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JEE Main 2014 Question Paper With Solutions (19th-April-2014)


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JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 1

The velocity of water in a river is 18 km/hr near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The co-efficient of viscosity of water = 10–2 poise.

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 1

F = – nA dv/dx

now stress = F/A = 10–3

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 2

​Four bulbs B1, B2, B3 and B4 of 100 W each are connected to 220 V main as shown in the figure. The reading in an ideal ammeter will be

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 2

Resistance of any bull

Net resistance of the cks

v = i Req
220 × i × 121
i = 1.81 Amp. (total current supplied by the battery)
Current in each branch in i = 1.81/4amp.   = 0.45 amp.
Reading of ammeter = 3 × 0.45 = 1.3575 amp.

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 3

In a Young's double slit experiment, the distance between the two identical slits is 6.1 times larger than the slit width. Then the number of intensity maxima observed within the central maximum of the single slit diffraction pattern is

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 3

d = 6.1 a
width of central maxima

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 4

A body is in simple harmonic motion with time period half second (T = 0.5 s) and amplitude one cm (A = 1 cm). Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude.

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 5

A bullet looses of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 5




O = V2 – 2 ans

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 6

Long range radio transmission is possible when the radiowaves are reflected from the ionosphere.For this to happen the frequency of the radiowaves must be in the range :

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 7

A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is θiC and the Brewster's angle of incidence is θiB, such that sinθiC/sinθiB = η = 1.28. The relative refractive index of the two media is :

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 8

If denote microwaves, X rays, infrared, gamma rays, ultra-violet, radio waves and visible parts of the electromagnetic spectrum by M, X, I, G, U, R and V, the following is the arrangement in ascending order of wavelength :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 8

The desending order of energy for following waves
Ey > Ex > Euv > Evissible > ViR > VMW

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 9

A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If half life of C14 is 5730 years, then age of the wooden piece placed in the museum is approximately :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 9


 

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 10

​A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of 10 ms–1 (see figure). The e.m.f induced at the time the left arm of the frame is at x = 10 cm from the wire is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 10


JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 11


Given : A and B are input terminals.
Logic 1 = > 5 V
Logic 0 = < 1 V
Which logic gate operation, the following circuit does ?

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 12

The gravitational field in a region is given by . The change in the gravitational potential energy of a particle of mass 2 kg when it is taken from the origin to a point (7m, –3 m) is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 12


Energy = 1 × 2 = 2J

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 13

Match List-I (Event) with List-II (Order of the time interval for happening of the event) and select the correct option from the options given below the lists.

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 14

Match List-I (Experiment performed ) with List-II (Phenomena discovered/ associated) and select the correct option from the options given below the lists :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 14

(a) Davisson - germar give experimental verification for wave nature of electron.
(b) Millikna's formed experiment about change of an electron
(c) Rutherford performed gold foil experiment and found the exisitance of nucleus.
(d) Franck - Hertz gives information about quantisation of energy level.

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 15

A heavy box is to be dragged along a rough horizontal floor. To do so, person A pushes it at an angle 30° from the horizontal and requires a minimum force FA, while person B pulls the box at an angle 60° from the horizontal and needs minimum force FB. If the coefficient of friction between the box and the floor is , the ratio is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 15

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 16

A gas is compressed from a volume of 2 m3 to a volume of 1m3 at a constant pressure of 100 N/m2. Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 16

Case1 Fcos30 = (mg + FAsin 30)µ

Case2 FB cos 60 = (mg – f sin 60) µ

Dividing (1) by (2) we get

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 17

A particle is released on a vertical smooth semicircular track from point X so that OX makes angle θ from the vertical (see figure). The normal reaction of the track on the particle vanishes at point Y where OY makes angle φ with the horizontal. Then :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 17





JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 18

In the diagram shown, the difference in the two tubes of the manometer is 5 cm, the cross-section of the tube at A and B is 6 mm2 and 10 mm2 respectively. The rate at which water flows through the tube is (g = 10 ms–2)

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 18




JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 19

Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration 'a' perpendicular to the axis of the cylinder. What is Ffriction at point P ? It is assumed that the cylinder does not slip.

