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

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90 Questions MCQ Test JEE Main & Advanced Mock Test Series | JEE Main 2014 Question Paper With Solutions (11th-April-2014)

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JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 1

A radioactive nuclei with decay constant 0.5/s is being produced at a constant rate of 100 nuclei/s. If at t=0 there were no nuclei, the time when there are 50 nuclei is:

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 1

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 2

Match the List - I (Phenomenon associated with electromagnetic radiation) with List - II (Part of electromagnetic spectrum) and select the correct code from the choices given below the lists :

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 3

A parallel plate capacitor is made of two plates of length l, width ω and separated by distance d. A dielectric slab (dielectric constant K) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force  where U is the energy of the capacitor when dielectric is inside the capacitor up to distance x (See figure). If the charge on the capacitor is Q then the force on the dielectric when it is near the edge is

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 3

C = C1 + C2

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 4

A cone of base radius R and height h is located in a uniform electric field  parallel to its base. The electric flux entering the cone is:

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 4

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 5

Three identical bars A, B and C are made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as follows :

Make the correspondence of these bars with their material being diamagnetic (D) ferromagnetic (F) and paramagnetic (P)

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 6

The average mass of rain drops is 3.0 × 10–5 kg and their average terminal velocity is 9 m/s. Calculate the energy transferred by rain to each square meter of the surface at a place which receives 100 cm of rain in a year.

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 6

= 500 × 81
= 40500 J
= 4.05 × 104 J

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 7

An ideal monoatomic gas is confinedinacy linder by a spring loaded piston of cross section 8.0 × 10–3 m2. Initially, the gas is at 300K and occupies a volume of 2.4 × 10–3 m3 and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is 1.0 × 105 N/m2 The cylinder and the piston are thermally insulated.
The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible):

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 7

A = 8 × 10-3 m2
T1 = 300 K
V1 = 2.4 × 10-3 m3
V2 = V1 + AΔx
= 2.4 × 10-3 × 8 × 10-3 × 0.1
= 3.2 × 10-3 m3
K = 8000 N/m
T2 = ?
P1 = 105N/m

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 8

The angular frequency of the damped oscillator is given by where k is the spring constant, m is the mass of the oscillator and r is the damping constant. If the ratio is 8%, the change in time period compared to the undamped oscillator is approximate as follows:

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 8

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 9

A coil of circular cross-section having 1000 turns and 4 cm2 face area is placed with its axis parallel to a magnetic field which decreases by 10-2 Wb m-2 in 0.01 s. The e.m.f. induced in the coil is:

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 9

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 10

Three straight parallel current carrying conductors are shown in the figure. The force experienced by the middle conductor of length 25 cm is:

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

A body of mass 5kg under the action of constant force  has velocity at t = 0 s as and at t = 10 s as  :-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 11

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 12

In the circuit diagrams (A, B, C, and D) shown below, R is a high resistance and S is a resistance the order of galvanometer G. The correct circuit, corresponding to the half deflection method for finding the resistance and figure of merit of the galvanometer, is the circuit labelled as:

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 13

A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of water is 3m and that of kerosene 2m. When the hole is opened the velocity of fluid coming out from it is nearly:
(take g = 10 ms-2 and density of water = 103 kg m-3)

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 13

1000 × 10 × 3 + 800 × 10 × 2 = 1/2 × 1000 v2

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 14

A photon of wavelength λ is scattered from an electron, which was at rest. The wavelength shift Δλ is three times of λ and the angle of scattering θ is 60°. The angle at which the electron recoiled is φ The value of tan φ is:
(electron speed is much smaller than the speed of light)

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 14

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 15

The Bulk moduli of Ethanol, Mercury and Water are given as 0.9, 25 and 2.2 respectively in units of 109 Nm-2. For a given value of pressure, the fractional compression in volume is  Which of the following statements about  for these three liquids is correct? :-

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 16

A hot body, obeying Newton's law of cooling is cooling down from its peak value 80ºC to an ambient temperature of 30ºC. It takes 5 minutes in cooling down from 80°C to 40°C. How much time will it take to cool down from 62°C to 32°C? (Given ln 2 = 0.693, ln 5 = 1.609)

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 16

ln 5 = 5c = 1.609
ln 16 = ct = 4 × 0.693
t = 8.6 min

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 17

A Zener diode is connected to a battery and a load as shown below :
The currents I, IZ and IL are respectively.

