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JEE Advanced Test- 13 - Question 1

In the Hofmann bromamide degradation reaction, the number of moles of NaOH and Br2 used per mole of amine produced are

JEE Advanced Test- 13 - Question 3

A long capillary tube of mass 'π' gm, radius 2mm and negligible thickness, is partially immersed in a liquid of surface tension 0.1 N/m. Take angle of contact zero and neglect buoyant force of liquid. The force required to hold the tube vertically, will be - (g = 10 m/s^{2})

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JEE Advanced Test- 13 - Question 4

In the chemical reaction, CH_{3}CH_{2}NH_{2} + CHCl_{3} + 3KOH ⟶ (A) + (B) + 3H2O, the compounds (A) and (B) are respectively

JEE Advanced Test- 13 - Question 5

A nonuniform sphere at rest on a rough horizontal surface is acted upon by a force F as shown. The friction force acting on it is

(1) towards left (2) towards right (3) zero

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JEE Advanced Test- 13 - Question 6

During synaptic transmission of nerve impulse, neurotransmitter (P) is released from synaptic vesicles by the action of ions (Q). Choose the correct P and Q.

JEE Advanced Test- 13 - Question 7

E. Coli about to replicate was placed in a medium containing radio active thymidine for five minutes. Then it was made to replicate in a normal medium. Which of the following observation shall be correct?

JEE Advanced Test- 13 - Question 8

To determine the coefficient of friction between a rough surface and a block, the surface is kept inclined at 45° and the block is released from rest. The block takes a time *t *in moving a distance *d*. The rough surface is then replaced by a smooth surface and the same experiment is repeated. The block now takes a time *t/2 *in moving down the same distance *d*. The coefficient of friction is

JEE Advanced Test- 13 - Question 9

Consider a boy on a trolley who throws a ball with speed 20 m/s at an angle 37° with respect to trolley in direction of motion of trolley which moves horizontally with speed 10 m/s then what will be distance travelled by ball parallel to road :

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JEE Advanced Test- 13 - Question 10

A block is pushed momentarily on a horizontal surface with initial velocity ‘v’. If ‘μ’ is the coefficient of sliding friction between the block and surface, the block will come to rest after time (‘g’ = acceleration due to gravity)

JEE Advanced Test- 13 - Question 11

Three blocks A, B and C of masses 4 kg, 2 kg and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied on the 4 kg block, then the contact force between A and B is

*Multiple options can be correct

JEE Advanced Test- 13 - Question 12

A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. :

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JEE Advanced Test- 13 - Question 13

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30º, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively

*Multiple options can be correct

JEE Advanced Test- 13 - Question 14

In a resonance tube experiment, a closed organ pipe of length 120 cm resonates when tuned with a tuning fork of frequency 340 Hz. If water is poured in the pipe then (given vair = 340 m/sec.) :

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JEE Advanced Test- 13 - Question 15

The force *F *acting on a particle of mass *m *is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is

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JEE Advanced Test- 13 - Question 16

A particle moving on a smooth horizontal surface strikes a stationary wall. The angle of strike is equal to the angle of rebound & is equal to 37° and the coefficient of restitution with wall is e = 1/5. Find the friction coefficient between wall and the particle in the form X/10 and fill value of X.

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JEE Advanced Test- 13 - Question 17

A spool of mass M = 3 kg and radius R = 20 cm has an axle of radius r = 10 cm around which a string is wrapped. The moment of inertia about an axis perpendicular to the plane of the spool and passing through the centre is Coefficient of friction between the surface and the spool is 0.4. If the maximum value of the tension is T (in N) that can be applied so that the spool rolls without slipping, then find T/2 [Take g = 10 m/s^{2}.]

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JEE Advanced Test- 13 - Question 18

A particle is projected at an angle 60º with speed 10√3 , from the point ' A ' as shown in the fig. At the same time the wedge is made to move with speed 10√3 towards right as shown in the figure. Then the time (in seconds) after which particle will strike the wedge is

Detailed Solution for JEE Advanced Test- 13 - Question 18

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JEE Advanced Test- 13 - Question 19

In a tank of horizontal cross-sectional area 1m^{2}, a spring with force constant 2000 Nm^{–1} is fixed in vertical position upto the height of the water as shown in figure 1. A block of mass 180 kg is gently placed over the spring and it attains the equilibrium position as shown in figure 2. If base area of the block is 0.2m^{2} and height 60 cm, then compression in the spring is 5X (in cm) in equilibrium position. Then find X (take g = 10 m/s^{2}; ρ_{w} = 1000 kg/m^{3})

