solutions · rest at height h. at time t, the speed of a relative to b is (a) u (b) u – 2 gt (c)...

SOL UTI ON S

WITH

ANSWER KEY

AITS-FT # 03

DROPPER ENGINEERING

(PHYSCIS, CHEMISTRY & MATHS)

TARGET : JEE (MAIN + ADVANCED) 2018-19

Exam. Date : 24-03-2019

AITS-FT # 03 (Engineering Dropper) - 2018-19


Potential & Concept Educations Page. 2

ANSWER KEYS FOR AITS-FT # 03 (TARGET – JEE-MAIN-2019)

DATE : 24-03-2019

ANSWERS [CHEMISTRY]

31. C 32. C 33. D 34. C 35. C 36. B 37. C 38. D 39. B 40. C41. A 42. C 43. D 44. C 45. C 46. C 47. B 48. C 49. A 50. C51. A 52. C 53. C 54. C 55. B 56. C 57. B 58. C 59. A 60. D

ANSWERS [PHYSICS]

1. A 2. B 3. D 4. B 5. B 6. D 7. C 8. C 9. A 10. D

11. A 12. A 13. A 14. D 15. A 16. B 17. D 18. C 19. D 20. C

21. A 22. C 23. A 24. A 25. B 26. D 27. B 28. C 29. C 30. C

ANSWERS [MATHS]

61. B 62. A 63. B 64. B 65. D 66. C 67. A 68. A 69. C 70. A

71. B 72. A 73. B 74. B 75. B 76. B 77. A 78. B 79. A 80. D

81. B 82. B 83. A 84. B 85. C 86. C 87. C 88. D 89. C 90. B



PHYSICS AITS-FT-03Engineering

Dropper Batch

1. A ball A is thrown vertically upwards with speed u. At the same instant another ball B is released fromrest at height h. At time t, the speed of A relative to B is

(A) u (B) u – 2 gt (C) 2u – 2gh (D) u – gt

Solution :

Hence the answer is (A).2. A river is flowing due east with a speed 3ms–1. A swimmer can swim in still water at a speed of 4 ms–1.

If swimmer starts swimming due north, then the resultant velocity of the swimmer is.(A) 3 ms–1 (B) 5 ms–1 (C) 7 ms–1 (D) 2 ms–1

Solution :

Hence the answer is (B).3. A ball of mass m strikes a rigid wall with speed u at an angle of 30º and get reflected with the same speed

and at the same angle as shown in the figure. If the ball is in contact with the wall for time t, then the forceacting on the wall is.

(A) omu sin30

t(B)

o2musin 30t

(C) omu cos30

t(D)

o2mu cos30t



Solution :

Hence the answer is (D).

4. A particle of mass 1 g moving with a velocity –11

ˆ ˆv 3i – 2j ms experiences a perfectly inelastic collision

with another particle of mass 2 g and velocity –12

ˆ ˆv 4 j – 6k ms . The velocity of the particle after collisions

is :-(A) 2.3 m s–1 (B) 4.6 m s–1 (C) 9.2 m s–1 (D) 6 m s–1

Solution :

Hence the answer is (B).



5. A planet moving along an elliptical orbit is closest to the sun at a distance r1 and farthest away at a

distance of r2. If v1 and v2 are the linear velocities at these points respectively, then the ration 1

2

vv

is -

(A) 2

1

2

rr

(B) 2

1

rr (C)

22

1

rr

(D) 1

2

rr

Solution :

Hence the answer is (B).6. A piece of solid weighs 120 g in air, 80 g in water and 60 g in a liquid. The relative density of the solid and

that of the liquid are respectively

(A) 2, 12

(B) 2, 32

(C) 3, 12

(D) 3, 32

Solution :


7. Consider 1ˆ ˆE xi j

and 2 2

2ˆ ˆE xy i x yj

; then :-

(A) only E1 is electrostatic (B) only E2 is electrostatic(C) both are electrostatic (D) none of theseSolution :The answer is (C).

8. Two identical positive charges are fixed on the y-axis at equal distance from the origin O. A negativelycharged particle starts on the x-axis, at a large distance from O, moves along the x-axis, passes throughO and moves far away from O. Its acceleration a is taken as positive along its direction of motion. Thebest graph between the particle's acceleration and its x-co-ordinate is represented by :-

(A) (B) (C) (D)

Solution :The answer is (C).