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 17

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 18

An air bubble of radius 0.1 cm is in a liquid having surface tension 0.06 N/m and density 103 kg/m3. The pressure inside the bubble is 1100 Nm-2 greater than the atmospheric pressure. At what depth is the bubble below the surface of the liquid? (g = 9.8 ms-2):-

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 18

= 980

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

In the circuit shown, current (in A) through the 50 V and 30 V batteries are, respectively:-

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

KVL in loop abgha
20 I1 = 50
I1 = 2.5 A
KVL in loop abcdefgha
50 – 5I2 – 30 – 5I2 = 0
I2 = 2A
KVL in loop cdefc
30 = 10 (I2 + I3)
⇒ I2 + I3 = 3
I3 = 3 – 2
= 1A
∴ Current through 50 V battery is = I1 + I2
= 2.5 + 2.0
= 4.5 A
current through 30V battery = I3 = 1A

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 20

During an adiabatic compression, 830J of work is done on 2 moles of a diatomic ideal gas to reduce its volume by 50%. The change in its temperature is nearly: (R = 8.3 JK-1mol-1)

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 21

A small ball of mass m starts at a point A with speed v0 and moves along a frictionless track AB as shown. The track BC has coefficient of friction μ. The ball comes to stop at C after traveling a distance L which is:

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 21

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 22

In a compound microscope the focal length of objective lens is 1.2 cm and focal length of eye piece is 3.0 cm. When object is kept at 1.25 cm in front of objective, final image is formed at infinity. Magnifying power of the compound microscope should be :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 22

= 200

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 23

A thin bar of length L has a mass per unit length λ, that increases linearly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is λ0, then the distance of the centre of mass from the lighter end is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 23

Mass per unit lengh = λ0 + kx

substitute'k'

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 24

In terms of resistance R and time T, the dimensions of ratio of the permeability μ and permittivity ε is :-

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 25

The initial speed of a bullet fired from a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target the rifle must be aimed in order to hit the target

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 26

An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm. The size of the images in two situations are in the ratio 3 : 2. What is the distance between the screen and the object?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 26

D = 99 cm

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 27

Two monochromatic light beams of intensity 16 and 9 units are interfering. The ratio of intensities of bright and dark parts of the resultant pattern is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 27

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 28

From a sphere of mass M and radius R, a smaller sphere of radius R/2 is carved out such that the cavity made in the original sphere is between its centre and the periphery. (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two spheres is:

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 28

Due to cavity field at P is

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 29

An electromagnetic wave of frequency 1 x 1014 hertz is propagating along z-axis. The amplitude of electric field is 4 V/m. If ε0 = 8.8 × 10-12 C2/N-m2, then average energy density of electric field will be:

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 30

Two factories are sounding their sirens at 800 Hz. A man goes from one factory to other at a speed of 2 m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in one second will be :

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 31

The appearance of colour in solid alkali metal halides is generally due to:

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 32

Complete reduction of benzene-diazonium chloride with Zn/HCl gives:

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 33

Which of the following statements about Na2O2 is not correct ?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 33

Na2O2 is a peroxide  which is occupied all paired electrons with π*2px & π*2py.

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 34

In allene (C3H4), the type(s) of hybridization of the carbon atoms is (are):

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 34

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 35

In the reaction of formation of sulphur trioxide by contact process  the rate of reaction was measured as  The rate of reaction in terms of [SO2] in mol L–1s–1 will be

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 35

= –5 × 10–4

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 36

Based on the equation

the wavelength of the light that must be absorbed to excite hydrogen electron from level n = 1 to level n = 2 will be (h = 6.625 × 10–34 Js, C = 3 × 108 ms–1)

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 36

= 13.25 × 10–8
= 1.325 × 10–7 m

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 37

Given :-
Fe3+(aq) + e- → Fe2+ (aq); E° = +0.77 V
Al3+(aq) + 3e- → Al (s); E° = -1.66 V
Br2(aq) + 2e- → 2Br- ; E° = + 1.09 V
Considering the electrode potentials, which of the following represents the correct order of reducing power?

