Joint Entrance Exam | Mains-2019100p.s3.amazonaws.com/vidyamandir/JEEMAIN2019JAN/09-Jan-Evening.pdfIn a communication system operating at wavelength 800 nm, only one percent of source

Vidyamandir Classes

VMC | JEE Mains-2019 1 9th JAN-Evening Paper | JEE Entrance Examination

Joint Entrance Exam | Mains-2019 9th JAN-Evening Paper | 2019 | 03.00 PM – 06.00 PM

PHYSICS, CHMISTRY & MATHEMATICS

Important Instructions: 1. Immediately fill in the particulars on this page of the Test Booklet with only Black Ball Point Pen

provided in the examination hall.

2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the Answer Sheet and fill in the particulars carefully.

3. The test is of 3 hours duration.

4. The Test Booklet consists of 90 questions. The maximum marks are 360.

5. There are three parts in the question paper A, B, C consisting of Physics, Chemistry & Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response.

6. Candidate will be awarded marks as stated above in instruction No. 5 for correct response of each

question. 14 (one-fourth) marks of the total marks allotted to the questions (i.e. 1 mark) will be

deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet.

7. There is only one correct response for each question. Filling up more than one response in any question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above.

8. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. except the Admit Card inside the examination room/hall.

9. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.

10. Do not fold or make any stray mark on the Answer Sheet.

Vidyamandir Classes


PART-A PHYSICS

1. In the given circuit the internal resistance of the 18 V cell is negligible.

If 1 3400 , 100R R and 4 500R and the reading of an ideal

voltmeter across 4R is 5 V, then the value of 2R will be :

(1) 230 (2) 450

(3) 300 (4) 550

2. A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs

towards the musician from another end of a hall at a speed of 10 km/h. If the wave speed is 330 m/s, the

frequency heard by the running person shall be close to :

(1) 333 Hz (2) 753 Hz (3) 500 Hz (4) 666 Hz

3. The position co-ordinates of a particle moving in a 3-D coordinate system is given by

cosx a t

siny a t

and z a t

The speed of the particle is :

(1) 2a (2) 2a (3) a (4) 3a

4. A force acts on a 2 kg object so that its position is given as a function of time as 23 5.x t What is the work done by this force in first 5 seconds ?

(1) 950 J (2) 900 J (3) 875 J (4) 850 J

5. The energy associated with electric field is ( )EU and with magnetic field is ( )BU for an electromagnetic wave in free space. Then:

(1) E BU U (2) E BU U (3) 2

BE

UU (4) E BU U

6. The magnetic field associated with a light wave is given, at the origin, by

7 70[sin(3.14 10 ) sin(6.28 10 ) ]. B B ct ct If this light falls on a silver plate having a work function of

4.7 eV, what will be the maximum kinetic energy of the photo electrons?

8 1 34( 3 10 , 6.6 10 - ) c ms h J s

(1) 12.5 eV (2) 8.52 eV (3) 7.72 eV (4) 6.82 eV

7. Two Carnot engines A and B are operated in series. The first one, A, receives heat at 1( 600 )T K and

rejects to a reservoir at temperature 2.T The second engine and, in turn, rejects to a heat reservoir at

3( 400 ).T K Calculate the temperature 2T if the work outputs of the two engines are equal :

(1) 600 K (2) 300 K (3) 500 K (4) 400 K

Vidyamandir Classes


8. A rod of length 50 cm is pivoted at one end. It is raised such that if

makes an angle of 30° from the horizontal as shown and released from

rest. Its angular speed when it passes through the horizontal

(in rad 1)s will be 2( 10 ms )g

(1) 302

(2) 30 (3) 302

(4) 203

9. A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about 0.x When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be :

(1) 2

A (2) 2 2

A (3) A (4) 2A

10. A series AC circuit containing an inductor (20 mH), a capacitor (120 )F and a resistor (60 ) is given by an AC source of 24 V/50 Hz. The energy dissipated in the circuit in 60 s is :

(1) 33.39 10 J (2) 32.26 10 J (3) 25.65 10 J (4) 25.17 10 J

11. In a communication system operating at wavelength 800 nm, only one percent of source frequency is available as signal bandwidth. The number of channels accommodated for transmitting TV signals of

band width 6 MHz are (Take velocity of light 8 343 10 / , 6.6 10 J-s) c m s h

(1) 56.25 10 (2) 54.87 10 (3) 63.75 10 (4) 63.86 10

12. A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5A and its efficiency is 90%, the output current would be :

(1) 35 A (2) 45 A (3) 25 A (4) 50 A

13. At a given instant, say 0,t two radioactive substances A and B have equal activities. The ratio B

A

RR

of

their activities after time t itself decays with time t as 3 . te If the half-life of A is 2,ln the half-life of B is:

