight E with rightwards arrow on top space close vertical bar end fraction end style
 
Question 32.
A test charge of 1.6 × 10-19 C is moving with a velocity  begin mathsize 11px style straight V with logical and on top equals left parenthesis 4 1 with logical and on top plus 3 straight k with logical and on top space straight N right parenthesis space straight m space straight s to the power of negative 1 end exponent end style in a magnetic field  begin mathsize 11px style straight B with logical and on top equals left parenthesis 3 straight k with logical and on top plus 4 1 with logical and on top right parenthesis space straight T end style . The force on this test charge is : 
  1.  begin mathsize 11px style 24 space straight J with logical and on top straight N end style 
  2.  begin mathsize 11px style negative 24 space straight i with logical and on top straight N end style 
  3.  begin mathsize 11px style 24 space straight k with logical and on top straight N end style 
  4. 0

Question 33.
In a series LCR circuit, at resonance the current is equal to :
  1.  begin mathsize 11px style straight V over straight R end style
  2. begin mathsize 11px style straight V over straight X subscript straight c end style
  3. begin mathsize 11px style fraction numerator straight V over denominator straight X subscript straight L minus space straight X subscript straight c end fraction end style
  4. begin mathsize 11px style fraction numerator straight V over denominator square root of straight R to the power of 2 space end exponent space left parenthesis straight X subscript straight L minus space straight X subscript straight c right parenthesis squared end root end fraction end style
 
Question 34.
The frequency of an ac source for which a 10 μF capacitor has  a reactance of 1000Ω is : 
  1. begin mathsize 11px style 1000 over straight pi Hz end style
  2. 50 Hz
  3. begin mathsize 11px style 50 over straight pi Hz end style
  4. begin mathsize 11px style 100 over straight pi Hz end style

Question 35.
In the given network all capacitors used are identical and each one is of capacitance C. Which of the following is the equivalent capacitance between the points A and B? 
 
  1. 6C 
  2. begin mathsize 11px style 5 over 2 straight C end style
  3. begin mathsize 11px style 3 over 2 straight C end style  
  4. begin mathsize 11px style 5 over 6 straight C end style 

Question 36.
The given figure shows I – V graph of a copper wire whose length and area of cross-section are L and A respectively. The slope of this curve becomes :
 
  1. less if the length of the wire is increased
  2. more if the length of the wire is increased  
  3. more if a wire of steel of same dimension is used 
  4. more if the temperature of wire is increased 
 
Question 37.
When a potential difference V is applied across a conductor at temperature T, the drift velocity of the electrons is proportional to :
  1. T
  2. begin mathsize 11px style square root of straight T end style
  3. V
  4. begin mathsize 11px style square root of straight V end style
 
Question 38.
Two identical thick wires and two identical thin wires, all of the same material and the same length form a square in three different ways P, Q and R as shown. Due to the current in these loops the magnetic field at the centre of the loop will be zero in case of :
 
  1. P and R only
  2. Q and R only
  3. P and Q only
  4. P, Q and R 
 
Question 39.
A circular current carrying coil produces a magnetic field B0 at its centre. The coil is rewound so as to have three turns and the same current is passed through it. The new magnetic field at the centre is:
  1. 3 B
  2.  begin mathsize 11px style straight B subscript 0 over 3 end style
  3. begin mathsize 11px style straight B subscript 0 over 9 end style
  4. 9 B0 
 
Question 40.
Which one of the following statements is true?
  1. An inductor has infinite resistance in a dc circuit.
  2. A inductor and a capacitor both cannot conduct in a dc circuit. 
  3. A capacitor can conduct in a dc circuit but not an inductor.
  4. An iductor can conduct in a dc circuit but not a capacitor.
 
Question 41.
The magnetic flux linked with a coil is given by ϕ = 5t2 + 3t + 16, where is ϕ in webers and t in seconds. The induced emf in the coil at t = 5 s will be:
  1. 53 V 
  2. 43 V 
  3. 10V 
  4. 6V
 
Question 42.
If a charge is moved against a coulomb force of an electric field, then the:
  1. intensity of the electric field increases
  2. intensity of the electric field decreases
  3. work is done by the electric field
  4. work is done by the external source

Question 43.
A charge Q is located at the centre of a circle of radius r. The work done in moving a test charge q0 from point A to point B (at opposite ends of diameter AB) so as to complete a semicircle is begin mathsize 11px style open square brackets straight k equals 1 over 4 subscript πε 0 end subscript close square brackets end style :
  1. begin mathsize 11px style straight k fraction numerator straight q subscript 0 straight Q over denominator straight r end fraction end style
  2. begin mathsize 11px style straight k fraction numerator straight Q straight q subscript 0 over denominator straight r squared end fraction end style
  3. kq0Qr
  4. Zero
 
Question 44.
A long solenoid carrying current produces a magnetic field B along its axis. If the number of turns in the solenoid is halved and current in it is doubled, the new magnetic field will be:
  1. begin mathsize 11px style straight B over 2 end style
  2. B
  3. 2B
  4. 4B
 
Question Nos. 45 to 49 are Assertion (A) and statements Reason (R) type questions. Given below are two statements labelled as Assertion (A) and Reason (R). Select the most appropriate answer from the options given below.
 
  1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

  2. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
  3. Assertion (A) is true, but Reason (R) is false.
  4. Assertion (A) is false, but Reason (R) is true.
 