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 38

Consider the following equilibrium ​White precipitate of AgCl appears on adding which of the following?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 38

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 39

Tischenko reaction is a modification of

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 40

Which one of the following does not have a pyramidal shape?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 40

In N(SiH3)3 lp present on nitrogen atom of 2nd shall has greater donating tendency to vacant 3dorbital of 'Si' but not this donating tendency to vacant 3d-orbital of 'Si' but not this donating tendency with P, due to 3rd pd element.

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 41

The following reaction

is known as

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 41

In (SiH3) N has strong back bonding tendency than other gsap.

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 42

Chlorobenzne reacts with trichloro acetaldehyde in the presence of H2SO

The major product formed is

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 43

Shapes of certain interhalogen compounds are stated below. Which one of them is not correctly stated?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 43

BrF5 has square pyramidal shape (sp3d2) with one lone pair at below the basal plane.

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 44

Which one of the following statements is not correct?

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 45

Which of the following series correctly represents relations between the elements from X to Y?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 45

el on moving down the gsaap shell number increases so its radii also increase from "C to Ge".

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 46

Which of the following statement s about the depletion of ozone layer is correct?

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 47

The initial volume of a gas cylinder is 750.0 mL. If the pressure of gas inside the cylinder changes from 840.0 mm Hg to 360.0 mm Hg, the final volume the gas will be

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 47

P1V1 = P2V
⇒ 840 × 750 = 360 × V2

= 1750 ml
= 1.75 L

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 48

If λ0 and λ be threshold wavelength and wavelength of incident light, the velocity of photoelectron ejected from the metal surface is:

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 48

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 49

Which one of the following is used as Antihistamine?

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 50

The molar heat capacity (Cp) of CD2O is 10 cals at 1000 K. The change in entropy associated with cooling of 32 g of CD2O vapour from 1000 K to 100 K at constant pressure will be (D = deuterium, at. mass = 2u)

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 50

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 51

The gas liberated by the electrolysis of Dipotassium succinate solution is

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 52

Which of the following name formula combinations is not correct?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 52

Correct Name of [Mn(CN)5]2- is Pentacyanomagnate (III) ion.

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 53

For the reaction, 2N2O5 → 4NO2 + O2, the rate equation can be expressed in two ways  k and k' are related as

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 53

Now

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 54

An organic compound A, C5H8O; reacts with H2O, NH3 and CH3COOH as described below:

A is

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 55

A gaseous compound of nitrogen and hydrogen contains 12.5%(by mass) of hydrogen. The density of the compound relative to hydrogen is 16. The molecular formula of the compound is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 55

Empirical formula = NH2
Since Vapour density = 16
∴ mol. wt. = 32
∵ Molecular formula = n × Emp. formula  = 2 × NH2
= N2H4

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 56

Assuming that the degree of hydrolysis is small, the pH of 0.1 M solution of sodium acetate (Ka = 1.0 × 10–5) will be

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 56

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 57

The reagent needed for converting  is

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 58

Consider the coordination compound, [Co(NH3)6]Cl3.  In the formation of this complex, the species which acts as the Lewis acid is:

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 58

Metalcation i.e. Ca3+ act as a lewis acid which accept lone pair from ligands of NH3.

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 59

The correct order of bond dissociation energy among N2, O2, O2– is shown in which of the following arrangements?

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 59

Bond energy ∝ Bond order bondorder:-
N2 = Nb = 10, Na = 4

Hence the order of B.O.