(1) 4 2ln (2) 2 2ln (3) 22

ln (4) 24

ln

14. Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to :

(1) 3c

Gh (2)

5hcG

(3) 5Ghc

(4) 3Ghc

15. Ge and Si diodes starts conducting at 0.3 V and 0.7 V respectively. In the following figure if Ge diode connection are reversed, the value of 0V changes by : (assume that the Ge diode has large breakdown voltage) : (1) 0.8 V (2) 0.6 V (3) 0.4 V (4) 0.2 V

Vidyamandir Classes


16. A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5T. If an electric field of 100 V/m makes it to move in a straight path,

then the mass of the particle is (Given charge of electron 191.6 10 ) C :

(1) 319.1 10 kg (2) 242.0 10 kg (3) 271.6 10 kg (4) 191.6 10 kg

17. Charge is distributed within a sphere of radius R with a volume charge density 2 /2( ) , r aAr e

r where A

and a are constants. If Q is the total charge of this charge distribution, the radius R is :

(1) log 12 2

a Q

aA (2) 1log

2 12

aQaA

(3) log 12

QaaA

(4) 1log1

2

a QaA

18. The energy required to take a satellite to a height ‘h’ above Earth surface (radius of Earth 36.4 10 km) is 1E and kinetic energy required for the satellite to be in a circular orbit at this height is

2.E The value of h for which 1E and 2E are equal, is:

(1) 36.4 10 km (2) 31.6 10 km (3) 41.28 10 km (4) 33.2 10 km

19. The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100

respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies

3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are

5.5 mm and 48 respectively, the thickness of this sheet is :

(1) 5.725 mm (2) 5.755 mm (3) 5.950 mm (4) 5.740 mm

20. Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror 1( )M and

parallel to the second mirror 2( )M is finally reflected from the second mirror 2( )M parallel to the first

mirror 1( ).M The angle between the two mirrors will be :

(1) 75° (2) 60° (3) 90° (4) 45°

21. A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27°C. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take 8.3J/K mole]R

(1) 10 kJ (2) 6 kJ (3) 0.9 kJ (4) 14 kJ

22. Two point charges 1( 10 )q C and 2 ( 25 ) q C are placed on the x-axis at 1x m and 4x m respectively. The electric field (in (V/m) at a point 3y m on y-axis is,

9 2 2

0

1take 9 10 Nm4

C

(1) 2ˆ ˆ(63 27 ) 10 i j (2) 2ˆ ˆ( 81 27 ) 10 i j

(3) 2ˆ ˆ( 63 27 ) 10 i j (4) 2ˆ ˆ(81 81 ) 10 i j

Vidyamandir Classes


23. In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed ‘v’ more than that of car B. Both the cars start from rest and travel with constant acceleration 1a and 2a respectively. Then ‘v’ is equal to :

(1) 1 22a a t (2) 1 2

1 2

2a a t

a a (3) 1 22a a t (4) 1 2a a t

24. A rod of mass ‘M’ and length ‘2L’ is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of ‘m’ are attached at distance ‘L/2’ from its centre on both sides, it reduces the oscillation frequency by 20%. The value of ratio m/M is close to :

(1) 0.57 (2) 0.37 (3) 0.77 (4) 0.17

25. One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the ratio of the magnetic

field at the central of the loop ( )LB to that at the centre of the coil ( ),CB i.e. L

C

BB

will be :

(1) N (2) 1N

(3) 21

N (4) 2N

26. A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants

1 2 3 4, , ,K K K K arranged as shown in the figure. The effective dielectric constant K will be :

(1) 1 2 3 4

1 2 3 4

( )( )2( )

K K K KKK K K K

(2) 1 4 2 3

1 2 3 4

( )( )2( )

K K K KKK K K K

(3) 1 2 3 4

1 2 3 4

( )( )

K K K KKK K K K

(4) 1 3 2 4

1 2 3 4

( )( )

K K K KKK K K K

27. A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle 45° at the roof point. If the suspended mass is at

equilibrium, the magnitude of the force applied is 2( 10 ms )g :

(1) 70 N (2) 140 N (3) 100 N (4) 200 N

28. A carbon resistance has a following colour code. What is the value of the resistance ?

(1) 6.4M 5% (2) 5.3M 5% (3) 530k 5% (4) 64M 10%

29. The top of a water tank is open to air and its water level is maintained. It is giving out 30.74 m water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to :

(1) 9.6 m (2) 4.8 m (3) 6.0 m (4) 2.9 m

30. In a Young’s s double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength 500 nm is incident on the slits. The total number of bright fringes that are observed in the angular

range 30 30 is : (1) 640 (2) 321 (3) 641 (4) 320

Vidyamandir Classes


PART-C CHEMISTRY 1. A solution containing 62g ethylene glycol in 250g water is cooled to 10 C. If fK for water is

11.86K kg mol , the amount of water (in g) separated as ice is :

(1) 64 (2) 32 (3) 16 (4) 48

2. In which of the following processes, the bond order has increased and paramagnetic character has changed to diamagnetic ?

