READ THE INSTRUCTIONS CAREFULLY GENERAL : 1. This sealed booklet is your Question Paper. Do not break the seal till you are told to do so. 2. Use the Optical Response sheet (ORS) provided separately for answering the questions. 3. Blank spaces are provided within this booklet for rough work. 4. Write your name, form number and sign in the space provided on the back cover of this booklet. 5. After breaking the seal of the booklet, verify that the booklet contains 28 pages and that all the 18 questions in each subject and along with the options are legible. If not, contact the invigilator for replacement of the booklet. 6. You are allowed to take away the Question Paper at the end of the examination. OPTICAL RESPONSE SHEET : 7. The ORS will be collected by the invigilator at the end of the examination. 8. Do not tamper with or mutilate the ORS. Do not use the ORS for rough work. 9. Write your name, form number and sign with pen in the space provided for this purpose on the ORS. Do not write any of these details anywhere else on the ORS. Darken the appropriate bubble under each digit of your form number. DARKENING THE BUBBLES ON THE ORS : 10. Use a BLACK BALL POINT PEN to darken the bubbles on the ORS. 11. Darken the bubble COMPLETELY. 12. The correct way of darkening a bubble is as : 13. The ORS is machine-gradable. Ensure that the bubbles are darkened in the correct way. 14. Darken the bubbles ONLY IF you are sure of the answer. There is NO WAY to erase or "un-darken" a darkened bubble. 15. Take g = 10 m/s 2 unless otherwise stated. Please see the last page of this booklet for rest of the instructions Time : 3 Hours Maximum Marks : 204 DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR PAPER-2 Test Pattern CLASSROOM CONTACT PROGRAMME (Academic Session : 2020 - 2021) SAMPLE PAPER-1 JEE(Advanced) REVIEW TEST English
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Tes Pttern Eglish REVIEW TEST CLAS ONT PROGRAMME ... - ALLEN
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READ THE INSTRUCTIONS CAREFULLY
GENERAL :
1. This sealed booklet is your Question Paper. Do not break the seal till you are toldto do so.
2. Use the Optical Response sheet (ORS) provided separately for answering the questions.
3. Blank spaces are provided within this booklet for rough work.
4. Write your name, form number and sign in the space provided on the back cover of thisbooklet.
5. After breaking the seal of the booklet, verify that the booklet contains 28 pages andthat all the 18 questions in each subject and along with the options are legible. If not,contact the invigilator for replacement of the booklet.
6. You are allowed to take away the Question Paper at the end of the examination.
OPTICAL RESPONSE SHEET :
7. The ORS will be collected by the invigilator at the end of the examination.
8. Do not tamper with or mutilate the ORS. Do not use the ORS for rough work.
9. Write your name, form number and sign with pen in the space provided for this purposeon the ORS. Do not write any of these details anywhere else on the ORS. Darkenthe appropriate bubble under each digit of your form number.
DARKENING THE BUBBLES ON THE ORS :