9. The ratio of the length of four wires is 1 : 2 : 3 : 4. The wires are of the same metal and same radius. If abattery is connected in parallel with them, the ratio of currents in these wires is :-(A) 12 : 6 : 4 : 3 (B) 6 : 3 : 2 : 1 (C) 4 : 3 : 2 : 1 (D) 1 : 2 : 3 : 4Solution :The answer is (A).

10. Two resistances R1 and R2 are made of different materials. The temperature coefficient of the materialof R1 is and of the material of R2 is –. The resistance of the series combination of R1 and R2 will notchange with temperature, if R1/R2 equals :-

(A) (B) –

(C)

2 2 (D)

Solution :The answer is (D).

11. A 20µF capacitor in a defibrillator is charged to 2000 V. The energy stored in the capacitor is sent throughthe patient during a pulse of duration 4ms the power delivered to the pateints is :-(A) 10 kW (B) 20 kW (C) 30 kW (D) 40 kWSolution :The answer is (A).

12. A circular current carrying loop of radius R is bent about its diameter by 90° and placed in a magnetic field

0ˆ ˆB B i j

as shown in figure. The torque on the loop is :-

(A) 0 (B) 2

0B I R ˆ ˆ–i – j2

(C) 2

0B I R ˆ ˆi – k2

(D) 2

0B I R k̂2

Solution :The answer is (A).

13. Box may have any series combination of L, C and R.

Column-I Column-II

(A) (B)

(C) (D)

(T) State of resonance(A) A P, T; B R; C P, S; D P, Q (B) A P, R; B S; C T; D P, Q



(C) A P, S; B R; C T; D P, Q (D) A P, T; B T; C R; D P, QSolution :The answer is (A).

14. A thin wire of length L and uniform linear mass density is bent into a circular loop with centre O asshown. the moment of inertia of the loop about the axis XX' is-

(A) 3

2L

8

(B) 3

2L

16

(C) 3

25 L16

(D) 3

23 L8


15. A cubical block of side ‘a’ moving with velocity v on a horizontal smooth plane as shown. It hits a ridge atpoint O. The angular speed of the block after it hits O is :-

(A) 3v4a

(B) 3v2a

(C) 32a (D) zero

Solution :The answer is (A).

16. Two particles of masses m and M are at infinity and at rest. Both particles move towards each other dueto mutual interaction. When the distance between them is d, the relative velocity of approach will be :–

(A) 1

22GdM m

(B)

122G M m

d

(C) M m2G

d

(D)

2GM m

Solution :The answer is (B).

17. A cone of radius R and height H, is hanging inside a liquid of density by means of a string as shown inthe figure. The force, due to the liquid acting on the slant surface of the cone is (Neglect atmospherepressure)

(A) gHR2 (B) HR2 (C) 43

gHR2 (D) 23

gHR2




18. Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1, T2), volume (V1, V2) andpressure (P1, P2) respectively. If the valve joining the two vessels is opened, the temperature inside thevessel at equilibrium will be :-

(A) T1 + T2 (B) (T1 + T2)/2 (C) 1 2 1 1 2 2

1 1 2 2 2 1

T T (P V P V )P V T P V T

(D) 1 2 1 1 2 2

1 1 1 2 2 2

T T (P V P V )P V T P V T

Solution :The answer is (C).

19. The temperature of the two outer surfaces of a composite slab, consisting of two materials havingcoefficients of thermal conductivity K and 2K and thickness x and 4x respectively are T2 and T1 (T2 >

T1). The rate of heat transfer through the slab, in a steady state is 2 1A(T – T )K fx

, with f equal to :-

(A) 1 (B) 1/2 (C) 2/3 (D) 1/3Solution :The answer is (D).

20. A Carnot engine has efficiency 1/5. Efficiency becomes 1/3 when temperature of sink is decreased by 50K. What is the temperature of sink?(A) 325 K (B) 375 K (C) 300 K (D) 350 KSolution :The answer is (C).

21. A body executes simple harmonic motion under the action of a force F1 with a time period (4/5) sec. If theforce is changed to F2 it executes SHM with time period (3/5) sec. If both the forces F1 and F2 actsimultaneously in the same direction on the body, its time period (in seconds) is :(A) 12/25 (B) 24/25 (C) 35/24 (D) 25/12Solution :

Hence the answer is (A).