(1) NO NO (2) 2 2N N (3) 22 2O O (4) 2 2O O

3. The pH of rain water, is approximately : (1) 7.0 (2) 6.5 (3) 5.6 (4) 7.5

4. The correct statement regarding the given Ellingham diagram is :

(1) Coke cannot be used for the extraction of Cu from 2Cu O

(2) At 1400°C, Al can be used for the extraction of Zn from ZnO (3) At 500°C, coke can be used for the extraction of Zn from ZnO (4) At 800°C, Cu can be used for the extraction of Zn from ZnO

6. The major product obtained in the following reaction is :

(1) (2)

(3) (4)

Vidyamandir Classes


7. Good reducing nature of 3 2H PO is attributed to the presence of :

(1) Two P OH bonds (2) One P H bond (3) One P OH bond (4) Two P H bonds

8. The correct sequence of amino acids present in the tripeptide given below is :

(1) Leu - Ser - Thr (2) Val - Ser - Thr (3) Thr - Ser - Val (4) Thr - Ser - Leu

9. The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapour at 383 K is :

(Specific heat of water liquid and water vapour are 1 14.2 kJ K kg and 1 12.0 kJ K kg ; heat of liquid

fusion and vapourisation of water are 1334 kJ kg and 12491 kJ kg , respectively). (log 273 = 2.436, log 373 = 2.572, log 383 = 2.583)

(1) 1 19.26 kJ kg K (2) 1 12.64 kJ kg K

(3) 1 17.90 kJ kg K (4) 1 18.49 kJ kg K

10. Consider the following reversible chemical reactions :

1K2 2A (g) B (g) 2AB(g) ........(1)

2K2 26AB(g) 3A (g) 3B (g) ........ (2)

The relation between 1 2K and K is :

(1) 32 1K K (2) 1 2

1K K3

(3) 1 2K K 3 (4) 32 1K K

11. The major product formed in the following reaction is :

(1) (2)

(3) (4)

12. When the first electron gain enthalpy eg( H) of oxygen is 141kJ / mol, its second electron enthalpy is :

(1) almost the same as that of the first (2) a more negative value than the first

(3) negative, but less negative than the first (4) a positive value

Vidyamandir Classes


13. The correct match between Item-I and Item-II is :

Item-I Item-II

(A) Benzaldehyde (P) Mobile phase

(B) Alumina (Q) Adsorbent

(C) Acetonitrile (R) Adsorbate

(1) (A) (Q) ; (B) (P) ; (C) (R) (2) (A) (Q) ; (B) (R) ; (C) (P)

(3) (A) (R) ; (B) (Q) ; (C) (P) (4) (A) (P) ; (B) (R) ; (C) (Q)

14. The major product of the following reaction is :

(1) (2) (3) (4)

15. The products formed in the reaction of cumene with 2O followed by reactant with dil. HCl are :

(1) (2)

(3) (4)

16. The major product of the following reaction is :

(1) (2) (3) (4)

Vidyamandir Classes


17. The tests performed on compound X and their inference are :

Test Inference

(a) 2, 4-DNP test Coloured precipitate

(b) Iodoform test Yellow precipitate

(c) Azo-dye test No dye formation

Compound 'X' is :

(1) (2) (3) (4)

18. The increasing basicity order of the following compounds is :

(A) 3 2 2CH CH CH (B)

2 3

3 2

CH CH|

CH CH NH

(C)

3

3 3

CH|

H C N CH (D)

3CH|

Ph N H

(1) (A) < (B) < (D) < (C) (2) (A) < (B) < (C) < (D) (3) (D) < (C) < (A) < (B) (4) (D) < (C) < (B) < (A)

19. For the following reaction, the mass of water produced from 445 g of 57 110 6C H O is :

57 110 6 2 2 22C H O (s) 163O (g) 114CO (g) 110H O( )

(1) 445 g (2) 495 g (3) 890 g (4) 490 g

20. Which of the following compounds is not aromatic ?

(1) (2) (3) (4)

21. The temporary hardness of water is due to : (1) NaCl (2) 3 2Ca(HCO ) (3) 2 4Na SO (4) 2CaCl

22. Which of the following combination of statements is true regarding the interpretation of the atomic orbital ? (a) An electron in an orbital of high angular momentum stays away from the nucleus than an

electron on the orbital of lower angular momentum. (b) For a given value of the principal quantum number, the size of the orbit is universally

proportional to the azimuthal quantum number.