10. Use a BLACK BALL POINT PEN to darken the bubbles on the ORS.
11. Darken the bubble COMPLETELY.
12. The correct way of darkening a bubble is as :
13. The ORS is machine-gradable. Ensure that the bubbles are darkened in the correctway.
14. Darken the bubbles ONLY IF you are sure of the answer. There is NO WAY to eraseor "un-darken" a darkened bubble.
15. Take g = 10 m/s2 unless otherwise stated.
Please see the last page of this booklet for rest of the instructions
· Stefan–Boltzmann constant s = 5.67 × 10–8 Wm–2–K–4
· Wien's displacement law constant b = 2.89 × 10–3 m–K· Permeability of vacuum µ0 = 4p × 10–7 NA–2
· Permittivity of vacuum Î0 = 20
1
cm· Planck constant h = 6.63 × 10–34 J–s
ALLEN
SAMPLE PAPER-1/Paper-2ALLEN
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BEWARE OF NEGATIVE MARKINGHAVE CONTROL ¾® HAVE PATIENCE ¾® HAVE CONFIDENCE Þ 100% SUCCESS
PART-1 : PHYSICSSECTION–I(i) : (Maximum Marks : 12)
� This section contains FOUR questions.� Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options
is correct.� For each question, darken the bubble corresponding to the correct option in the ORS.� For each question, marks will be awarded in one of the following categories :
Full Marks : +3 If only the bubble corresponding to the correct option is darkened.Zero Marks : 0 If none of the bubbles is darkened.Negative Marks : –1 In all other cases
1. The operating temperature of a tungsten filament in an incandescent lamp is 2450 K and itsemissivity is 0.30. The surface area of the filament of a 25 watt lamp is :(Take : s = 5.67 × 10–8 S.I. unit)(A) 0.1 cm2 (B) 0.2 cm2 (C) 0.3 cm2 (D) 0.4 cm2
2. Two long wires are placed on a pair of fixed parallel rails perpendicular to the wires.The spacing d between the rails is large compared with x, the distance between the wires.Both wires and rails are made of a material of resistance r per unit length. A magnetic fluxdensity B is applied perpendicular to the rectangle so formed, and one wire is moved alongthe rails with a uniform speed v while the other is held stationary. It is seen that the forcerequired to hold the stationary wire vanishes at a particular value of x. Find x.
3. What horizontal force F must be applied to block (figure), so that it moves down the inclinedplane with constant velocity? Mass of the block m = 2 kg, the coefficient of friction between theblock and the surface of the plane is 0.2; plane forms angle of 45° to horizontal.
Fm
a
(A) 20 N (B) 13.33 N (C) 8 2N (D) 4 2N
4. An athelete runs up and projects Javelin at a certain angle to the horizontal. If the speed ofthe Javelin relative to the athelete is equal to the speed of the athelete at the time of projection,what should be the angle at which he should throw relative to himself so that the range ismaximum? The height of the athelete can be considered negligible.(A) 45° (B) 30° (C) 60° (D) 37°
SAMPLE PAPER-1/Paper-2ALLEN
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SECTION-I(ii) : (Maximum Marks: 32)� This section contains EIGHT questions.� Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these
four option(s) is (are) correct option(s).� For each question, choose the correct option(s) to answer the question.� Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (all) the correct option(s) is (are) chosen.Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.Partial Marks : +2 If three or more options are correct but ONLY two options are chosen,
both of which are correct options.Partial Marks : +1 If two or more options are correct but ONLY one option is chosen
and it is a correct option.Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).Negative Marks : –1 In all other cases.
� For Example : If first, third and fourth are the ONLY three correct options for a question withsecond option being an incorrect option; selecting only all the three correct options will resultin +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options),without selecting any incorrect option (second option in this case), will result in +2 marks.Selecting only one of the three correct options (either first or third or fourth option), withoutselecting any incorrect option (second option in this case), will result in +1 marks. Selectingany incorrect option(s) (second option in this case), with or without selection of any correct option(s)will result in –1 marks.
5. A part of radiation spectrum corresponding to Lyman series from a hydrogen like atom is
shown here. One of the lines is missing. (Take : R = 7 11610 m
15-´ )
1254 nm
25 nm
(A) The atom is helium
(B) The missing line is 3375
nm128
(C) The spectrum shown here is absorption spectrum(D) Some atoms are excited to the third excited state.
6. Two sources are connected in the chain, as shown in Figure. Determine the potential difference V1between points A and B with an open external circuit, if e1 = 5 V, r1 = 1 ohm, e2 = 3V,r2 = 2 ohms. What will be the potential difference V2 between points A and B if you close thekey K ? Resistance R = 5 ohms. Also find the current through the batteries after closing theswitch.
A Be1 1, r
e2 2, rK
R
(A) V1 = 4.3 V approx(B) V2 = 3.8 V approx(C) Current through battery e1 = 1.2 A approx.(D) Current through battery e2 = 0.4 A approx
7. Two homogenous spheres of mass 1 kg each, radius 10 cm are released from same height on aninclined plane of inclination 37°. The coefficient of friction for the first sphere is 0.1 and for thesecond sphere is 0.3
37°
(A) The ratio of time taken by first and second to reach the bottom is 7591 .
(B) The ratio of translational kinetic energy of first and second when they reach the bottom is 1:1
(C) The ratio of speed of first and second when they reach the bottom is 9175 .
(D) The ratio of angular velocity of first and second about their center when they reach the
bottom is 9175 .