22. In the figure, the intensity of waves arriving at D from two coherent sources S1 and S2 is I0. The wavelengthof the wave is = 4m. Resultant intensity at D will be :

(A) 4I0 (B) I0 (C) 2I0 (D) ZeroSolution :

Hence the answer is (C).23. A glass tube 1.5 m long and open at both ends is immersed vertically in a water tank completely. A tuning

fork of 600 HZ is vibrated and kept at the upper end of tube and the tube is gradually raised out of water.The total number of resonances heard before when the tube comes out of water, (taking v = 330m/s) is:(A) 12 (B) 6 (C) 8 (D) 4Solution :The answer is (A).

24. An observer moves towards a stationary source of sound with a speed (1/5)th of the speed of sound. Thewavelength and frequency of the source emitted are and f respectively. The apparent frequency andwavelength recorded by the observer are respectively :(A) 1.2 f and (B) f and 1.2 (C) 0.8 f and 0.8 (D) 1.2 f and 1.2 Solution :




25. In plane convex lens the radius of curvature of convex lens is 10 cm. If the plane side is polished then thefocal length will be (µ = 1.5) :-(A) 20.5 cm (B) 10 cm (C) 15.5 cm (D) 5 cmSolution :

Hence the answer is (B).26. The focal length of the lenses of a telescope are 50 cm & 5 cm the tube of length of telescope when the

image is formed at the least distance of distinct vision is :-

(A) 45 cm (B) 55 cm (C) 275 cm

6(D)

325 cm6

Solution :

Hence the answer is (D).27. Ratio of slit width in Y.D.S.E. is 4 : 9. Then calculate ratio of max to min intensity

(A) 1 : 25 (B) 25 : 1 (C) 36 : 1 (D) 1 : 36Solution :

Hence the answer is (B).28. The energy liberated on complete fission of 1 kg of 92U235 is (Assume 200 MeV energy is liberated on

fission of 1 nucleus) :-(A) 8.2 × 1010 J (B) 8.2 × 109 J (C) 8.2 × 1013 J (D) 8.2 × 1016 JSolution :The answer is (C).

29. For a substance the average life for -emission is 1620 years and for emission is 405 years. After howmuch time the 1/4 of the material remains after and emission :-(A) 1500 years (B) 300 years (C) 449 years (D) 810 yearsSolution :The answer is (C).

30. In the following combinations of logic gates, the outputs of A, B and C are respectively :-

(A) (B)

(C)

(A) 0, 1, 1 (B) 0, 1, 0 (C) 1, 1, 0 (D) 1, 0, 1Solution :The answer is (C).



CHEMISTRY AITS-FT-03Engineering

Dropper Batch

31. The molecule has sp3d2, hybridisation and square planar shape :(A) SF4 (B) 4BF (C) 4ICl (D) XeO2F2

Solution :Hence the answer is (C).

32. The correct statements is / are :(A) IE1 of In > IE1 of Al(B) Out of Na and Al3+, Na has largest size in aqueous solution(C) 2NO and O3 are isoelectronic species(D) The decreasing order of E.A. is F > Cl > Br


33. In a closed pack structure of mixed oxides, the lattice is composed of mixed oxide ions. One eighth oftetrahedral voids are occupied by divalent cations (A+2) while one half of octahedral voids are occupiedby trivalent cations (B+3). The formula of mixed oxide is(A) A2BO3 (B) AB2O3 (C) A2BO4 (D) AB2O4

Solution :Hence the answer is (D).

34. Observe the following reaction :XeF4 + SbF5 [XeF3]+ [SbF6]¯The correct statement(s) regarding the product is / are :(A) XeOF2 and anionic part of the product have same hybridisation(B) 3I

and cationic part of product have same number of lone pair on the central atom

(C) Anionic part of [XeF] + [PF6]¯ is isostructural with the anionic part of product(D) None of these


35. Consider on following moleculesNH3, PH3, AsH3, SbH3Which of the following has the highest boiling point ?(A) NH3 because of hydrogen bonding(B) SbH3 because of hydrogen bonding(C) SbH3 because of higher molecular weight(D) PH3 because of lower molecular weight




36.

B will be :(A) CH3 – COOH (B) CH3 – CH2 – OH (C) CH3 – CHO (D)

Solution :Hence the answer is (B).