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 60

In some solutions, the concentration of H3O+ remains constant even when small amounts of strong acid or strong base are added to them. These solutions are known as:-

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 61

If X has a binomial distribution, B(n, p) with parameters n and p such that P(X = 2) = P(X = 3), then E(X), the mean of variable X, is

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 61

P(x = 2) = P (x = 3)

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 62

The integral  is equal to

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 62

= θ tan2θ - tanq + θ + C
= tan-1 x . x2 - x + tan-1 x + C
= - x + (1 + x2) tan-1 x + C

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 63

Let f be an odd function defined on the set of real numbers such that for x ≥ 0,
f(x) = 3sinx + 4cosx
Then f(x) at

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 63

f(–x) = – f(x) as f(x) is odd function

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 64

The plane containing the line  and parallel to the line  passes through the point

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 64

Normal vector =
point (1,2,3) lies in plane so equation of plane = 5(x – 1) –1(y – 2) –1(z – 3) = 0
5x – y – z = 0
so option [1] is correct

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 65

The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius = √3 is

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 65

h2 + r2 = 3

r2 = 3 – h2 ...(1)
∴ V = πr2 . 2h
= 2π  (r2 h)
V = 2π  (3h - h3)

∴ r2 = 3 – h2
r2 = 3 – 1 = 2
So Vmax = 2π  (2 × 1)
= 4π

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 66

The proposition ~(pv~q)v~ (pvq) is logically equivalent to

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 66

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 67

If the general solution of the differential equation for some function is given by y ln |cx| = x, where c is an arbitrary constant, then (2) is equal to

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 67

...(1)
is solution of y ln |cx| = x ...(2)
d.w.r. to x

use y' in equation (1)

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 68

For the curve y = 3 sinθ cosθ , x = eθsinθ, 0 ≤ θ  ≤ π, the tangent is parallel to x-axis when θ is

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 68

cos 2θ = 0
Reject (3π/4) because at q = 3π/4
Denomentor cosθ + sinθ = 0
So θ = π/4 ans

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 69

is equal to

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 69

Integrate by parts

= – 9e

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 70

Let f(x) = x|x|, g(x) = sinx and h(x) = (gof)(x). Then

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 70

h' (0) = h' (0+) = h' (0)
so h'(x) is continuous at x = 0

h"(0+) ≠  h"(0–) so h"(x) is not continuous at
x = 0
so h'(x) is not differentiable at x = 0

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 71

A set S contains 7 elements. A non-empty subset A of S and an element x of S are chosen at random. Then the probability that x∈A is

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 71

Total non empty subsects = 27 –1 = 127 Let x ∈ S also present in A
So no. of A's containg x = 26

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 72

then k is equal to

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 72

1. (2 + k) = 5
K = 3

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 73

Let P(3secθ, 2tanθ) and Q(3secφ, 2tanφ) where θ + φ = π/2 be two distinct points on the hyperbola Then the ordinate of the point of intersection of the normals at P and Q is

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 73

p (3sec θ, 2tan θ) Q  = (3 sec φ, 2 tan φ) θ + φ = π/2 Q  = (3 cosec θ, 2 cot θ)
Equation of normal at p
= 3x cos θ + 2y cot θ = 13
= 3x sin θ  cos θ  + 2y cos θ = 13 sin θ ...(1)
equation of normal at Q ⇒
= 3x sin θ  + 2y tan θ = 13
= 3x sin θ cos θ  + 2y sin θ = 13 cos θ ...(2)
(1)-(2) ⇒
2y (cos θ  – sin θ) = 13 (sin θ  - cos θ)
2y = – 13 ⇒ y = -13/2

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 74

In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 74

Let first term is a & C.R = r

a2 r4 = 49 ⇒ ar2 = 7, -7
also given that a + ar2 = 35
if ar2 = 7 ⇒  a = 35 - 7 = 28
if ar2 = - 7 ⇒  a = 35 + 7 = 42
but if a = 42 then r2 = -7/42
which is not possible so
a = 28

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 75

Let A {2, 3, 5}, B (– 1, 3, 2) and C(λ, 5, μ) be the vertices of a ΔABC. If the median through A is equally inclined to the coordinate axes, then

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 75

A = (2, 3, 5)

λ = 7 & µ = 10

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 76

The set of all real values of λ for which exactly two common tangents can be drawn to the circles
x2 + y2 - 4x - 4y + 6 = 0
and x2 + y2 - 10x - 10y + λ = 0 is the interval