Question 45.
Assertion (A): A bar magnet experiences a torque when placed in a magnetic field.
Reason (R): A bar magnet exerts a torque on itself due to its own magnetic field.
 
Question 46.
Assertion (A): In a series LCR circuit connected to an ac source, resonance can take place.
Reason (R): At resonance XL = XC.
 
Question 47
Assertion (A): When a charged particle moves with velocity begin mathsize 11px style straight V with rightwards arrow on top end style  in a magnetic field begin mathsize 11px style straight B with rightwards arrow on top space open parentheses straight V with rightwards arrow on top perpendicular straight B with rightwards arrow on top close parentheses end style , the force on the particle does no work.
Reason (R): The magnetic force is perpendicular to the velocity of the particle.

 

Question 48.
Assertion (A): Induced emf in two coils made of wire of the same length and the same thickness, one of copper and another of aluminium is same. The current in copper coil is more than the aluminium coil.
Reason (R): Resistance of aluminium coil is more than that of copper coil.

 

Question 49.
Assertion (A): A transformer is used to increase or decrease ac voltage only.
Reaon (R): A transformer works on the basis of mutual induction.

 

SECTION C

This section consists of 6 multiple choice questions with an overall choice to attempt any 5 questions. In case more than the desirable number of questions are attempted, only the first 5 questions will be considered for evaluation.

 

Question 50.
Two charged spheres A and B having their radii in the ratio 1: 2 are connected together with a conducting wire. The ratio of their surface charge densities begin mathsize 11px style open parentheses fraction numerator straight A presuperscript straight sigma over denominator straight B presuperscript straight sigma end fraction close parentheses end style will be.
  1. begin mathsize 11px style 1 half end style
  2. 2
  3. begin mathsize 11px style 1 fourth end style
  4. 4
 

Question 51.
A current carrying square loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is  , the net force on the remaining three arms of the loop will be.
  1. 3begin mathsize 11px style straight F with rightwards arrow on top end style  
  2. -3 begin mathsize 11px style straight F with rightwards arrow on top end style  
  3. begin mathsize 11px style straight F with rightwards arrow on top end style  
  4. begin mathsize 11px style straight F with rightwards arrow on top end style  
Case – Study
 
A battery is a combination of two or more cells. In the following figure, a single batter is represented in which two cells of emf Ɛ1 and Ɛ2, and internal resistance r1 and r2 respectively are connected.
 
Answer the following questions:
 
 
Question 52.
The equivalent emf of this combination is :
  1. begin mathsize 11px style fraction numerator straight epsilon subscript 1 straight r subscript 1 plus straight epsilon subscript 2 straight r subscript 2 over denominator straight r subscript 1 plus straight r subscript 2 end fraction end style
  2. begin mathsize 11px style fraction numerator straight epsilon subscript 1 straight r subscript 1 minus space straight epsilon subscript 2 straight r subscript 2 over denominator straight r subscript 1 plus straight r subscript 2 end fraction end style
  3. begin mathsize 11px style fraction numerator straight epsilon subscript 1 straight r subscript 2 minus space straight epsilon subscript 2 straight r subscript 1 over denominator straight r subscript 1 plus space straight r subscript 2 end fraction end style
  4. begin mathsize 11px style straight epsilon subscript 1 minus space straight epsilon subscript 2 end style
 
Question 53.
For terminal B to be negative :
  1. begin mathsize 11px style straight epsilon subscript 1 straight r subscript 2 space greater than space straight epsilon subscript 2 straight r subscript 1 end style 
  2. begin mathsize 11px style straight epsilon subscript 1 straight r subscript 2 space less than space space straight epsilon subscript 2 straight r subscript 1 end style 
  3. begin mathsize 11px style straight epsilon subscript 1 straight r subscript 1 space greater than space straight epsilon subscript 2 straight r subscript 2 end style 
  4. begin mathsize 11px style straight epsilon subscript 1 straight r subscript 2 space equals space straight epsilon subscript 2 straight r subscript 1 end style 

Question 54.
The current in the internal circuit is:
  1. begin mathsize 11px style fraction numerator straight epsilon subscript 1 plus straight epsilon subscript 2 over denominator straight r subscript 1 plus straight r subscript 2 end fraction end style 
  2. begin mathsize 11px style fraction numerator straight epsilon subscript 2 minus space straight epsilon subscript 1 over denominator straight r subscript 1 plus space straight r subscript 2 end fraction end style 
  3. begin mathsize 11px style straight epsilon subscript 1 over straight r subscript 1 minus straight epsilon subscript 2 over straight r subscript 2 end style 
  4. begin mathsize 11px style straight epsilon subscript 1 over straight r subscript 2 minus straight epsilon subscript 2 over straight r subscript 1 end style 
 
Question 55.
The equivalent internal resistance of the combination is:
 
  1. begin mathsize 11px style fraction numerator straight r subscript 1 plus straight r subscript 2 over denominator straight r subscript 1 straight r subscript 2 end fraction end style 
  2. begin mathsize 11px style straight r subscript 1 plus space straight r subscript 2 end style 
  3. begin mathsize 11px style fraction numerator straight r subscript 1 straight r subscript 2 over denominator straight r subscript 1 plus straight r subscript 2 end fraction end style 
  4. begin mathsize 11px style straight r subscript 1 minus space straight r subscript 2 end style 

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