(0999dja110321008) )) test pattern distance learning

READ THE INSTRUCTIONS CAREFULLY / Ïi;k bu funsZ'kks a dks /;ku ls i<+ s a GENERAL / lkekU; % 1. This sealed booklet is your Question Paper. Do not break the seal till you are told to do so.
;g eksgjcU/k iqfLrdk vkidk iz'ui= gSA bldh eqgj rc rd u rksM+s tc rd bldk funsZ'k u fn;k tk;sA 2. Use the Optical Response sheet (ORS) provided separately for answering the questions.
iz'uksa dk mÙkj nsus ds fy, vyx ls nh x;h vkWfIVdy fjLikal 'khV (vks- vkj- ,l-) (ORS) dk mi;ksx djsaA 3. Blank spaces are provided within this booklet for rough work.
dPps dk;Z ds fy, bl iqfLrdk esa [kkyh LFkku fn;s x;s gSaA 4. Write your name, form number and sign in the space provided on the back cover of this booklet.
bl iqfLrdk ds fiNys i`"B ij fn, x, LFkku esa viuk uke o QkWeZ uEcj fyf[k, ,oa gLrk{kj cukb;sA 5. After breaking the seal of the booklet, verify that the booklet contains 36 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. bl iqfLrdk dh eqgj rksM+us ds ckn Ïi;k tk¡p ysa fd blesa 36 i`"B gSa vkSj izR;sd fo"k; ds lHkh 18 iz'u vkSj muds mÙkj fodYi Bhd ls i<+ s tk ldrs gSaA ;fn ugha] rks iz'ui= dks cnyus ds fy, fujh{kd ls lEidZ djsaA
6. You are allowed to take away the Question Paper at the end of the examination. ijh{kkFkhZ iz'ui= dks ijh{kk dh lekIrh ij ys tk ldrs gSaA
OPTICAL RESPONSE SHEET / vkWfIVdy fjLikal 'khV (vks-vkj-,l-) % 7. The ORS will be collected by the invigilator at the end of the examination.
vks- vkj- ,l- dks ijh{kk ds lekiu ij fujh{kd ds }kjk ,d= dj fy;k tk,xkA 8. Do not tamper with or mutilate the ORS. Do not use the ORS for rough work.
vks- vkj- ,l- esa gsj&Qsj@foÏfr u djsaA vks-vkj-,l- dk dPps dke ds fy, iz;ksx u djsaA 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. viuk uke vkSj QkWeZ uEcj vks-vkj-,l- esa fn, x, [kkuksa esa dye ls fy[ksa vkSj vius gLrk{kj djsaA buesa ls dksbZ Hkh fooj.k vks-vkj-,l- esa dgha vkSj u fy[ks aA QkWeZ uEcj ds gj vad ds uhps vuq:i cqycqys dks dkyk djsaA
DARKENING THE BUBBLES ON THE ORS / vks-vkj-,l- ij cqycqyks a dks dkyk djus dh fof/k % 10. Use a BLACK BALL POINT PEN to darken the bubbles on the ORS.
vks-vkj-,l- ds cqycqyksa dks dkys ckWy ikWbUV dye ls dkyk djsaA
11. Darken the bubble COMPLETELY. / cqycqys dks iw.k ± :i ls dkyk djsaA
12. The correct way of darkening a bubble is as : / cqycqys dks dkyk djus dk mi;qDr rjhdk gS : 13. The ORS is machine-gradable. Ensure that the bubbles are darkened in the correct way.
vks-vkj-,l- e'khu tk¡P; gSA lqfuf'pr djsa dh cqycqys lgh fof/k ls dkys fd, x;sa gSaA 14. Darken the bubbles ONLY IF you are sure of the answer. There is NO WAY to erase or
"un-darken" a darkened bubble. cqycqys dks rHkh dkyk djsa tc vki mÙkj ds ckjs esa fuf'pr gksA dkys fd, gq, cqycqys dks feVkus vFkok lkQ djus dk dksbZ rjhdk ugha gSA
15. Take g = 10 m/s2 unless otherwise stated. / g = 10 m/s2 iz;qDr djsa] tc rd fd vU; dksbZ eku ugha fn;k x;k gksA QUESTION PAPER FORMAT AND MARKING SCHEME / iz'ui= dk izk:i vkSj vadu ;kstuk % 16. The question paper has three parts : Physics, Chemistry and Mathematics.