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JEE Advanced Test- 13 - Question 20

A planet revolves about the sun in elliptical orbit of semimajor axis 2 × 10^{12} m. The areal velocity of the planet when it is nearest to the sun is 4.4 × 10^{16} m^{2}/s. The least distance between planet and the sun is 1.8 × 10^{12} m. The minimum speed of the planet is a × 10^{1} (in km/sec) then find a

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JEE Advanced Test- 13 - Question 21

A light spring balance hangs from the hook of the other light spring balance and a block of mass *M *kg hangs from the former one. Then the true statement about the scale reading is

JEE Advanced Test- 13 - Question 22

A roller is made by joining together two cones at their vertices *O*. It is kept on two rails AB and *CD *which are placed asymmetrically (see figure), with its axis perpendicular to *CD* and its centre *O* at the centre of line joining *AB* and *CD* (see figure). It is given a light push so that it starts rolling with its centre *O* moving parallel to *CD* in the direction shown. As it moves, the roller will tend to

JEE Advanced Test- 13 - Question 23

A block of mass *m* is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally, so that the block does not slip on the wedge. The force exerted by the wedge on the block (g is acceleration due to gravity) will be :

JEE Advanced Test- 13 - Question 24

A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is 0**.**2. The weight of the block is** **

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JEE Advanced Test- 13 - Question 25

BF_{3} & CCl_{4} on reaction with water produce _________ & _________ respectively :

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JEE Advanced Test- 13 - Question 26

In manufacture of sodium carbonate from solvay (or ammonia soda) process the raw material used is :

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JEE Advanced Test- 13 - Question 27

For the following flow diagram :

Which of the following option describes the reagents, products and the reaction conditions given in parentheses as small alphabets ?

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JEE Advanced Test- 13 - Question 28

The acceptable resonating structures of the following molecule are

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JEE Advanced Test- 13 - Question 29

Which is not the correct order as per property given for the following pair of compounds:

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Detailed Solution for JEE Advanced Test- 13 - Question 30

*Multiple options can be correct

Detailed Solution for JEE Advanced Test- 13 - Question 31

*Multiple options can be correct

JEE Advanced Test- 13 - Question 32

The solubility of a sparingly soluble salt A_{x} B_{y} in water at 25ºC = 1.4 × 10^{–4} M. The solubility product is 1.1 × 10^{–11}. The possibilities are

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JEE Advanced Test- 13 - Question 33

Which of the following property(ies) of alkali metals/alkali metal salts increase(s) with increase in atomic number?

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JEE Advanced Test- 13 - Question 34

Suppose the elements X and Y combine to form two compounds XY_{2} and X_{3}Y_{2}. When 0.1 mole of XY_{2} weighs 10 g and 0.05 mole of X_{3}Y_{2} weighs 9 g, the atomic weights of X and Y are

JEE Advanced Test- 13 - Question 35

The energies of activation for forward and reverse reactions for A_{2} + B_{2} 2AB are 180 kJ mol^{–1} and 200 kJ mol^{–1} respectively. The presence of a catalyst lowers the activation energy of both (forward and reverse) reactions by 100 kJ mol^{–1}. The enthalpy change of the reaction (A_{2} + B_{2} → 2AB) in the presence of catalyst will be (in kJ mol^{–1}):

*Answer can only contain numeric values

JEE Advanced Test- 13 - Question 36

The number of visible lines when an electron returns from the 5^{th} orbit to ground state in the hydrogen spectrum is P. Then value of P is :

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JEE Advanced Test- 13 - Question 37

A spherical balloon of volume 5 litre is to be filled up with H_{2} at NTP from a cylinder of 6 litre volume containing the gas at 6 atm at 0°C. The no. of balloons that can be filled up is :

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JEE Advanced Test- 13 - Question 38

For the equilibrium reaction K_{p}=81_{ }atm^{2} The total pressure at equilibrium is 'X' times the pressure of NH_{3}. The value of X will be :

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JEE Advanced Test- 13 - Question 39

How many structure isomers of primary amines are possible with molecular formula C_{5}H_{13}N ?

