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Detailed Solution for JEE Main Practice Test- 13 - Question 2

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JEE Main Practice Test- 13 - Question 4

Given that x + sin y = 2008 and x + 2008 cos y = 2007 where 0 ≤ y ≤ π/2. The value of [x + y], is. (Here [x] denotes greatest integer function)

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JEE Main Practice Test- 13 - Question 5

Let p be the statement ' Ram races' and q be the statement 'Ram wins'. Then ~ (p v (~ q)) is

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JEE Main Practice Test- 13 - Question 6

A vertical pole PS has two marks at Q and R such that portions PQ, PR and PS subtend angles α, β, γ respectively at a point on the ground which is at distance x from the bottom of pole P. If PQ = a, PR = b, PS = c and α + β + γ = 180º, then x^{2} is equal to

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JEE Main Practice Test- 13 - Question 7

Then the number of subsets of set A×(A ∩ B) which contains exactly 3 elements is

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JEE Main Practice Test- 13 - Question 8

The relation P defined from R to R as a P b ⇔ 1+ ab > 0, for all a,b ∈ R is

JEE Main Practice Test- 13 - Question 9

If x_{1}, x_{2} & x_{3} are the three real solutions of the equation

where x_{1} > x_{2} > x_{3} , then

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JEE Main Practice Test- 13 - Question 10

The variance of 20 observations is 5. If each observation is multiplied by 2 then the new variance of the resulting observations, is

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JEE Main Practice Test- 13 - Question 12

There exist positive integers A, B and C with no common factors greater than 1, such that A log_{200}5 + B log_{200}2 = C. The sum (A + B + C) equals

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JEE Main Practice Test- 13 - Question 14

Smallest positive x satisfying the equation cos^{3}3x + cos^{3}5x = 8 cos^{3}4x · cos^{3}x is

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JEE Main Practice Test- 13 - Question 15

If the quadratic equations 3x^{2} + ax + 1 = 0 and 2x^{2} + bx + 1 = 0 have a common root, then the value of the expression 5ab - 2a^{2} - 3b^{2} is

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JEE Main Practice Test- 13 - Question 18

Consider the sequence 8A + 2B, 6A + B, 4A, 2A – B, ........ Which term of this sequence will have a coefficient of A which is twice the coefficient of B?

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JEE Main Practice Test- 13 - Question 20

Let k_{1}, k_{2} (k_{1} < k_{2}) be two values of k for which the expression x^{2} – y^{2} +kx +1 can be factorised into two real linear factors, then (k_{2} – k_{1}) is equal to

Detailed Solution for JEE Main Practice Test- 13 - Question 20

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JEE Main Practice Test- 13 - Question 21

**(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)**

Rolle’s theorem holds for the function f(x) = x3 + bx2 + cx, 1 ≤ x ≤ 2 at the point 4/3, then the value of 100c − 500b must be

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JEE Main Practice Test- 13 - Question 22

If p, q, r are three distinct real numbers, p ≠ 0 such that x^{2} + qx + pr = 0 and x^{2} + rx + pq = 0 have a common root, then the value of p + q + r is .....

Detailed Solution for JEE Main Practice Test- 13 - Question 22

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JEE Main Practice Test- 13 - Question 23

The number of solutions of the equation [2x] - [x + 1] = 2x must be equal to (where [.] denotes the greatest integer function)

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JEE Main Practice Test- 13 - Question 25

The three angles of a quadrilateral are 60°, 60^{g} and 5π/6, if fourth angle is λ^{∘}, then the value of λ must be

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JEE Main Practice Test- 13 - Question 26

A special kind of ruler can be used to measure reaction time. You position the 'zero' mark between your friend's first finger and thumb. Without warning, you let go of the the rular, and your friend has to grab it as soon as possible. You can read the reaction time from labelled marks on the ruler. The marks, are separated from each other by 0.01 s intervals of falling time. This means that

JEE Main Practice Test- 13 - Question 27

An object moves to the East across a frictionless surface with constant speed. A person then applies a constant force to the North on the object. What is the resulting path that the object takes?

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JEE Main Practice Test- 13 - Question 28

An aeroplane is flying vertically upwards. When it is at a height of 1000m above the ground and moving at a speed of 367 m/s., a shot is fired at it with a speed of 567 m/s from a point directly below it. What should be the acceleration of aeroplane so that it may escape from being hit ?