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8. A fixed long ideal solenoid is encircled by a coaxial circular loop of radius R greater thanradius of the solenoid. A current I is passed through the circular loop. In which of the followingcases, no emf is induced in the solenoid ?
y
x
z
(A) The current in the loop is held constant and the loop is stationary.(B) The current in the loop is I = I0 sinwt and the loop is stationary.(C) The current in the loop is constant and the loop performs angular SHM about its diameter
(y axis) (but does not reach the solenoid surface)(D) The current in the loop is constant and the loop performs SHM about its mean position in
a direction perpendicular to the axis (but does not cross the solenoid)9. A vertically hanging rod of mass 5 kg is suspended from a hinge at A. A massless inextensible
cord is attached to the midpoint of the rod and is pulled at an angle of 37 degree to the vertical asshown. At the other end, a mass of 20 kg is hanging. Find F1 and F2 applied to keep the system inequilibrium, tension T in the cord and force F at the hinge.
20kgF1
F2
A
37°
(A) F1 = 75 N (B)F2 = 200 N (C) T = 250 N (D) F = 25 10N
10. A Rod of length L and mass m is suspended from the ceiling using two cords of same length L.It can be oscillated in two ways:(1) perpendicular to the plane of paper and (2) in the plane ofthe paper. The cords are massless and inextensible. Find the time period in each case.
LL
L
(A) in way (1) = p3 L
T 22 g
(B) in way (2) = p3 L
T 22 g
(C) in way (1) 5LT 2
3 3g= p (D) in way (2) 5L
T 23 3g
= p
11. In an infinite flat layer of thickness of h the spherical cavity in diameter of h (figure) is cut out.The layer is uniformly charged with volume charge density of r.
A
B
(A) The electric field at A is 0
h
6
re towards right.
(B) The electric field at B is 0
h
3
re in the upwards direction
(C) If the potential at the center of the cavity is zero, the potential at A is 2
0
h12r
e
(D) If the potential at the center of the cavity is zero, the potential at B is 2
0
13 h12
re
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SAMPLE PAPER-1/Paper-2ALLEN
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12. A triangular prism of sides 4m × 3m × 1m is completely filled with water. If we neglect theatmospheric pressure, the force by water (density = 1000 kg/m3) on
A
B
D
E
F
C3m
4m
1m
(A) On surface ABCD is zero(B) On surface CDEF is 2 × 104 N(C) On surface ADE is 8 × 104 N(D) On surface ABEF is 10 × 104 N
SECTION-II : (Maximum Marks: 24)� This section contains SIX questions.� The answer to each question is a NUMERICAL VALUE.� For each question, enter the correct numerical value (in decimal notation, truncated/rounded-
off to the second decimal place; e.g. 6.25, 7.00, –0.33, –.30, 30.27, –127.30, if answer is 11.36777.....then both 11.36 and 11.37 will be correct) by darken the corresponding bubbles in the ORS.For Example : If answer is –77.25, 5.2 then fill the bubbles as follows.
� Answer to each question will be evaluated according to the following marking scheme:Full Marks : +4 If ONLY the correct numerical value is entered as answer.Zero Marks : 0 If none of the bubbles is darkened.Negative Marks : –1 In all other cases
1. The external and internal radius of a hollow sphere are measured to be (4.20 ± 0.01) cm and(3.90 ± 0.01) cm. Maximum percentage error in the measurement of volume will be.
2. A ring of radius R and mass m is uniformly charged with charge Q. It is rolling purely asshown. A uniform magnetic field of magnitude B is present perpendicular to plane of the ring. Ifthe normal force exerted by the ground is lmg, find l. Take QvB = mg.
+ + ++
++
+++
+++
v
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SAMPLE PAPER-1/Paper-2ALLEN
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3. Refer to the circuit given below. Initially the switch S is in position–1 for 0.2 ln 2 s. Then theswitch is changed to position–2. After a time t (measured from the change over of the switch) the
voltage across 5 kW resistance is found to be 35
volt. Then, find the value of t (in milli sec)
10V 2
1S
5kW
10kW
20 Fm
4. In the figure shown below, the maximum possible unknown resistance (X), that can be measuredby the post office box are Xmax is given by R × 105 W, then R is : (In this experiment, we take outonly one plug in arm AB and only one plug in arm BC, but in arm AD we can take out manyplugs):
5. What is the difference in liquid levels (in mm) of the two intercommunicating capillarieswith diameters 2 mm and 1mm ? Liquid surface tension is 0.07 N/m. Meniscus contact anglesare zero for both the capillaries. Fluid density is 1000 kg/m3.