bl iz'ui= esa rhu Hkkx gSa % HkkSfrd foKku] jlk;u foKku ,oa xf.krA
Time : 3 Hours Maximum Marks : 198
)0999DJA110321008)(0999DJA110321008) Test Pattern
JEE(Advanced) TEST # 07
JEE(Main + Advanced) : LEADER TEST SERIES / JOINT PACKAGE COURSE
Test Type : Review (Unit Test # 01, 02, 03, 04 & 05) 12th Undergoing/Pass Students
PAPER – 1
0999DJA110321008
Note : In case of any correction in the test paper, please mail to [email protected] within 2 days along with Paper Code & Your Form No. (uksV % ;fn bl iz'u i= esa dksbZ Correction gks rks Ïi;k Paper Code ,oa vkids Form No. ,oa iw.kZ Test Details ds lkFk 2 fnu ds vUnj [email protected] ij mail djsaA)
ALLEN
Space for Rough Work / dPps dk;Z ds fy, LFkku
SOME USEFUL CONSTANTS Atomic No. : H = 1, B = 5, C = 6, N = 7, O = 8, F = 9, Al = 13, P = 15, S = 16,
Cl = 17, Br = 35, Xe = 54, Ce = 58 Atomic masses : H = 1, Li = 7, B = 11, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24,
Al = 27, P = 31, S = 32, Cl = 35.5, Ca=40, Fe = 56, Br = 80, I = 127, Xe = 131, Ba=137, Ce = 140
· Boltzmann constant k = 1.38 × 10–23 JK–1
· Coulomb's law constant pe 9
0
1 = 9×10 4
· Universal gravitational constant G = 6.67259 × 10–11 N–m2 kg–2
· Speed of light in vacuum c = 3 × 108 ms–1
· 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 = 2 0
1
SYLLABUS : PHYSICS : Basic Mathematics used in Physics, Vectors, Units, Dimensions and Measurement,
Electrostatics, Kinematics, Current electricity, Laws of Motion and Friction & Capacitors, Work, Energy & Power, Magnetic effect of current, Magnetism and Matter, Centre of Mass & Collisions, Electromagnetic Induction (EMI)
CHEMISTRY : Mole Concept, Atomic structure, Organic nomenclature, Basic principles of practical organic chemistry, Periodic properties, Basic inorganic nomenclature, Chemical thermodynamics, Thermochemistry & GOC(complete), Chemical Bonding, Solid state, Chemical kinetics, Isomerism, Chemical Equilibrium, State of matter (gaseous state),Redox & equivalent concept
MATHEMATICS : Logarithms, Trigonometric Ratios and Identities, Matrices, Determinants, Quadratic Equations & Linear Inequilities, Functions and Inverse Trignometric Function, Trigonometric Equations, Solution of Triangles, Height and Distance, Differential Calculus (Limit, Continuity, Differentiability, Differentiation), Point and Straight Line, Indefinite integration, Circle, Definite integration.