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JEE Main Practice Test- 13 - Question 29

A jet plane flying at a constant velocity V at a height h = 8 km is being tracked by a radar R located at O directly below the line of flight. If the angle θ is decreasing at the rate of 0.025 rad/s., when θ = 60° the velocity of the plane is :

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JEE Main Practice Test- 13 - Question 30

The figure Shows the acceleration of a particle versus time graph. The particle starts from rest at t = 0. Find the approximate velocity at t = 1s.

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JEE Main Practice Test- 13 - Question 31

A uniform rope of length L and mass M is placed on a smooth fixed wedge as shown. Both ends of rope are at same horizontal level.The rope is initially released from rest, then the magnitude of initial acceleration of rope is

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JEE Main Practice Test- 13 - Question 32

Figure shows two 45° wedges, the smaller wedge w has a horizontal top face. It can slide down the larger wedge W, which is on a horizontal table. All the surfaces are smooth. A mass m sits on the top face of the upper wedge.

Describe qualitatively the motion of the system once it is released from rest.

JEE Main Practice Test- 13 - Question 33

A block of mass m is kept on a rough inclined plane with coefficient of friction µ. The force required to just move the block up is

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JEE Main Practice Test- 13 - Question 34

The variation of the vertical speed with time of a ball falling in air is shown below.

During the time from 0 to T, the ball gains kinetic energy and loses gravitational potential energy ΔE_{P}.

Which of the following statements must be correct?

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JEE Main Practice Test- 13 - Question 35

One end of a light rope is tied directly to the ceiling. A man initially at rest on the ground starts climbing the rope hand over hand upto a height ℓ.

From the time he starts at rest on the ground to the time he is hanging at rest at a height ℓ, how much work was done on the man by the rope?

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JEE Main Practice Test- 13 - Question 36

A car of mass 1000 kg moves on a circular road with a speed of 20 m/s. Its direction changes by 90° after travelling 628 m on the road. The centripetal force acting on the car is

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JEE Main Practice Test- 13 - Question 37

A pendulum bob is released from horizontal position shown. At an angular position θ, its total acceleration makes an angle ϕ with string, ϕ is -

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JEE Main Practice Test- 13 - Question 38

A ball of mass m is released from A inside a smooth wedge of mass m as shown in the figure. What is the speed of the wedge when the ball reaches point B?

JEE Main Practice Test- 13 - Question 39

A light particle moving horizontally with a speed of 12 m/s strikes a very heavy block moving in the same direction at 10 m/s. The collision is one dimensional and elastic. After the collision, the particle will

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JEE Main Practice Test- 13 - Question 40

A particle A suffers an oblique elastic collision with a particle B that is at rest initially. If their masses are the same, then, after the collision :

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JEE Main Practice Test- 13 - Question 41

A space vehicle of mass 200 kg is observed at t = 0 to pass through the origin of reference frame oxyz with velocity relative to the frame. Due to explosive charges, the vehicle separates into three parts A, B and C of mass 100 kg, 60 kg and 40 kg respectively. At t = 2s the positions of parts A and B are observed to be at A (500, – 200, 250) and B (250, 0, – 100), where the coordinates are expressed in metres. The position of part C at that time is

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JEE Main Practice Test- 13 - Question 42

Figure shows three coplanar forces acting on an object which does not have any other forces acting on it. Marks the correct options.

JEE Main Practice Test- 13 - Question 43

Figure below shows the variation of the moment of inertia of a uniform rod about an axis normal to its length with the distance of the axis from the end of the rod. The moment of inertia of the rod about an axis passing through its centre and perpendicular to the its length is

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JEE Main Practice Test- 13 - Question 44

A semi-circular disc of radius 1 m and mass = 4 kg is lying on the horizontal x-y plane. If XX' is the axis of rotation of the body and a is applied at point P, the magnitude of angular acceleration is equal to (the region is gravity free)

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JEE Main Practice Test- 13 - Question 45

A uniform disk, a thin hoop (ring), and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according to their angular momentum after a given time t, least to greatest.

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JEE Main Practice Test- 13 - Question 46

**(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)**

A person wants to see AB part of his image (see figure). His eye level is at 1.8 m above the ground. If he uses minimum size of mirror required for this, find the height of the lowest point of the mirror above the ground.

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JEE Main Practice Test- 13 - Question 47

A charged particle of mass m = 1 mg and charge q = 1 μC enters along AB at point A in a uniform magnetic field B = 1.2 T existing in the rectangular region of size a × b, where a = 4 m and b = 3m. The particle leaves the region exactly at corner point C. What is the speed v (in ms^{–1}) of the particle?

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JEE Main Practice Test- 13 - Question 48

Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 27 W. How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference?