(c) According to wave mechanics, the ground state angular momentum is equal to h .2

(d) The plot of vs r for various azimuthal quantum numbers, shows peak shifting towards higher r value.

(1) (a), (b) (2) (b), (c) (3) (a), (d) (4) (a), (c)

Vidyamandir Classes


23. The transition element that has lowest enthalpy of atomisation, is : (1) V (2) Fe (3) Zn (4) Cu

24. For coagulation of arsenious sulphide sol, which of the following salt solution will be most effective ? (1) 3 4Na PO (2) NaCl (3) 2BaCl (4) 3AlCl

25. The metal that forms nitride by reacting directly with 2N of air, is :

(1) Cs (2) K (3) Rb (4) Li

26. Homoleptic octahedral complexes of a metal ion 3'M ' with three monodentate ligands 1 2 3L , L and L absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is :

(1) 1 2 3L L L (2) 3 2 1L L L (3) 3 1 2L L L (4) 2 1 3L L L

27. If the standard electrode potential for a cell is 2V at 300 K, the equilibrium constant (K) for the reaction 2 2Zn(s) Cu (aq) Zn (aq) Cu (s) at 300 K is approximately :

1 1 1(R 8 JK mol , F 96000C mol )

(1) 160e (2) 320e (3) 160e (4) 80e

28. Which of the following conditions in drinking water causes methemoglobinemia ? (1) > 100 ppm of sulphate (2) > 50 ppm of lead (3) > 50 ppm of chloride (4) > 50 ppm of nitrate

29. For the reaction, 2A B products, when the concentrations of A and B both were doubled, the rate of

the reaction increased from 1 10.3mol L s to 1 12.4 mol L s . When the concentration of A alone is

doubled, the rate increased from 1 10.3 mol L s to 1 10.6 mol L s . Which of the following statements is correct ? (1) Order of the reaction with respect to A is 2 (2) Order of the reaction with respect to B is 1 (3) Order of the reaction with respect to B is 2 (4) Total order of the reaction is 4

30. The complex that has highest crystal field splitting energy ( ), is :

(1) 3 5 2 3[Co(NH ) (H O)]Cl (2) 3 6K [Co(CN) ]

(3) 3 5 2[CO(NH ) Cl]Cl (4) 2 4K [CoCl ]

Vidyamandir Classes


PART-B MATHEMATICS

1. If 3 tanx t and 3 sec ,y t then the value of 2

2d ydx

at 4

t , is:

(1) 16

(2) 32 2

(3) 16 2

(4) 13 2

2. The number of all possible positive integral values of for which the roots of the quadratic equation, 26 11 0x x are rational numbers is:

(1) 3 (2) 2 (3) 4 (4) 5

3. For each x R , let [x] be the greatest integer less than or equal to x. Then 0

([ ] | |) sin [ ]lim| |x

x x x xx

is

equal to: (1) sin 1 (2) 0 (3) 1 (4) – sin 1

4. If

cos sin

cos sin sin

2 sin 2 cos

t t t

t t t t t t

t t t

e e t e t

A e e t e t e t e e cos t

e e t e t

then A is:

(1) Invertible for all t R (2) Invertible only if 2

t

(3) Not invertible for any t R (4) Invertible only if t

5. The area of the region {( , ) : 0 | | 1A x y y x x and 1 1}x in square units is:

(1) 2 (2) 13

(3) 43

(4) 23

6. The coefficient of 4t in the expansion of 361

1tt

is:

(1) 10 (2) 14 (3) 15 (4) 12

7. If 3

0

tan 11 , ( 0)2 sec 2

d kk

, then the value of k is:

(1) 1 (2) 12

(3) 2 (4) 4

8. If 02

x , then the number of values of x for which sin sin 2 sin 3 0x x x , is:

(1) 4 (2) 3 (3) 1 (4) 2

9. Let a, b and c be the 7th, 11th and 13th terms respectively of a non-constant A.P. If these are also the three

consecutive terms of a G.P., then ac

is equal to:

(1) 713

(2) 12

(3) 4 (4) 2

10. Let (4, 4)A and (9, 6)B be points on the parabola, 2 4y x . Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of ACB is maximum. Then, the area (in square units) of ACB , is:

(1) 3314

(2) 1302

(3) 32 (4) 1314

Vidyamandir Classes


11. If the circles 2 2 216 20 164x y x y r and 2 2( 4) ( 7) 36x y intersect at two distinct points, then:

(1) r = 11 (2) 1 11r (3) 11r (4) 0 1r

12. If

8 6

22 7

5 7( ) , 01 2

x xf x dx xx x

, and (0) 0f , then the value of f(1) is:

(1) 14

(2) 12

(3) 14

(4) 12

13. Let 0z be a root of the quadratic equation, 2 1 0x x . If 81 930 03 6 3z iz iz , then arg z is equal to:

(1) 4 (2)

6 (3) 0 (4)

3

14. Let { :A x R x is not a positive integer}. Define a function :f A R as 2( )1

xf xx

, then f is:

(1) Injective but not surjective (2) Surjective but not injective (3) Neither injective nor surjective (4) Not injective

15. The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits allowed) is equal to:

(1) 372 (2) 374 (3) 250 (4) 375

16. Let 1 22 , 2a i j k b b i b j k

and 5 2c i j k be three vectors such that the projection

vector of on isb a a

. If a b

is perpendicular to ,c

then | |b

is equal to:

(1) 4 (2) 22 (3) 32 (4) 6

17. If the lines , x ay b z cy d and ' ', ' 'x a z b y c z d are perpendicular, then: (1) ' ' 0cc a a (2) ' ' 1 0bb cc (3) ' ' 1 0ab bc (4) ' ' 0aa c c

18. Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinates axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is:

(1) 32 (2) 9 (3) 18 (4) 36

19. If 1sin (sin 10)x and 1cos (cos10),y then y x is equal to:

(1) 10 (2) (3) 7 (4) 0

20. Let f: [0, 1] R be such that ( ) ( ) ( ),f xy f x f y for all , [0,1]x y , and (0) 0f . If

( )y y x satisfies the differential equation ( )dy f xdx

with (0) 1y , then 1 34 4

y y

is equal to:

(1) 5 (2) 4 (3) 2 (4) 3

21. The sum of the following series 2 2 2 2 2 2 29(1 2 3 ) 12(1 2 3 4 )1 6

7 9

2 2 215(1 2 ... 5 ) ...

11

up to 15 terms, is:

(1) 7820 (2) 7830 (3) 7520 (4) 7510

Vidyamandir Classes


22. A data consists of n observations:

1 2, , ..., nx x x . If 21

1 9n

ii

x n

and 2

11 5

n

ii

x n

, then the standard derivation of this data is:

(1) 5 (2) 2 (3) 7 (4) 5

23. Let f be a differential function from R to R such that 3

2( ) ( ) 2f x f y x y , for all ,x y R .

If (0) 1f , then 1

2

0

( )f x dx is equal to:

(1) 0 (2) 2 (3) 12

(4) 1

24. The equation of the plane containing the straight line 2 3 4x y z and perpendicular to the plane containing

the straight lines 3 4 2

x y z and 4 2 3x y z is:

(1) 2 0x y z (2) 5 2 4 0x y z

(3) 2 2 0x y z (4) 3 2 3 0x y z

25. A hyperbola has its centre at the origin passes through the point (4, 2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is:

(1) 2 (2) 3 (3) 23

(4) 32

26. If both the roots of the quadratic equation 2 4 0x mx are real and distinct and they lie in the interval [1, 5], then m lies in the interval:

(1) ( 5, 4) (2) (3, 4) (3) (5, 6) (4) (4, 5)

27. The logical statements [~ (~ ) ( )] (~ )p q p r q r is equivalent to:

(1) ( ) ~p r q (2) ( ~ )p q r (3) (~ ~ )p q r (4) ~ p r

28. If the system of linear equations 4 7x y z g 3 5y z h 2 5 9x y z k is consistent, then:

(1) 2 0g h k (2) 0g h k

(3) 2 0g h k (4) 2 0g h k

29. An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is:

(1) 2649

(2) 3249

(3) 749 (4) 21

49

30. Let the equations of two sides of a triangle be 3 2 6 0x y and 4 5 20 0x y . If the orthocentre of this triangle is at (1, 1), then the equation of its third side is:

(1) 122 26 1675 0y x (2) 26 61 1675 0x y

(3) 26 122 1675 0x y (4) 122 26 1675 0y x

Documents

Joint Entrance Exam | Mains-2019100p.s3.amazonaws.com/vidyamandir/JEEMAIN2019JAN/09-Jan-Evening.pdfIn a communication system operating at wavelength 800 nm, only one percent of source