ALLEN Leader Test Series/Joint Package Course/03-10-2021/Paper-1
PART-1 : PHYSICS
-1 : SECTION-I (i) : (Maximum Marks: 18)
-I (i) : ( : 18)
Full Marks : +3 If ONLY the correct option is chosen. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered) Negative Marks : –1 In all other cases
: +3 : 0 : –1
1. If the mass, time and work are taken as fundamental physical quantities then dimensional formula of length will be
(A) M T W (B) M T W
(C) M T W (D) None of these
, -
(A) M T W (B) M T W
(C) M T W (D)
BEWARE OF NEGATIVE MARKING
This section contains SIX (06) questions. Each question has Four options (A), (B), (C) and (D). ONLY ONE of these four options is correct. For each question, choose the option corresponding to the correct answer. Answer to each question will be evaluated according to the following marking scheme :
(06) (A), (B), (C) (D)
1/2 1 –1/2 –1/2 1 1/2
–1 2 1/2
–1 2 1/2
Space for Rough Work/
0999DJA110321008 LTS-3/36
ALLEN Target : JEE(Main + Advanced) 2022/03-10-2021/Paper-1
2. An object is thrown horizontally from a point 'A' from a tower and hits the ground 3s later at B. The line from 'A' to 'B' makes an angle of 30° with the horizontal. The initial velocity of the object is : (take g = 10 m/s )
A 3s B A B 30° :- (g = 10 m/s )
(A) (B) 15 m/s (C) (D)
3. A 50 kg person stands on a 25 kg platform. He pulls on the rope which is attached to the platform via the frictionless pulleys as shown in the figure. The platform moves upwards at a steady rate if the force with which the person pulls the rope is
(A) 500 N (B) 250 N (C) 25 N (D) None of these
50 kg 25 kg , -
(A) 500 N (B) 250 N (C) 25 N (D)
2
2
LTS-4/36 0999DJA110321008
4. A small ball of mass m is released from height h on a wedge having circular track as shown in figure. Find the normal force on ball due to wedge just after it enters in circular track. (Assume it enters at point P tangentially and all surfaces are smooth)
(A) (B) (C) (D) zero
m h 'pk ( P )
(A) (B) (C) (D)
5. The circuit is completed at t = 0, then total work done by batteries till the capacitor gets full charged.
[q = 64μC and C = 16μF]
t = 0
-[q = 64μC C = 16μF]
(A) 1024 μJ (B) 512 μJ (C) 320 μJ (D) 64 μJ
2mgh R
0999DJA110321008 LTS-5/36
6. A small ball having charge +q and mass m lies on a horizontal smooth surface (take it as xy-plane) at distance b from origin. A magnetic field exists within the region enclosed by the circle x + y = b and directed towards negative z-axis as shown. If magnetic field starts increasing with time as B = B (10 + t), then :-
(A) The ball will start to move towards +ve x-axis with acceleration
(B) The ball will start to move towards –ve x-axis with acceleration .
(C) The ball will start to move towards +ve y-axis with acceleration .
(D) The ball will start to move towards –ve y-axis with acceleration .
+q m ( xy- ) b x + y = b z- B = B (10 + t) :-
(A) x-
(B) x-
(C) y-
(D) y-
2 2 2
LTS-6/36 0999DJA110321008
SECTION-I (ii) : (Maximum Marks: 24)
-I (ii) : ( : 24)
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 and both of which are correct. 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 : –2 In all other cases.
: +4 () () : +3 : +2 : +1 : 0 ( ) : –2
This section contains SIX (06) questions. Each question has FOUR options. ONE OR MORE THAN ONE of these four option(s) is (are) correct answer(s). For each question, choose the option(s) corresponding to (all ) the correct answer(s) Answer to each question will be evaluated according to the following marking scheme:
For Example : If first, third and fourth are the ONLY three correct options for a question with second option being an incorrect option; selecting only all the three correct options will result in +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), without selecting any incorrect option (second option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case), with or without selection of any correct option(s) will result in –2 marks.
(06) () () , () () :
: , ; +4 ( ) ( ) +2 ( ), ( ) +1 ( ), –2 , ()
0999DJA110321008 LTS-7/36
7. A particle of mass m and charge q is projected in a region where an electric field is existing and given by , with a velocity from the origin at time t = 0, then choose the correct statements
(assuming m v = 2qE mx ).
(A) radius of curvature of the particle when its x–coordinate becomes x is 2x .
(B) radius of curvature of the particle when its x–coordinate becomes x is 4 x .
(C) speed of the particle when its x–coordinate becomes x is .
