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30 Questions MCQ Test AMU B.Tech Entrance Exam Mock Tests - AMU B.Tech Entrance Exam Mock Test- 2

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AMU B.Tech Entrance Exam Mock Test- 2 - Question 1

Four liters of a diatomic ideal gas ( λ =1.4) confined to a cylinder is subject to a closed cycle. Initially, the gas is at 1.00 atm and at 300 K. First, its pressure is tripled under constant volume. Then, it expands adiabatically to its original pressure. Finally, the gas is compressed isobarically to its original volume. Find the temperature at the end of the cycle

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 1

AMU B.Tech Entrance Exam Mock Test- 2 - Question 2

A U-tube having horizontal arm of length 20 cm, has uniform cross-sectional area = 1 cm2. It is filled with water of volume 60 cc. What volume of a liquid of density 4 g/cc should be poured from one side into the U-tube so that no water is left in the horizontal arm of the tube?

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 2

AMU B.Tech Entrance Exam Mock Test- 2 - Question 3

Two cells, having the same e.m.f., are connected in series through an external resistance R. Cells have internal resistances r1 and r2 (r1 > r2) respectively. When the circuit is closed, the potential difference across the first cell is zero. The value of R is [2006

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 3

Current in the circuit

P.D. across first cell = E – ir1

AMU B.Tech Entrance Exam Mock Test- 2 - Question 4

The output of a 2-input OR gate is zero only when its:

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 4

The truth table for 2-input OR gate is as shown in the figure. Thus, the output is zero only when both inputs are zero.

AMU B.Tech Entrance Exam Mock Test- 2 - Question 5

The Young’s double slit experiment is performed with blue and with green light of wavelengths 4360Å and 5460Å respectively. If x is the distance of 4th maxima from the central one, then           [1990]

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 5

Distance of nth maxima, 

AMU B.Tech Entrance Exam Mock Test- 2 - Question 6

A radioactive substance has a half life of four months. Three fourths of the substance will decay in

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 6

Substance left undecayed, N0​−(3/4)​N0​=(1/4)​N0
N/N0​ ​=1/4​=(1/2​)n
 
∴ Number of atoms left undecided, n=2 i.e, in two half-lives
∴ t=nT=2×4=8 months

AMU B.Tech Entrance Exam Mock Test- 2 - Question 7

A particle, with restoring force proportional to displacement and resistve force proportional to velocity is subjected to a force F sin ω0. If the amplitude of the particle is maximum for ω = ω1 and the energy of the particle is maximum for ω = ω2, then [1989,1998]

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 7

At maximum energy of the particle, velocity resonance takes place, which occurs when frequency of external periodic force is equal to natural frequency of undamped vibrations, i.e. ω2 = ω0.
Further, amplitude resonance takes place at a frequency of external force which is less than the frequency of undamped natural vibrations, i.e. ω1 ≠  ω0 .

AMU B.Tech Entrance Exam Mock Test- 2 - Question 8

The position of a particle is given by where t is in seconds and the coefficients have the proper units forto be in metres. The direction of velocity of the particle at t = 1 s is

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 8


Let θ be angle which the direction ofmakes with the

*Multiple options can be correct
AMU B.Tech Entrance Exam Mock Test- 2 - Question 9

A painter is applying force himself to raise him and the box with an  cceleration of 5 m/s2 by a massless rope and pulley arrangement as shown in figure. Mass of painter is 100 kg and that of box is 50 kg. If g = 10 m/s2, then : 

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 9

For the whole system, 2T – 1500 = 150 x 5 ⇒ T = 1125 N
For the person, T – 1000 + N = 100 x 5 N = 1500 – 1125 = 375 N 

AMU B.Tech Entrance Exam Mock Test- 2 - Question 10

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that Emech = 8 J, the incorrect statement for this system is:

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 10

Emech. = 8 J
(A) At x < x1, U = constant = 8 J
K = Emech - U = 8 - 8 = 0 J
The particle is at rest.

(B) At x = x2, U = 0 ⇒ Emech. = K = 8 J
K.E. is greatest and the particle is moving at fastest speed.

(C) At x = x3, U = 4 J
U + K = 8 J
K = 4 J

Hence the incorrect statement is : at x < x1, K.E is smallest and the particle is moving at the slowest speed.

(D) At x > x4, U = constant = 6 J
K = Emech. - U = 2 J = constant

AMU B.Tech Entrance Exam Mock Test- 2 - Question 11

The blue compound formed in the positive test for nitrogen with Lassaigne solution of an organic compound is

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 11

Ferriferrocyanide is the blue complex formed by sodium ferrocyanide and NaCN.

AMU B.Tech Entrance Exam Mock Test- 2 - Question 12

Which of the following molecules contains covalent and coordinate bonds?