Detailed Solution for JEE Advanced Test- 13 - Question 39

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JEE Advanced Test- 13 - Question 40

What is the minimum pH required to prevent the precipitation of ZnS in a solution that is 0.01M ZnCl_{2} and saturated with 0.10 M H_{2}S ? Given K_{sp} of ZnS = 10^{–21}, for H_{2}S K_{a1 }x K_{a2} = 10^{-20 }.

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JEE Advanced Test- 13 - Question 41

If x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, .... is a Geometric Progression of natural number and x_{1}x_{2}x_{3}x_{4} = 64, then complete set of solutions of x_{4} is

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JEE Advanced Test- 13 - Question 42

From a point P __=__ (3, 4) perpendiculars PQ and PR are drawn to line 3x + 4y – 7 = 0 and a variable line y – 1 = m (x – 7), then maximum area ΔPQR is

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JEE Advanced Test- 13 - Question 43

If P(x_{1}, y_{1}), Q(x2, y2) be any two points on the curve y = 3x – 2 – x_{2} for 1 < x < 2, then maximum value of 3x_{1} + 3x_{2} – x_{1}^{2} – x_{2}^{2} is

Detailed Solution for JEE Advanced Test- 13 - Question 43

JEE Advanced Test- 13 - Question 44

A point O is situated on a circle of radius R and with centre O another circle of radius 3R/2 is described. Inside the smaller crescent-shaped region intercepted between these circles a circle of radius R/8 is placed. If smaller circle moves in contact with the circle of radius R, then the length of the arc described by its centre in moving from one extreme position to other extreme position is

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JEE Advanced Test- 13 - Question 45

If is a non terminating and is a recurring decimal rational number. After decimal at some stage, digits start repeating in groups continuously. If smallest such group has r digits, then

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JEE Advanced Test- 13 - Question 46

All the three vertices of an equilateral triangle lie on the parabola y = x^{2} and one of its sides has a slope of 2, then sum of x-coordinates of the three vertices of triangle is

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JEE Advanced Test- 13 - Question 47

The number of common tangents to the hyperbola xy = c^{2} and the circle x^{2} + y^{2} = 2c^{2} is

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JEE Advanced Test- 13 - Question 48

If x_{1} x_{2} x_{3} = 2.5.7^{2}, then the number of different solutions for the ordered triplets (x_{1}, x_{2}, x_{3}) where x_{i} N, x_{i} > 1 is

Detailed Solution for JEE Advanced Test- 13 - Question 48

JEE Advanced Test- 13 - Question 49

Consider the reaction,

2A + B → Products

When concentration of B alone was doubled, the half-life did not change. When the concentration of A alone was doubled, the rate increased by two times. The unit of rate constant for this reaction is:

JEE Advanced Test- 13 - Question 50

If f(x) = cosec 2x + cosec 2^{2}x + .......... + cosec 2^{n}x and g(x) = f(x) + cot 2^{n}x, then is equal to

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JEE Advanced Test- 13 - Question 51

Consider a reaction, aG + bH → Products.

When concentration of both the reactants G and H is doubled, the rate increases by eight times. However, when the concentration of G is doubled keeping the concentration of H fixed, the rate is doubled. The overall order of the reaction is:

JEE Advanced Test- 13 - Question 52

The mass of carbon anode consumed (giving only carbon dioxide) in the production of 270 kg of aluminium metal from bauxite by the Hall process is:

(Atomic mass : Al = 27)

*Multiple options can be correct

JEE Advanced Test- 13 - Question 53

If z_{1} = a + ib & z_{2} = c + id are complex numbers such that |z_{1}| = |z_{2}| = 1 and

Re (z_{1} z_{2}) = 0, then the pair of complex numbers w_{1} = a + ic & w_{2} = b + id satisfies :

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JEE Advanced Test- 13 - Question 54

If z is a complex number satisfying |z – i Re (z) | = |z – Im (z)| then z lies on

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JEE Advanced Test- 13 - Question 55

Concentrated aqueous sulphuric acid is 98% H_{2}SO_{4} by mass and has a density of 1.80 g.mL^{–1}. Volume of acid required to make 1 litre of 0.1 M H_{2}SO_{4} solution is:

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Detailed Solution for JEE Advanced Test- 13 - Question 57

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JEE Advanced Test- 13 - Question 58

The tangent at any point P of a curve C meets the x - axis at Q whose abscissa is positive and OP = OQ O being the origin, if C is a family of parabolas having vertix (α, β) and latus rectum = 4a, then evaluate

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Detailed Solution for JEE Advanced Test- 13 - Question 59

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