(D) speed of the particle when its x–coordinate becomes x is 2v .
m q t =0 ,
( m v = 2qE mx )
(A) x- x 2x
(B) x- x 4 x
(C) x- x
(D) x- x 2v
=E E 0 i v0 j 2
0 2
0 0
0 0
2 0 0
LTS-8/36 0999DJA110321008
8. Uniform magnetic field B = –B present from X = 0 to X = . A super conducting loop of given side length and self inductance L. Start with speed v with no initial current choose incorrect options. (mass of loop is m)
(A) If v is slightly greater than then loop will oscillates
(B) If v is slightly greater than then loop never returns to initial position
(C) If v is slightly less than then loop returns to initial position only one time
(D) If v is slightly less than then loop oscillates
B = –B ; X = 0 X = L v ( m )
(A) v
(B) v
(C) v
(D) v
0
0
0
0
0
0
0
0
0
0
0
0
0999DJA110321008 LTS-9/36
9. What should be the values of R and R so that the current through the branch BD is zero :-
R R BD :-
(A) R = 3Ω, R = 4Ω (B) R = 4Ω, R = 4Ω
(C) R = 5Ω, R = 3Ω (D) R = 3Ω, R = 2Ω
1 2
1 2
LTS-10/36 0999DJA110321008
10. Consider a Gaussian surface as shown. A and C are the circular faces while B is the curved surface. A charge q is moved along the axis of cylinder with constant velocity v. Choose the correct variation of flux through the surface of cylinder.

0999DJA110321008 LTS-11/36
11. A lamina is made by removing a disc of diameter R from a uniform disc of radius R and mass m.
(A) Mass of remaing lamina is m/2 (B) mass of remaining lamina is
(C) the y-coordinate of COM is (D) x-cordinate of COM of lamina is zero.
R m R
(A) m/2 (B)
(C) y- (D) x-
3m 4
− R 6
3m 4
− R 6
LTS-12/36 0999DJA110321008
12. In a region of space, where a uniform vertical magnetic field of induction B exists, a light rod of length L and mass m rigidly connected between two sleeves can slide on two horizontally fixed very long parallel conducting rails. A capacitor of capacitance C charged to voltage V is connected through a switch to the rails as shown. Initially the switch is open and the rod is at rest. Now the switch is closed. Assume the rails to be long enough and ignoring electrical resistance and frictional forces. Which of the following conclusion can you make?
.
(C) Heat released in the resistance of the jumper is .
(D) None of the above is correct
B L m C V ?
(A)
(B)
(C)
(D)
0
0999DJA110321008 LTS-13/36
SECTION-II : (Maximum Marks: 24)
-II : ( : 24)
Full Marks : +4 If ONLY the correct numerical value is entered. Zero Marks : 0 In all other cases.
: +4 (Numerical value) : 0
1. A metal rod of mass 10 gm and length 25 cm is suspended on two springs in a vertical plane as shown in figure. The springs are extended by 4cm. When a 20 ampere current passes through the rod it rises by 1 cm. Determine the magnetic field (in milli Tesla) assuming acceleration due to gravity to be 10 m/s .
10 gm 25 cm 4cm 20 1 cm 10 m/s ( )
This section contains SIX (06) questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the answer in the place designated to enter the answer. If the numerical value has more than two decimal places, truncate/round-off the value to Two decimal places; 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) Answer to each question will be evaluated according to the following marking scheme:
(06) (NUMERICAL VALUE) ( , /; 6.25, 7.00, –0.33, –.30, 30.27, –127.30, 11.36777..... , 11.36 11.37 )
2
2
LTS-14/36 0999DJA110321008
2. Two masses of 1 kg each carry equal charges Q and are suspended by light strings of length 1m from a point. The strings are hung at 30° inclination to the vertical. The value of charge Q when the charges are in equilibrium is p × 10 C, value of p is :
1 kg Q 1m 30° Q p × 10 C p
3. A galvanometer gives full scale reading of 50 mA, when a p.d. across its terminals is 0.15 V. It can be used as an ammeter of range 0-100 A by connecting a shunt resistance of P × 10 Ω. Value of P is.