6. Proton separation energy is the amount of energy we must supply to remove a proton from a
nucleus. Find the proton separation energy of He42 (in MeV) . The mass of
( )Hm 11 = 1.007825 amu
( )Hm 31 = 3.016049 amu
( )Hem 42 = 4.002603 amu
(Take : 1amu = 931 MeV).
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PART-2 : CHEMISTRYSECTION–I(i) : (Maximum Marks : 12)
� This section contains FOUR questions.� Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options
is correct.� For each question, darken the bubble corresponding to the correct option in the ORS.� For each question, marks will be awarded in one of the following categories :
Full Marks : +3 If only the bubble corresponding to the correct option is darkened.Zero Marks : 0 If none of the bubbles is darkened.Negative Marks : –1 In all other cases
1. A vessel contains He gas at 20 atm and CH4 gas at 'P' atm. When a pin-hole is made in the
vessel, the gases coming out initially contains 80% He gas, by mole. The value of 'P' is(A) 1 atm (B) 40 atm (C) 2.5 atm (D) 10 atm
3. Which of the following reaction gives carboxylic acid as final product
(A) O
O
O 3(i)H O(ii)Δ
ž¾¾¾® (B) CH – CH – C – H3 2
O mcpba
Δ¾¾¾¾®
(C) O O
OEt3(i)H O
(ii)Δ
ž¾¾¾® (D)
32
–
(i) O(ii) Zn,H O(iii)O H,Δ
¾¾¾¾¾®
4. Which is NOT produce in given reaction change?
Sodium-amalgam water¾¾¾¾®
(A) H2 (B) NaOH (C) Hg (D) O2
SAMPLE PAPER-1/Paper-2ALLEN
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SECTION-I(ii) : (Maximum Marks: 32)� This section contains EIGHT questions.� Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of
these four option(s) is (are) correct option(s).� For each question, choose the correct option(s) to answer the question.� Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (all) the correct option(s) is (are) chosen.Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.Partial Marks : +2 If three or more options are correct but ONLY two options are chosen,
both of which are correct options.Partial Marks : +1 If two or more options are correct but ONLY one option is chosen
and it is a correct option.Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).Negative Marks : –1 In all other cases.
� For Example : If first, third and fourth are the ONLY three correct options for a question withsecond option being an incorrect option; selecting only all the three correct options will resultin +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options),without selecting any incorrect option (second option in this case), will result in +2 marks.Selecting only one of the three correct options (either first or third or fourth option), withoutselecting any incorrect option (second option in this case), will result in +1 marks. Selectingany incorrect option(s) (second option in this case), with or without selection of any correctoption(s) will result in –1 marks.
5. Select the correct statements -(A) More solute is adsorbed on activated charcoal when solution is diluted(B) All colloidal solutions show Tyndall effect significantly(C) Dialysis may be used to coagulate the sol.
(D) Lyophobic sols can be coagulated easily compared to the lyophilic sols.
6. In a voltmeter, mass of a metal deposited in 30 seconds in 200 gms. Analyse the currentv/s time graph shown below and identify the correct statement(s):
i
100 mA
10sec 20sec 30sec
t(A) Electrochemical equivalent of the metal is 100 g/coulomb(B) 33.33 grams got discharged in the first 10 seconds.(C) A constant current of 66.66 mA would also discharge approximately the same amount in
same time(D) 100 gms of metal got discharged in the first 15 seconds
7. The reaction : A(s) �������� 2B(g) is in equilibrium at 4 atm and 27°C. If the volume of systemis increased at constant temperature, then at new equilibrium, relative to initialequilibrium :-(A) Moles of A(s) decreases (B) Moles of B(g) increases
(C) Molar concentration of A(s) decreases (D) Molar concentration of B(g) decreases
8. Which of the following is classified into free radical substitution reaction
(A) R – C – OAgO
2 4Br ,CClΔ¾¾¾¾¾® (B)
2 2
HBrR O ,hν¾¾¾¾¾®
(C) NBSΔ¾¾¾® (D) 2
4
BrCCl¾¾¾®
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9. Which of the following is/are used for preparation of aldehyde?(A) Stephen reduction(B) Rosenmund reduction(C) Clemmensen reduction(D) Reaction of 1-propanol by cromic anhydride in glacial acetic acid.