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 76

C1 (2, 2)C2 (5, 5)

λ ∈ (18, 42)

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 77

If z1, z2 and z3, z4 are 2 pairs of complex conjugate numbers, then

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JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 78

If 2cosθ + sinθ =  then 7cosθ + 6sinθ is equal to

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 78

2 cos θ  + sin θ  = 1 ...(1)
7 cos θ  + 6 sin θ  = k (let) ...(2)

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 79

An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 79

Eight digit no divisible by 9 i.e. sum of digits divisible by 9
(i) Total no formed by 1,2,3,4,5,6,7,8 = 81
(ii) Total no formed by 0,2,3,4,5, 6,7,9 = 7×7!
(iii) Total no formed by 1,0,3,4,5,6,9,8 = 7×7!
(iv) Total no formed by 1,2,0,4,5,9,7,8 = 7×7!
(v) Total no formed by 1,2,3,0,5,6,7,8 = 7×7!
8! + 28 × 7 !
= 36 × 7 !

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 80

The coefficient of x50 in the binomial expansion of
(1 + x)1000 + x(1 + x)999 + x2(1 + x)998 + ......... + x1000  is

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 80

Coefficient of x50 en

= (1 + x)1001 – x1001

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 81

Let L1 be the length of the common chord of the curves x2 + y2 = 9 and y2 = 8x, and L2 be the length of the latus rectum of y2 = 8x then

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x2 + y2 = 9  & y2 = 8x
L2 = L.R. of y2 = 8x ⇒ L2 = 8
Solve x2 + 8x = 9 ⇒  x = 1, – 9
x = – 9 reject
∴ y2 = 8x so y2 = 8

L1 < L2

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 82

The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be α. After moving a distance 2 metres from P towards the foot of the tower, the angle of elevation changes to β. Then the height (in metres) of the tower is

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 82

From figure

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 83

Two ships A and B are sailing straight away from a fixed point O along routes such that ∠AOB is always 120°. At a certain instance, OA = 8 km, OB = 6 km and the ship A is sailing at the rate of 20 km/hr while the ship B sailing at the rate of 30 km/hr. Then the distance between A and B is changing at the rate (in km/hr)

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 83

Let at any time t
OA = x OB = y

AB2 = x2 + y2 + xy ...(1)
D.w.R. To . t
...(2)

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 84

If α and β are roots of the equation  for some k, and α2 + β2 = 66, then α3 + β3 is equal to

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JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 85

Let for i = 1, 2, 3 pi(x) be a polynomial of degree 2 in x, pi'(x) and pi''(x) be the first and second order derivatives of pi(x) respectively.

and B(x) = [A(x)]TA(x). Then determinant of B(x)

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 85

Let Pi = ai x2 + bix + ci ai ≠ 0
bi, ci ∈ R

use (i) C2 →  C2 – x C

So |B| = |AT| |A| = |A|2 = constant independent from n

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 86

The sum of the first 20 terms common between the series 3 + 7 +11 +15 +.....and 1 + 6 + 11 +16 +....., is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 86

New A.P of common terms having
a = 11 as Ist term & d = 20

= 4020

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 87

then a value of

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JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 88

Let A be a 3 × 3 matrix such that

Then A–1 is

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 88

∴ AA–1 = I

use column transformation and make RHS as I

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 89

A stair-case of length l rests against a vertical wall and a floor of a room,. Let P be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio 1 : 2. If the stair-case begins to slide on the floor, then the locus of P is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 89

Let any time one end is A (x, 0) & other and B(0, y) so
l2 = x2 + y2 ...(1)
Let P is (h, k) using section formula

use in (1)

Locus of Pt p is ellipse
which equation is

JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 90

The base of an equilateral triangle is along the line given by 3x + 4y = 9. If a vertex of the triangle is (1, 2), then the length of a side of the triangle is :

Detailed Solution for JEE Main 2014 Question Paper With Solutions (11th-April-2014) - Question 90

Let BC is base of equilater triangle ABC with side a and A (1, 2)

AD is perpendicular distance of PtA from line 3x + 4y – 9 = 0

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