50 mA , 0.15 V
P × 10 Ω 0-100A P -
4. A capacitor of 2μF is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is :
2μF S 2 , -
–6
–6
–3
–3
0999DJA110321008 LTS-15/36
5. A transformer with 20 turns in its secondary coil is used to step down the input 220 V ac emf. The output of the transformer is fed to a rectifier circuit which converts the ac input into dc output. The input and output of rectifier are as shown in Figure (there is no change in peak voltage). The rectifier output has an average emf of 8.98 volt. Calculate the number of turns in the primary coil of the transformer. Take
and report the nearest integer as the answer.
20 220 V (Stop down) ( ) .. 8.98

6. Two elastic balls of masses m and m are placed on top of each other (with a small gap between them) and then dropped onto the ground. What is the ratio m /m , for which the upper ball ultimately receives the largest possible fraction of the total energy ?
m m - m /m ?
= 1.412–√
= 1.412–√
LTS-16/36 0999DJA110321008
PART-2 : CHEMISTRY
-2 : SECTION-I (i) : (Maximum Marks: 18)
-I (i) : ( : 18)
: +3 : 0 : –1
1. In ICl , ICl and ICl sum of bond pair and lone pair on each iodine atom are respectively -
(A) 2, 2 and 4 (B) 2, 3 and 2 (C) 4, 5 and 4 (D) 4, 5 and 6
ICl , ICl ICl -
(A) 2, 2 4 (B) 2, 3 2 (C) 4, 5 4 (D) 4, 5 6
2. What is the INCORRECT bond angle order for the following molecule ?
, ?
(A) PF > PH
(B) NH > NF
(D) > CO >
(06) (A), (B), (C) (D)
2 +
2 –
4 –
2 +
2 –
4 –
0999DJA110321008 LTS-17/36
3. Choose the correctly matched order ?
(A)
?
(A)
(B)
(C)
(D)
LTS-18/36 0999DJA110321008
4. In which of the following reactions white precipitate of AgCl will be obtained ?
AgCl 'os ?
(A) (B)
(C) (D)
5. If crystal AB shows rock salt type of arrangement then calculate distance between two closest cation, if density of crystal is 50 gm/cc and molecular weight of AB is 60 amu. [Take N = 6 × 10 ]
AB 50 gm/cc AB 60 amu [ N = 6 × 10 ]
(A) (B) 2Å (C) (D)
6. If a be the radius of first Bohr's orbit of H-atom, the de-Broglie's wavelength of an electron revolving in the second Bohr's orbit of H-atom will be :
(A) 6 πa (B) 4 πa (C) 2 πa (D) None of these
H- a H- - –
(A) 6 πa (B) 4 πa (C) 2 πa (D)
A 23
A 23
0999DJA110321008 LTS-19/36
-I (ii) : ( : 24)
: +4 () () : +3 : +2 : +1 : 0 ( ) : –2
(06) () () , () () :
: , ; +4 ( ) ( ) +2 ( ), ( ) +1 ( ), –2 , ()
LTS-20/36 0999DJA110321008
7. In which of the following options order of arrangement does not agree with the variation of property indicated against it?
(A) Al < Mg < Na < F (increasing ionic size)
(B) B < C < N < O (increasing first ionisation enthalpy)
(C) I < Br < Cl < F (increasing electron gain enthalpy)
(D) Li < Na < K < Rb (increasing metallic radius)
?