10. Out of given select correct order(s) :-(A) F > N > C > B > Si (Non metallic character)(B) F2 > Cl2 > O2 > N2 (Chemical reactivity in term of oxidising property)(C) K > Mg > Al > B (Metallic character)(D) Ne > F > O > N (First ionisaton energy)
11. Which is/are CORRECTLY represented with the explanation for colour of given species?(A) FeSO4.7H2O Þ t2g to eg transition(B) Br2 = s* to p* transition(C) KMnO4 = L ® M transition(D) Balmer series emission of H atom Þ De-excitation of electron from n = 3,4...... to n = 2
12. Which of the following is/are water insoluble?(A) Rhombic sulphur (B) Hydrogen bromide(C) Beryte salt (D) Ferric chloride
SECTION-II : (Maximum Marks: 24)� This section contains SIX questions.� The answer to each question is a NUMERICAL VALUE.� For each question, enter the correct numerical value (in decimal notation, truncated/rounded-
off to the second decimal place; e.g. 6.25, 7.00, –0.33, –.30, 30.27, –127.30, if answer is11.36777..... then both 11.36 and 11.37 will be correct) by darken the corresponding bubblesin the ORS.For Example : If answer is –77.25, 5.2 then fill the bubbles as follows.
� Answer to each question will be evaluated according to the following marking scheme:Full Marks : +4 If ONLY the correct numerical value is entered as answer.Zero Marks : 0 If none of the bubbles is darkened.Negative Marks : –1 In all other cases
1. Glutathione ( molecular weight = 307 gm/mol) is important antioxidant preventing damageto cellular components from free radicals, where it dimerises as
HS
NH
NH2
HO
O O
NH
HO
O
O
¾¾® OHN
HOO
SS
NHNH2
HO
O O
NH
HO
OO
HNH2N
OH
OO
Calculate gm equivalent weight of glutathione.2. A solution is prepared by mixing 1 M HA (pK
a = 4.2) and 1 M NaA. If pH of solution is 4.5. Find
the ratio of volume of NaA to HA added. (take : log 2 = 0.3).
SAMPLE PAPER-1/Paper-2ALLEN
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3. How many compounds give yellow liquid with NaNO2 + HCl
(i) CH3 – CH2 – NH2 (ii) N – CH3
H(iii) NH2 (iv) N
H
(v) CH – N – CH3 3
CH3(vi) CH – – N – CH3 3CH2
H
(vii) CH – – NH – CH3 3C
O
(viii) CH – – NH3 2C
O
4. How many total synthetic condensation polymers are :(i) Glyptal (ii) PVC (iii) Cellulose (iv) Dacron(v) Orlon (vi) Nylon-66 (vii) Bakelite(viii) Urea formaldehyde resin
5. Most common oxidation number of 3d series metals is +2 but Sc+2 is virtually unknown.Find sum of 3d electrons in all the known M+2 ions of 3d-series.
6. In the three dimensional structure of a chiral complex compound [Co(Co(NH3)4(OH)2)3]Br6.Find total number of Co–N & Co–O linkages.
PART-3 : MATHEMATICSSECTION–I(i) : (Maximum Marks : 12)
� This section contains FOUR questions.� Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options
is correct.� For each question, darken the bubble corresponding to the correct option in the ORS.� For each question, marks will be awarded in one of the following categories :
Full Marks : +3 If only the bubble corresponding to the correct option is darkened.Zero Marks : 0 If none of the bubbles is darkened.Negative Marks : –1 In all other cases
1. The sum of maximum & minimum values of expression y = 10sin2x + 6sinx cosx + 14 cos2x is-(A) 12 (B) 24 (C) 36 (D) 48
2. Number of integral solution(s) of the inequality 2sin2x – 5sinx + 2 > 0 in x Î [0,2p], is-(A) 3 (B) 4 (C) 5 (D) 6
3. Absolute value of slope of a line, common tangent to both the curves given by y = x2 andx2 + y + 1 = 0 will be -(A) 5 (B) 2 (C) 3 (D) 2
4. Complex numbers z1 & z2 are such that |z1| = 3, |z2| = 5 & |z1 + z2| = 7. The value of 6162
zarg
zmay be-
(A) p (B) 2
3
p(C)
3
p(D) 2p
SAMPLE PAPER-1/Paper-2ALLEN
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SECTION-I(ii) : (Maximum Marks: 32)� This section contains EIGHT questions.� Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of
these four option(s) is (are) correct option(s).� For each question, choose the correct option(s) to answer the question.� Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (all) the correct option(s) is (are) chosen.Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.Partial Marks : +2 If three or more options are correct but ONLY two options are chosen,
both of which are correct options.Partial Marks : +1 If two or more options are correct but ONLY one option is chosen
and it is a correct option.Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).Negative Marks : –1 In all other cases.