37. Potential energy of electron present in He+ is

(A) 2

0

e2 r (B)

2

0

3e4 r (C)

2

0

e2 r (D)

2

20

e4 r

Solution :

Hence the answer is (C).38. Critical constant for a real gas are given as

TC = 180 K ; Vc = 0.123 L/molPC = 45 atm ; R = 0.082 Latm/mol KThe correct statement for the real gas is -

(A) The volume of single gas molecule is 3

23

0.123 10 cc6.023 10

(B) b = 3 × 0.123L mol–1

(C) The Boyle’s temperature is less than 180K(D) Gas cannot be liquified at 200K

Solution :

Hence the answer is (D).39. Which of the following will coagulate starch sol :-

(A) NaCl (B) C2H5OH (C) BaCl2 (D) CaSO4




40. For the the reactionI– + 3ClO + H2SO4 Cl– + 4HSO + I2(no free H+ is present).Select the correct statement in the balanced equation (Coefficients in smallest whole number ratio.)(A) Iodide ion is reduced (B) Sulphur is oxidised(C) Stoichiometric coefficient of 4HSO is 6 (D) Stoichiometric coefficient of H2O is 2

Solution :

Hence the answer is (C).41. Insulin has :-

(A) 51 amino acid (B) 41 amino acid (C) 31 amino acid (D) 101 amino acid

Solution :Hence the answer is (A).

42. Select the correct order of the property indicated against them :(A) Li+(g)<Be2+(g) < Mg2+(g) (Ionisation energy)(B) Li+ < Mg2+ > Al3+ (Polarisation power)(C) [Ma3b3] < [M(AA)2cd] < [M(AB)2cd] (Number of stereo isomers)(D) Mg < Fe < Al (Ascending position of element in Ellingham graph, element nearer to Gº = 0line is kept at last)


43. Identify the major product ?

(A) (B)

(C) (D)

Solution :




44. Which of the following carbohydrate can not reduce tollen's reagent(A) Fructose (B) Maltose (C) Sucrose (D) Lactose

Solution :

Hence the answer is (C).45. Identify the basic amino acid.

(A) Glycine (B) Alanine (C) Arginine (D) Aspartic acid

Solution :

Hence the answer is (C).46. Which of the following compound do not gives isocyanide test.

(A) (B)

(C) CH3–NH–CH2–CH3 (D)

Solution :

Hence the answer is (C).47. Identify the compound which rotate the plane polarised light.

(A) (B) (C) (D) CH2ClF

Solution :

Hence the answer is (B).48. 4.3 gm of an alkane is burnt in sufficient oxygen. The CO2 formed reacts completely with 300 ml, 2N

NaOH solution producing Na2CO3. The alkane should be(A) C3H8 (B) C12H26 (C) C6H14 (D) C2H6

Solution :

Hence the answer is (C).



49. Z vs P graph of four gases is given below at same temperature

Which of the gases will have the highest value of critical temperature.(A) D (B) C (C) B (D) A


50. What is the pH of solution obtained by mixing 5.076 gm of methyl ammonium nitrate (CH3NH3NO3) to120 ml, 0.225 M methylamine (CH3NH2 ; Kb = 4 × 10–4).(A) 3.7 (B) 4.3 (C) 10.3 (D) 11

Solution :

Hence the answer is (C).51. Which of the following planar complex is diamagnetic and show stereo isomerism :

(A) [Ni(gly)2] (B) [Pt(NH3)3Cl]+ (C) [Co(H2O)3Cl3] (D) [Co(en)3]3+


52. Which of following does not represent correct major product.

(A) (B)

(C) (D)


53. Which of the following can be used to differentiate pentan-2-one & pentan-3-one(A) Iodoform test (B) NaHSO3 (C) Both (A) & (B) (D) Tollen's reagent




54. In the absorption of a gas solid, Freundlich isotherm is obeyed. The slope of the plot is zero. Thus theextent of adsorption is :-(A) directly proportional to the pressure of the gas(B) inversely proportional to the pressure of thegas(C) independent of the pressure of the gas(D) proportional to the square of the pressure of the gas


55. Enthalpy of dilution of 4M HCl to 2M HCl is –2.5 kJ/mol. Find enthalpy change when 500 ml of HCl isdiluted from 4M to 2M(A) –2.5 kJ/mol (B) –5 kJ/mol (C) –10 kJ/mol (D) –1.25 kJ/mol

Solution :

Hence the answer is (B).56. Total number of compounds / ions which have atleast two bond lengths same out of

2 23 2 3 2CO ,HCOOH,S O , NO Θ

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


57. A metal (M) which exists in oxide form and its oxide is not possible to reduce by carbon up to 800ºC butit is possible to reduce by Al even below 800ºC. Select correct Ellingham diagram for metal (M)

(A) (B) (C) (D)


58. Which of the following hydride is 'electron- precise' type ?(A) HF (B) H2O (C) SiH4 (D) PH3Solution :Hence the answer is (C).