(A) Al < Mg < Na < F ( )
(B) B < C < N < O ( )
(C) I < Br < Cl < F ( )
(D) Li < Na < K < Rb ( )
8. Which of the following is/are CORRECT order :
(A) LiF > NaF > KF > RbF > CsF (Thermal stability)
(B) MgF > MgO > Mg N : (lattice energy)
(C) Be(NO ) > Mg(NO ) > Ca(NO ) : (thermal stability)
(D) BaO > CaO > ZnO > GeO : (Basic strength)
:
(A) LiF > NaF > KF > RbF > CsF ( )
(B) MgF > MgO > Mg N : ( )
(C) Be(NO ) > Mg(NO ) > Ca(NO ) : ( )
(D) BaO > CaO > ZnO > GeO : ( )
3+ 2+ + –
3+ 2+ + –
2 3 2
0999DJA110321008 LTS-21/36
9. Which of following pair an example of tautomerism :
:
(A) (B)
(C) (D)
10. Which of the following compound can not show metamerism :
:
(A) CH – O – CH – CH – CH (B)
(C) (D)
LTS-22/36 0999DJA110321008
11. Making of SO (g) by contact process using suitable catalyst is an exothermic process 2SO (g) + O (g) 2SO (g) ; ΔH = –ve Assuming that equilibrium has been estabilished. Select the correct statement(s) on increasing pressure on the system at constant temperature.
(A) Reaction shifts forward to attain new equilibrium.
(B) Average molar mass of gaseous mixture increases.
(C) Partial pressure of SO , SO & O will increase.
(D) Concentration of SO increases whereas concentration of SO & O decreases.
SO (g) 2SO (g) + O (g) 2SO (g) ; ΔH = –ve
(A)
(B)
(C) SO , SO O
(D) SO SO O
12. For the reaction A + 3B → C, select the correct statement -
(A)
(B)
(C) Rate law must be r = k [A][B]
(D) Units for rate of reaction are independent of order of reaction
A + 3B → C , -
(A)
(B)
(C) r = k [A][B]
(D)
3
-II : ( : 24)
1. Find the total number of neutral oxides out of following compounds.

BaO, Al O , SiO , CO, CO , NO , N O
2. Total number of compounds which have diamagnetic anions :-
:-
SO , Na O , CsO , KO , NaNO
3. How many benzenoid isomer are possible for C H O which will give effervesences with NaHCO :
C H O NaHCO :
(06) (NUMERICAL VALUE) ( , /; 6.25, 7.00, –0.33, –.30, 30.27, –127.30, 11.36777..... , 11.36 11.37 )
2 3 2 2 2 2
3 2 2 2 3 2
8 8 2 3
8 8 2 3

(i) (ii) (iii)
(iv) (v) (vi)
(vii) (viii) (ix)
0999DJA110321008 LTS-25/36
5. Find (ΔS) (in Joule/mole/K) for a chemical reaction at 300 K given ΔHº = 75 kJ / mol ;
ΔSº300 K = 300 J/K/mole
300 K (ΔS) ( //K ) : ΔHº = 75 kJ / mol ; ΔSº300 K = 300 J/K/mole
6. Calculate the enthalpy of ionisation of weak acid H A(H A→2H +A ) in Kcal/ mol, if enthalpies of neutralisation of HCl and H A by a strong base are 14 Kcal/eq and 11 Kcal/eq respectively.
H A(H A→2H +A ) Kcal/ mol HCl
H A 14 Kcal/eq 11 Kcal/eq
universe 300 K
LTS-26/36 0999DJA110321008
PART-3 : MATHEMATICS
-I (i) : ( : 18)
: +3 : 0 : –1
1. is equal to
2. If , then the solution set for x is
, x
(A) (B) (C) (D)
3. If 2x – 3xy + y + x + 2y – 7 = 0, then is equal to -
2x – 3xy + y + x + 2y – 7 = 0 , -
(A) (B) (C) (D)
(06) (A), (B), (C) (D)
sin (4 + sec )3–√ π 9
π 9
π 9
1 3
− 1 3
4 x − 8 sin x + 3 0, 0 x 2πsin2
4 x − 8 sin x + 3 0, 0 x 2πsin2
[0, ]π 6 [0, ]5π
6 [ , 2π]5π 6