� For Example : If first, third and fourth are the ONLY three correct options for a question withsecond option being an incorrect option; selecting only all the three correct options will resultin +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options),without selecting any incorrect option (second option in this case), will result in +2 marks.Selecting only one of the three correct options (either first or third or fourth option), withoutselecting any incorrect option (second option in this case), will result in +1 marks. Selectingany incorrect option(s) (second option in this case), with or without selection of any correctoption(s) will result in –1 marks.
5. Let k Î Q and ƒ(x) = x2 – (3 – 2k)x + 2 – 4k, then identify the correct statement-(A) roots of ƒ(x) = 0 are rational
(B) if roots of ƒ(x) = 0 are of opposite sign, then 1k
2>
(C) if 1k
2£ , then roots of ƒ(x) = 0 are always of same sign.
(D) if exactly one root of ƒ(x) = 0 is greater than 2, then greatest integral value of 'k' is –1.
6. 7 points are given in a plane (as shown in adjacent figure), then using these 7 points -1
2
34 5 6 7
(A) Number of lines that can be formed is 10.(B) Number of triangles that can be formed is 24.(C) Number of quadrilateral that can be formed is 6.(D) Maximum number of circles that can be formed is 24, where each circle contains atleast three
of 7 points.7. There are 3 bags A, B & C. Bag A contains 1 Red & 2 Green balls, bag B contains 2 Red &
1 Green balls and bag C contains only one green ball. One ball is drawn from bag A & put intobag B then one ball is drawn from B & put into bag C & finally one ball is drawn from bag C &put into bag A. When this operation is completed, probability that bag A contains 2 Red &1 Green balls, is -
(A) 1
4(B) 1
2(C)
1
3(D)
1
68. If A and B are square matrices of order of 3 such that AB = aA + bB, where a, b Î R – {0}, then
the correct statements is/are.(A) A and B cummute (B) A – bI is invertible(C) B – aI is invertible (D) A = B
SAMPLE PAPER-1/Paper-2ALLEN
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9. Function ƒ(x) satisfies the relation ƒ(xy) = ƒ(x).ƒ(y) for all positive numbers x,y and ƒ(2) = 10,then-(ƒ–1(x) represent inverse of ƒ(x))
11. Let ƒ(x) is a continuous function in [a, b] such that ƒ(a) ¹ ƒ(b) and ƒ(a), ƒ(b) > 0, then which ofthe following is CORRECT ?
(A) If ƒ(c) =ƒ(a) ƒ(b)
2
+, then there always exist at least one 'c' in (a, b)
(B) If ƒ(c) ƒ(a)ƒ(b)= , then there always exist at least one 'c' in (a, b)(C) If 5ƒ(c) 3ƒ(a) 2ƒ(b)= + , then there always exist at least one 'c' in (a, b)
(D) If 2ƒ(c) 3ƒ(a) ƒ(b)= - , then there always exists at least one 'c' in (a, b)
12. If ( )3xP e cos 2013x dx= ò and ( )3xQ e sin 2013x dx= ò (where P & Q both have integration
constant zero) & ƒ(x) = ln((P2 + Q2) (32 + 20132)) then(A) ƒ(1) + ƒ(2) = 18 (B) ƒ'(1) = ƒ'(–1)(C) ƒ(x) is an odd degree polynomial (D) ƒ(x) is symmetric about x = 0
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SECTION-II : (Maximum Marks: 24)� This section contains SIX questions.� The answer to each question is a NUMERICAL VALUE.� For each question, enter the correct numerical value (in decimal notation, truncated/rounded-
off to the second decimal place; e.g. 6.25, 7.00, –0.33, –.30, 30.27, –127.30, if answer is11.36777..... then both 11.36 and 11.37 will be correct) by darken the corresponding bubblesin the ORS.For Example : If answer is –77.25, 5.2 then fill the bubbles as follows.