59. How are the following compounds related

(A) Diastereomers (B) Enantiomers(C) Meso compounds (D) Identical


60. The dissociation of SO3(g) into SO2(g) & O2(g) is carried out in a closed container at a constant temperatureT. The equilibrium constant for the reaction is KP = x atm2. The partial pressure variation for the threegases is as shown

The value of x is

(A) 3

2

32

3

2(B) 22 (C) 1 (D)

6

6

32

Solution :Hence the answer is (D).



61. If a, b and c are unit vectors, then|a – b|2 + |b – c|2 + |c – a|2 does not exceed.(A) 6 (B) 9 (C) 5 (D) 2Solution :


62.2x

f (x) (–1) , g(x) = |sin x| – |cos x| and (x) = f(x) · g(x) (where, [.] denote the greatest integer

function), then the respective fundamental period of f(x), g(x) and (x) are(A) , , /2 (B) , 2, /2 (C) /2, /2, /2 (D) None of theseSolution :


MATHS AITS-FT-03Engineering

Dropper Batch



63. The only statement among the following that is a tautology is

(A) p (p q) (B) [p (p q)] q (C) p (p q) (D) q [p (q q)]Solution :


64. If n 3 3 5 3 5 7(1 x) 1 ...4 4 8 4 8 12

, then the set of values of x and n are respectively

(A) 1 –1,2 2

(B) –1 –3,2 2

(C) 1 3,2 2

(D) None of these

Solution :




65. Suppose f is such that f(–1) = –f(x) for every real x and 1

0f (x)dx 5 , then

0

–1f (t)dt is equal to

(A) – 4 (B) – 2 (C) – 6 (D) – 5Solution :

Hence the answer is (D).66. An closed cylindrical can has to be made with 100 m2 of copper. If its volume is maximum, then ratio of

its base radius and height is(A) 3 : 2 (B) 2 : 3 (C) 1 : 2 (D) 2 : 1Solution :

Hence the answer is (C).67. The value of

nx1/ x 1/ x 1/ x 1/ x

x

1 2 3 ... nlimn

is

(A) n! (B) n (C) (n – 1)! (D) 0Solution :




68. The equation of tangent parallel to y = x drawn to 2 2x y– 1

3 2 is

(A) y = x ± 1 (B) y = x ± 2 (C) y + 3x = 2 (D) None of theseSolution :


69. If A + B + C = , ei = cos + i sin and

2iA –iC –iB

iC 2iB –iA

–iB –iA 2iC

e e e

z e e e

e e e

, then

(A) Re (z) = 4 (B) lm (z) = 1 (C) Re (z) = –4 (D) lm (z) = –1Solution :



Hence the answer is (C).70. At the foot of the mountain, the elevation of its summit is 45o, after ascending 1000 m towards the

mountain up a slope of 30o inclination, the elevation is found to be 60o. The height of the mountain is

(A) 3 1 m2 (B) 3 – 1 m

2(C)

3 1 m2 3

(D) None of these

Solution :

Hence the answer is (A).71. If both roots of x2 – (p – 4)x + 2e2 log p – 4 = 0 are negative, then p belongs to

(A) (– 2, 4) (B) ( 2, 4) (C) (4, ) (D) None of these

Solution :



Hence the answer is (B).72. Two sides of triangle are the lines

(a + b)x + (a – b)y – 2ab = 0 and(a – b)x + (a + b)y – 2ab = 0. If the triangle is isosceles and the third side passes through point (b – a, a– b), then the equation of third side can be(A) x + y = 0 (B) x – b + a = 0 (C) y – a + b = 0 (D) None of the aboveSolution :

Hence the answer is (A).73. A die is rolled three times, the prohability of getting a large number than the previous number is

(A) 1

54(B)

554

(C) 5

108(D)

13108

Solution :




74. 2 2 n nn

1 1 1lim tan tan tan ... tan2 2 2 2 2 2

(A) 1

(B) 1 – 2cot 2

(C) 2 cot 2 (D) None of the above

Solution :




75. Let f(x) = max. {|x2 – 2|x||, |x|} andg(x) = min.{|x2 – 2|x||, |x|}, then :(A) both f(x) and g(x) are non-differentiable at 5 points.(B) f(x) is not differentiable at 5 points whether g(x) is non-differentiable at 7 points.(C) number of points of non-differentiability for f(x) and g(x) are 7 and 5 respectively.(D) both f(x) and g(x) are non-differentiable at 3 and 5 points respectively.Solution :