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JEE Main Practice Test- 13 - Question 49

Pertaining to two planets, the ratio of escape velocities from respective surfaces is 1 : 2, the ratio of the time periods of the same simple pendulum at their respective surfaces is 2 : 1 (in same order). Then, the ratio of their average densities is 1 : n. Find value of n.

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JEE Main Practice Test- 13 - Question 50

Two particles P and Q have mass 4.0 kg and 1.0 kg respectively. They are projected along a vertical line with velocity up = 20m/s and u_{Q} = 5m/s when separation between them was 60 m. P was projected vertically up while Q was projected vertically down. Calculate the maximum height attained (in m) by the centre of mass of the system of two particles, measured from the initial position of P. Assume that the particles do not collide and that the ground is far below their point of projection [g = 10 m/s^{2}].

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JEE Main Practice Test- 13 - Question 52

Arrange the given intermediates in decreasing order of their hydride donation tendency :

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JEE Main Practice Test- 13 - Question 53

The following cell at 298K,two weak acids (HA) and(HB) with pk_{a} (HA) = 5 and pk_{a} (HB) = 7 of equal molarity have been used as shown.

Pt|H_{2}(g, 1atm) | HA(1M) || HB(1M)|H_{2}(g,1atm)|Pt

Thus, emf of the cell is -

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JEE Main Practice Test- 13 - Question 54

Which of the following addition reaction will result into a complex salt?

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JEE Main Practice Test- 13 - Question 55

Identify compounds which give precipitate with Tollen's reagent.

(c) Me – C ≡ C – H

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JEE Main Practice Test- 13 - Question 56

The standard half-cell reduction potential of Fe^{3+} (aq) | Fe is – 0.036 V and that of OH^{–} | Fe(OH)_{3}(s) | Fe is – 0.756 V. The value of log K_{sp} for Fe(OH)_{3} at 298 K is

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JEE Main Practice Test- 13 - Question 57

Which of the following co-ordination entity is chiral?

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JEE Main Practice Test- 13 - Question 58

In which compound the products obtained upon prolonged heating can not be separated by fractional distillation.

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JEE Main Practice Test- 13 - Question 60

Two complexes [Co(NH_{3})_{5}Cl]SO_{4} and [Co(NH_{3})5SO_{4}]Cl can't be distinguished by -

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JEE Main Practice Test- 13 - Question 62

Select the incorrect statement based on the following half-reaction -

JEE Main Practice Test- 13 - Question 63

In which of the following complexes, change in colour is not observed on heating ?

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JEE Main Practice Test- 13 - Question 64

Find the total number of Aldol products in given reaction.

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JEE Main Practice Test- 13 - Question 65

The reaction : 2NO_{2}(g) ⇌ N_{2}O_{4}(g), has ΔG^{0}_{298K} = -6kJ mol^{-1}. If in the reaction mixture the partial pressure of NO_{2} is 0.4 atm and partial pressure of N_{2}O_{4} is 0.2 atm than -

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JEE Main Practice Test- 13 - Question 68

The standard heat of combustion of carbon(s), sulphur(s) and carbon disulphide(l) are – 390, – 290 and – 1100 kJ/mol respectively. The standard heat of formation of carbon disulphide (l) is -

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JEE Main Practice Test- 13 - Question 69

of Mn, Fe and Co is +1.57, + 0.77 and + 1.97 respectively then this irregularity is due to

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JEE Main Practice Test- 13 - Question 70

Which of the following ketones has the largest equilibrium constant for addition of water?

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JEE Main Practice Test- 13 - Question 71

**(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)**

In hydrogen atom an orbit has a diameter of about 16.92 Å. What is the maximum number of electrons that can be accommodated?

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JEE Main Practice Test- 13 - Question 72

The diagonal relationship is shown by the elements upto how many groups only?

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JEE Main Practice Test- 13 - Question 73

In an iodometric estimation, the following reactions occur

2Cu^{+2} + 4I^{–} → Cu_{2}I_{2} + I_{2};

I_{2} + 2Na_{2}S_{2}O_{3} → 2Nal + Na_{2}S_{4}O_{6}

0.12 mole of CuSO_{4}, was added to excess of Kl solution and the liberated iodine required 120 ml of hypo.

The molarity of the hypo solution was

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JEE Main Practice Test- 13 - Question 74

Equivalent weight of potash alum is M_{1}/x and equivalent weight of gypsum is M_{2}/y. Then x – y will be

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JEE Main Practice Test- 13 - Question 75

How much amount of CaCO_{3} in gram having percentage purity 50 per cent produces 0.56 litre of CO_{2} at STP on heating?

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