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 19


Ma = f

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 20

A large number of liquid drops each of radius r coalesce to from a single drop of radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given surface tension of liquid T, density r)

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 20


JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 21

The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose permittivity varies linearly from at one plate toat the other. The capacitance of capacitor is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 21


JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 22

A gas molecule of mass M at the surface of the Earth has kinetic energy equivalent to 0°C. If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than radius of the earth, (kB is Boltzmann constant)

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 22


JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 23

​The electric field in a region of space is given by, The flux of this field through a circular surface of radius 0.02 m parallel to the Y-Z plane is nearly

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 23

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 24

A ball of mass 160 g is thrown up at an angle of 60° to the horizontal at a speed of 10 ms–1. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly (g = 10 ms–2)

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 24

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 25


In an experiment for determining the gravitational acceleration g of a place with the help of a simple pendulum, the measured time period square is plotted against the string length of the pendulum in the figure.
Q. What is the value of g at the place?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 25



g = π2 = 9.87

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 26

An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity B, the magnetic field Bs inside the superconductor will be such that :

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 27

The total length of a sonometer wire between fixed ends is 110 cm. Two bridges are placed to divide the length of wire in ratio 6 : 3 : 2. The tension in the wire is 400 N and the mass per unit length is 0.01 kg/m. What is the minimum common frequency with which three parts can vibrate?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 27


JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 28

A black coloured solid sphere of radius R and mass M is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature T0. The initial temperature of the sphere is 3T0. If the specific heat of the material of the sphere varies as  αT3 per unit mass with the temperature T of the sphere, where α is a constant, then the time taken for the sphere to cool down to temperature 2T0 will be (σ is Stefan Boltzmann constant) 

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 28



JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 29

Figure shows a circular area of radius R where a uniform magnetic field is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r)?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 29

B = B0t
r > R



  

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 30

The diameter of the objective lens of microscope makes an angle β at the focus of the microscope. Further, the medium between the object and the lens is an oil of refractive index n. Then the resolving power of the microscope. 

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 31

For an ideal solution of two components A and B, which of the following is true?

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 32

Choose the correct statement with respect to the vapour pressure of a liquid among the following-:

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 32

The reason behind helical structure of DNA is Hydrogen bonding.

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 33

Which of these statements is not true?

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 34

Nickel(Z = 28) combines with a uninegative monodentate ligand to form a dia magnetic complex [NiL4]2–. The hybridisation involved and the number of unpaired electrons present in the complex are respectively :

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 35

Zirconium phosphate [Zr3(PO4)4] dissociates into three zirconium cations of charge +4 and four phosphate anions of charge –3. If molar solubility of zirconium phosphate is denoted by S and its solubility product by Ksp then which of the following relationship between S and Ksp is correct ?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 35

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 36

For the reaction 3A + 2B → C + D the differential rate law can be written as

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 36

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 37

Which one of the following molecules is paramagnetic?

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 38

Ionization energy of gaseous Na atoms is 495.5 kjmol–1. The lowest possible frequency of light that ionizes a sodium atom is (h = 6.626 × 10–34 Js, NA = 6.022 × 1023 mol–1)

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 38


v = 1.24 × 1015 sec–1

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 39

The major product formed when 1,1,1 - trichloro - propane is treated with aqueous potassium hydroxide is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 39

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 40

The final product formed when Methyl amine is treated with NaNO2 and HCI is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 40

CH3–NH2 + HNO2 → CH3–OH
it is third order reaction.

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 41

Which one of the following has largest ionic radius ?