Hence the answer is (B).76. If A(1, 4) and B(3, 0), the maximum area of triangle ABC inscribed in the ellipse 2x2 + y2 = 18 is

(A) 6 6 (B) 3 6 6 (C) 6 3 (D) 2 5Solution :


77. The solution of dy 2y cos xdx

is

(A) 2x

2x ey e [2cos x sin x] C5

(B) 2x

2x ey e [2cos x – sin x] C5

(C) y·e2x = e2x (sin x + cos x) (D) None of the aboveSolution :




78. The hyperbola 2 2

2 2x y– 1a b

, the area of the triangle formed by the asymptotes and the tangent drawn toit at (a, 0) is

(A) 3ab (B) ab (C) 2ab (D) 1 ab3

Solution :

Hence the answer is (B).79. The number of ordered triplet of positive integers which satisfy the inequality 20 x + y + z 50 is

(A) 50C3 – 19C3 (B) 50C2 – 19C2 (C) 51C3 – 20C3 (D) None of theseSolution :




80. Evaluate –1 1cos dxx

.

(A) 2elog [x (x –1)] C (B) –1 1x cos C

x

(C) 2elog [x – (x –1)] C (D)

–1 2e

1x cos – log [x (x –1)] Cx

Solution :

Hence the answer is (D).81. If A, B and C are angles of a triangle and

2 2 2

1 1 11 sin A 1 sin B 1 sin C 0

sin A sin A sin B sin B sin C sin C

, then the triangle is a/an

(A) equilateral (B) isosceles (C) right-angled triangle (D) any triangleSolution :




82. Chords of the curve 4x2 + y2 – x + 4y = 0, which subtend a right angle at the origin pass through a fixedpoint whose coordinates are

(A) –1 4,5 5

(B) 1 –4,5 5

(C) 1 4,5 5

(D) –1 –4,5 5

Solution :


83. If |z1| = |z2| and arg 1

2

zz

, then z1 + z2 is equal to

(A) 0 (B) purely imaginary (C) purely real (D) None of the aboveSolution :




84. Let f(x) be a function satisfying

1fxx f (x) 0

x

then value of

sec

cosf (x)dx

is :

(A) dependent on (B) 0 (C) 1 (D) –1Solution :

Hence the answer is (B).85. The area of the figure bounded by the parabola (y – 2)2 = x – 1 and tangent to it at the point with the

ordinate 3 and the x-axis is

(A) 3 (B) 6 (C) 9 (D) None of the aboveSolution :




86. The geometric mean of 3, 32, ..., 3m is

(A) 3m + 1 (B) 3m(m + 1)/2 (C) m 1

23

(D) None of the aboveSolution :

Hence the answer is (C).87. Coefficient of x11 in the expansion of (1 + x2)4(1 + x3)7(1 + x4)12 is :

(A) 1051 (B) 1106 (C) 1113 (D) 1120Solution :


88. If e ie the eccentricity of 2 2

2 2x y– 1a b

and be the angle between the asymptotes, then sec/2 is equal to

(A) 3e2 (B) 2/e (C) 3e (D) eSolution :




89. Statement-I : The value of the determinant

5 4 3x 51 y41 z31

x y z is zero. Let x, y and z are three integers

lying beween 1 and 9 such that x 51, y 41 and z 31 are three digit numbers.

Statement-II : The value of a determinant is zero, if the entries in any two rows (or columns) of thedeterminant are correspondingly proportional.(A) Both Statement-I and Statement-II are true and the Statement-II is the correct explanation of theStatement-I.(B) Both Statement-I and Statement-II are true but the Statement-II is not the correct explanation of theStatement-I.(C) Statement-I is false but Statement-II is true.(D) Statement-I is true but Statement-II is false.Solution :

Hence the answer is (C).90. The line which contains all points (x, y, z) which are of the form (x, y, z) = (1, –1, 1) + (1, –2, –3) intersects the

plane x – y + 4z + 3 = 0 at P and intersects the yz-plane at Q. Find the distance PQ.

(A) 14 (B) 2 14

(C) 3 14 (D) None of theseSolution :


solutions · rest at height h. at time t, the speed of a relative to b is (a) u (b) u – 2 gt (c)...

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