0999DJA110321008 LTS-27/36
4. is -
-
5. is equal to –
–
(A) (B)
(C) (D)
(A) (B) (C) (D) None of these

(A) (B) (C) (D)
lim x→0
(1 − cos 2x)2
lim x→0
(1 − cos 2x)2
xsec2
xsec2
2
π 4
π 3
π 6
π 4
π 3
π 6
LTS-28/36 0999DJA110321008
SECTION-I (ii) : (Maximum Marks: 24)
-I (ii) : ( : 24)
: +4 () () : +3 : +2 : +1 : 0 ( ) : –2
(06) () () , () () :
: , ; +4 ( ) ( ) +2 ( ), ( ) +1 ( ), –2 , ()
0999DJA110321008 LTS-29/36
7. If α and β are two distinct roots of the equation x + px + q = 0 and α , β are the roots of x – rx + s = 0, then equation x – 4qx + 2q – r = 0 has always (p, q, r, s are real numbers)
(A) two real roots (B) two positive roots
(C) two negative roots (D) one positive & one negative root
α β x + px + q = 0 , α , β x – rx + s = 0 , x – 4qx + 2q – r = 0 (p, q, r, s ) -
(A) (B)
(C) (D)
8. In a ΔABC if 2sinAcosC = sinB then which of the following is/are true
(A)
(B) a + c = ac
(C) length of median through vertices A and C are equal
(D) incentre, orthocentre, centroid and circumcentre are collinear
ABC 2sinAcosC = sinB , /
(A)
(B) a + c = ac
(C) A C
(D) , ,
2 4 4 2
LTS-30/36 0999DJA110321008
9. A circle S passes through the point (0, 1) and is orthogonal to circle (x – 1) + y = 16 and x + y = 1. Then :
(A) Radius of S is 8 (B) Radius of S is 7
(C) Centre of S is (–7, 1) (D) Centre of S is (–8, 1)
S (0, 1) (x – 1) + y = 16 x + y = 1 ,
(A) S 8 (B) S 7
(C) S (–7, 1) (D) S (–8, 1)
10. The given lines 2x + my = 1, mx + 2y = 4, 3x + 2y = 1 do not form a triangle if m is equal to
2x + my = 1, mx + 2y = 4, 3x + 2y = 1 m
(A) 3 (B) 2 (C) –2 (D) 1
11. The value of x satisfying , can be
x
(A) 0 (B) 1 (C) –2 (D) –12
2 2 2 2
2 2 2 2

12. Consider a function y = ƒ(x) defined implicitly as 2 + 2 = 2, then identify the correct statement(s) :-
(A) Domain of ƒ(x) is
(B) Domain of ƒ(x) is
(C) ƒ(0) = 0
(D) Explicit form of the function is
y = ƒ(x) 2 + 2 = 2, , / :-
(A) Domain of ƒ(x) is
(B) Domain of ƒ(x) is
(C) ƒ(0) = 0
x+y y–x
LTS-32/36 0999DJA110321008
-II : ( : 24)
1. Let f is a real valued bijective function defined from R to R such that f(x) + f(–x) = 5 ∀ x ∈ R, then the
value of is equal to
f R R f(x) + f(–x) = 5 ∀ x ∈ R ,

2. , where k is
, k
(06) (NUMERICAL VALUE) ( , /; 6.25, 7.00, –0.33, –.30, 30.27, –127.30, 11.36777..... , 11.36 11.37 )
(t) dt∫ 1−x
0999DJA110321008 LTS-33/36
3. Number of points where ƒ(x) = |(2 – 1).(3 – 3)x.(x – 1).(x – 2)| is not differentiable
, ƒ(x) = |(2 – 1).(3 – 3)x.(x – 1).(x – 2)| ,
4. The number of point of discontinuity of function f(x) = [sinx], x ∈ [0, 2π]
f(x) = [sinx], x ∈ [0, 2π] :
5. The number of solutions of the equation log (2x + 7x + 5) + log (x + 1) – 4 = 0, x > 0, is
log (2x + 7x + 5) + log (x + 1) – 4 = 0, x > 0
6. If 7(A + A ) = and det(A) = –7, then positive square root of value of determinant of
matrix (A – I ) is
7(A + A ) = det(A) = –7 , (A – I )

LTS-34/36 0999DJA110321008
LTS-35/360999DJA110321008
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