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 42

Which one of the following is an example of thermosetting polymers?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 42

Bakelite becomes find on heating and the process is irreversible

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 43

​Consider the reaction
 
Q. Which of the following statements is correct?

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 44

The correct IUPAC name of the following compound is:
 

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 45

Which one of the following ores is known as Malachite

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 46

For the decomposition of the compound, represented as

the K= 2.9 × l0–5 atm3.
If the reaction is started with 1 mol of the compound, the total pressure at equilibrium would be :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 46


JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 47

The reason for double helical structure of DNA is the operation of :

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 48

Amongst LiCl , RbCl , BeCl2 and MgCl2 the compounds with the greatest and the least ionic character, respectively are:

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 49

Which one of the following compounds will not be soluble in sodium bicarbonate?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 49

Bicarbonates are weak bases can 't react with wenler acid

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 50

Among the following organic acids, the acid present in rancid butter is:

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 51

The total number of octahedral void(s) per atom present in a cubic close packed structure is :-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 51

CCP no. of octrahedral void = 
per atom octrahedral void is 1.

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 52

The observed osmotic pressure for a 0.10 M solution of Fe(NH4)2(SO4)2 at 25°C is 10.8 atm.
The expected and experimental (observed) values of Van't Hoff factor (i) will be respectively : (R= 0.082 L atm k mol–1)

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 52

π = CRTi

i = 4.42 (observed)

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 53

Sulphur dioxide and oxygen were allowed to diffuse through a porous partition. 20 dm3 of SO2 diffuses through the porous partition in 60 seconds. The volume of O2 in dm3 which diffuses under the similar condition in 30 seconds will be (atomic mass of sulphur = 32u)

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 53



JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 54

An octahedral complex with molecular composition M.5NH3.Cl.SO4 has two isomers, A and B. The solution of A gives a white precipitate with AgNO3 solution and the solution of B gives white precipitate with BaCl2 solution.
The type of isomerism exhibited by the complex is :

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 55

In a set of reactions p - nitrotoluene yielded a product E

The product E would be :-

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 56

​How many electrons are involved in the following redox reaction ?

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 57

Amongst the following, identify the species with an atom in +6 oxidation state :

*Multiple options can be correct
JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 58

Example of a three-dimensional silicate is :

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 59

Williamson synthesis of ether is an example of

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 59

Nucleophilic substitution

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 60

​Which one of the following substituents at para-position is most effective in stabilizing the phenoxide ion?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 60

is an electron withdrawing group which stabilises the anion.

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 61

Let, M and σ2 be respectively the mean, mode and variance of n observations x1, x2, ...., xn and di = - xi - a, i = 1, 2, ..., n, where a is any number.
Statement I : Variance of d1, d2, ..., dn is σ2.
Statement II : Mean and mode of d1, d2, ..., dn are –– a and – M –a, respectively

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 61

Mean & mode depends upon change in origin and scale so mean & mode of –x; – a is –x – a and – M – a
but variance never depends upon change in origin & it is always positive so veriance if – x – a is same i.e. σ2

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 62

Let function F be defined as then the value of the integral , where a > 0, is:-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 62



t + a = p , dt = dp




 

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 63

If the function  is continuous at x = π, then k equals:-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 63

x = π - h





JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 64

​For all complex numbers z of the form 1 + iα ,α  ∈ R, If z2 = x + iy, then:-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 64


JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 65

If the volume of a spherical ball is increasing at the rate of 4π cc/sec, then the rate of increase of its radius (in cm/sec), when the volume is 288π cc, is :-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 65

 v  = 288π

2 × 2 × 2 × 2 × 2 × 3 × 3 = 
r = 6
 


JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 66

​The equation where x is real, has:-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 66


No solution [∵ both values are not satisfied]

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 67

The tangent at an extremity (in the first quadrant) of latus rectum of the hyperbola , meets x -axis and y-axis at A and B respectively. Then (OA)2 – (OB)2 , where O is the origin, equals:-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 67

Eq of tangent
3x – 2y = 4

OA2 – OB2 = 16/20 = -4 = 

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 68

A chord is drawn through the focus of the parabola y2 = 6x such that its distance from the vertex of this parabola is  then its slope can be :-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 68

Eq of chord
y – 0 = m (x – 3/2)

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 69

​Let f : R → R be defined by f(x) = then f is:-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 69

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 70

The circumcentre of a triangle lies at the origin and its centroid is the mid point of the line segment joining the points (a2 + 1, a2 + 1) and (2a, –2a), a ≠ 0. Then for any a, the orthocentre of this triangle lies on the line :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 70


JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 71

​Let f(n) = , where [n] denotes the greatest integer less than or equal to n. Then is equal to :-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 71





= 11 (5 × 28 – 23) + 112
= 11 × 117 + 112
= 1287 + 112
= 1399

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 72

​If and  then the magnitude of the projection of on :-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 72

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 73

The equation of the circle described on the chord 3x + y + 5 = 0 of the circle x2 + y2 = 16 as diameter is:-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 73

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 74

The principal value of tan–1 is:-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 74

 tan–1[cot (11π - π/4)]
= tan-1 [-cot π/4]
= -tan-1 (cot π/4)
= - tan-1 (1)
= – π/4

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 75

​Let A and E be any two events with positive probabilities :
Statement - 1 : P(E/A) ≥ P(A/E)P(E)
Statement - 2 : P(A/E) ≥ P(A∩E).

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 75

L.H.S.

R.H.S. 



So, 

St. - I is true
St. - 2 
So 
st - 2 is true

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 76

If a line L is perpendicular to the line 5x – y = 1, and the area of the triangle formed by the line L and the coordinate axes is 5, then the distance of line L from the line x + 5y = 0 is :-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 76

Equation = of line L is x + 5y + c = 0

⇒ c = ± 5√2
∴ Eq of line L is
x + 5y ± 5√2 = 0
Its distance from x + 5y = 0 is 

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 77

Let A and B be any two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB – BA is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 77


      

So AB – BA is symmetric

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 78

If the angle between the line 2(x + 1) = y = z + 4 and the plane  is π/6, then the value of λ is:-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 78


JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 79

​ If and y (0) = 1, then y(π) is equal to :-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 79


JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 80

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 80

Let n men participated

n2 – 5n – 66 = 0
n = 11, (not possible)
which lies in [10, 12]

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 81

​The number of terms in an A.P. is even; the sum of the odd terms in it is 24 and that the even terms is 30. If the last term exceeds the first term by , then the number of terms in the A.P. is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 81

Let no. of terms = 2n

sum of even terms
....... (i)
sum of odd terms
........ (ii)
....... (iii)
eq. (i)....eq. (ii)
........(iv)
........... (v)

n = 4 so no. of terms = 8

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 82

If Δr = then the value of :-
 

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 82



R1 and R3 are identical so
is independent of a, and n

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 83

If non-zero real numbers b and c are such that min f(x) > max g(x), where
f (x) = x2 + 2bx + 2c2 and
g(x) = – x2 – 2cx + b2 (x ∈ R) ; then lies in the interval:-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 83




JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 84

Equation of the line of the shortest distance between the lines and is:

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 84




JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 85

The coefficient of x 1012 in the expansion of (where n ≤ 22 is any positive integer), is:-  

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 85

let x1012 occurs in general terms


0 ≤ r1, r2 r3 ≤ 10
when
r1 + r2 + r3 = 10
nr2 + 253r3 = 1012
only one case possible
r1 = 6, r2 = 0, r3 = 4
so coeff = 10C4

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 86

The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 86

Let p: I m not feeling well
q: I will go to doctor
Given statement :- p → q
its contrapositive ~ q → ~ p
∵ If I will not go to the doctor then i am feeling well.

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 87

The function f(x) = |sin 4x| + |cos 2x|, is a periodic function with period :-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 87

f(x) = |sin 4x| + |cos 2x|
         

Period = π/2

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 88

​Let f : R → R be a function such that for all x ∈ R. Then, at x = 0 , f is:

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 88


≤ 0
     = 0
Conti at x = 0


L.H.D. = R.H.D.

JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 89

The area of the region above the x-axis bounded by the curve y = tan x, 0 ≤ x ≤ and the tangent to the curve at x = is :-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 89



tangent at point 
y – 1 = 2 (x – π/4) on x-axis

Area = 


JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 90

If m is a non - zero number and  = f (x) + c, then f(x) is:-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (19th-April-2014) - Question 90



put 

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