� Answer to each question will be evaluated according to the following marking scheme:Full Marks : +4 If ONLY the correct numerical value is entered as answer.Zero Marks : 0 If none of the bubbles is darkened.Negative Marks : –1 In all other cases
1. If P1, P2, P3 are the points on ellipse 3x2 + y2 – 12 = 0 and P1', P2', P3' are their correspondingpoints on the auxillary circle, then the area of triangle P1' P2' P3' is l times the area of triangleP1P2P3, then l2 is
2. If the family of integral curves of the differential equation 3dyx y x
dx+ = is cut by the line
x = 2; the tangents at the points of intersection are concurrent at (l, µ). Then the value oflµ
QUESTION PAPER FORMAT AND MARKING SCHEME :16. The question paper has three parts : Physics, Chemistry and Mathematics.17. Each part has two sections as detailed in the following table.
I have read all the instructionsand shall abide by them.
____________________________Signature of the Candidate
I have verified the identity, name and Formnumber of the candidate, and that questionpaper and ORS codes are the same.
____________________________Signature of the Invigilator
NAME OF THE CANDIDATE ................................................................................................
FORM NO. .............................................
Que. No. Category-wise Marks for Each Question MaximumSection Type of Full Partial Zero Negative Marks of the
Que. Marks Marks Marks Marks section+3 0 –1
I(i) Single If only the bubble If none In allcorrect option 4 corresponding to — of the other 12
the correct option bubbles is casesis darkened darkened
+4 +1 0 –1One or more If only the bubble(s) For darkening a bubble If none In all
I(ii) correct 8 corresponding corresponding to each of the other 32option(s) to all the correct correct option, provided bubbles is casesoption(s) is(are) NO incorrect option darkened
darkened darkened+4 0 –1
Numerical If only the bubble If none In all II Value Type 6 corresponding — of the other 24
(Up to second to correct answer bubbles is cases decimal place) is darkened darkened
Your Target is to secure Good Rank in JEE 2021
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(B) jkstsueq.M vip;u dk
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(A) F > N > C > B > Si (v/kkfRod y{k.k)(B) F2 > Cl2 > O2 > N2 (vkWDlhdkjd xq.k ds in esa jklk;fud lfØ;rk)(C) K > Mg > Al > B (/kkfRod y{k.k)(D) Ne > F > O > N (izFke vk;uu ÅtkZ)
11. fuEu eas ls dkSu ls fodYi esa] nh x;h Lih'kht ds jax ds fy, lgh Li"Vhdj.k iznf'kZr fd;k x;k gS?(A) FeSO4.7H2O Þ t2g ls eg laØe.k(B) Br2 = s* ls p* laØe.k(C) KMnO4 = L ls M laØe.k(D) gkbMªkstu ijek.kq dk ckej Js.kh mRltZu Þ n = 3,4...... ls n = 2 esa bysDVªkWu dk vuqÙkstu
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7. 3 FkSys A, B rFkk C gSA FkSys A esa 1 yky ,oa 2 gjh xsnsa] FkSys B esa 2 yky ,oa 1 gjh xsan rFkk FkSys C esa dsoy 1 gjh xsangSA FkSys A ls 1 xsan fudky dj mldks FkSys B esa j[krs gS] mlh le; FkSys B ls 1 xsan fudky dj FkSys C esa j[krs gS rFkkvUr esa FkSys C ls 1 xsan fudky dj FkSys A esa j[krs gSA ;g izfØ;k iw.k± gksus ij izkf;drk rkfd FkSys A esa 2 yky rFkk 1gjh xsan gks] gksxh -
(A) 1
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2(C)
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68. ;fn A rFkk B dksfV 3 ds oxZ vkO;wg bl izdkj gS fd AB = aA + bB, tgk¡ a, b Î R – {0} gks] rks fuEu esa ls
dkSulk@dkSuls lgh dFku gksxk@gksaxs(A) A rFkk B Øefofues; gSA (B) A – bI O;qRØe.kh; gSA(C) B – aI O;qRØe.kh; gSA (D) A = B