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 12

AMU B.Tech Entrance Exam Mock Test- 2 - Question 13

What is the major final product of the following sequence of reaction?

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 13

AMU B.Tech Entrance Exam Mock Test- 2 - Question 14

In the reaction N2 + 3H2 ⇌ 2NH3

 and at some instant if  

then at this instant value of  is :

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 14

Hence the reaction will be at equilibrium at the given instant

AMU B.Tech Entrance Exam Mock Test- 2 - Question 15

The shift in electron density is symbolized by the crossed arrow in the below diagram. It depicts:

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 15

Arrows represent the direction of the dipole moment.

AMU B.Tech Entrance Exam Mock Test- 2 - Question 16

What is the major bromination product in the following reaction? 

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 16

The correct answer is option c

Thus, a racemic mixture is obtained. A racemic mixture is one that has an equal amount of left and right handed enantiomers of a chiral molecule.

AMU B.Tech Entrance Exam Mock Test- 2 - Question 17

The following reaction obey rate law 

It can follow mechanism

I. NO2 + O3  NO3 + O2 ,   

NO3+NO2  N2O5

II.  NO2 + O  NO3

NO3+NO2  N2O5

Select the correct mechanism.

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 17

 In I, slow step is

Thus,
 

∴ 
In fast reversible step,

∴ 
 

 

AMU B.Tech Entrance Exam Mock Test- 2 - Question 18

What product are formed during the electrolysis of a concentrated aqueous solution of sodium chloride using an electrolytic cell in which electrodes are separated by a porous pot?

I. Cl2(g)
II. NaOH(aq)
III. H2(g)
IV. NaClO(aq)
V. NaClO3(aq) 

Select the correct choice.  

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 18

Cl2(g) is formed at anode and NaOH and H2 are formed at cathode. Since, cathode and anode are separated. Hence. there is no reaction between the products formed at the cathode and anode. 

Note: but these reaction do not occur

Note: NaCl is neutral pH = 7 initially. After electrolysis , NaOH is formed

Hence, solution become, basic pH >7

AMU B.Tech Entrance Exam Mock Test- 2 - Question 19

When (S)-2-bromopentane is brominated, several 2, 3-dibromopentane molecules are formed. Which of the following is not formed?

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 19

​​​​​

S- configuration at C-2 would not change because the change will only takes place where the new bond is formed.

AMU B.Tech Entrance Exam Mock Test- 2 - Question 20

 Which of the following relations are not correct?

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 20

The correct answer is Option B 
 
k =G*l/A      (Since, G = 1/R)
   = l/AR 
Therefore, kR = l/A 
So, l/A = kR not k/R

AMU B.Tech Entrance Exam Mock Test- 2 - Question 21

If 2 sec 2α = tan β + cot β, then one of the values of α + β is

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 21

Given, 2 sec2α = tanβ + cotβ 

AMU B.Tech Entrance Exam Mock Test- 2 - Question 22

If y = y(x) is the solution of the differential equation e such that y(0) = 0, then y(1) is equal to:

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 22

Option D is correct; y(1) = 1 + loge 2.

Set u = y - x. Then du/dx = dy/dx - 1.

Using the differential relation leads to du/dx = e-u.

Rewrite as eu (du/dx) = 1, so d/dx(eu) = 1.

Integrating both sides gives eu = x + C.

Using the initial condition x = 0, y = 0 gives u = 0 and hence C = 1.

Therefore ey-x = x + 1. For x = 1, ey(1)-1 = 2, so y(1) = 1 + loge 2.

AMU B.Tech Entrance Exam Mock Test- 2 - Question 23

If x = acos3t, y = a sin3t, then  is equal to

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 23


AMU B.Tech Entrance Exam Mock Test- 2 - Question 24

From a point P(3,3) on the circle x+ y= 18 two chords PQ and PR each of length 2 units are drawn on this circle. Then, the value of the length PM is equal to (where, M is the midpoint of the line segment joining Q and R)

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 24

AMU B.Tech Entrance Exam Mock Test- 2 - Question 25

The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x < y, are 6 and 9/4 , respectively. Then x4 + y2 is equal to

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 25

AMU B.Tech Entrance Exam Mock Test- 2 - Question 26

The mean and standard deviation of 10 observations x₁, x₂, x₃, ... x₁₀ are x̄ and σ respectively. Let 10 be added to x₁, x₂, ... x₉ and 90 be subtracted from x₁₀. If the standard deviation remains the same, then x₁₀ - x̄ is equal to:

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 26

From (1) and (2)

AMU B.Tech Entrance Exam Mock Test- 2 - Question 27

The solution of  satisfying y(1) = 0, is

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 27


2xydy = (x+ 1)dx + y2dx

Integrating, we get

⇒ y2 = x- 1 + cx
At x = 1, y = 0
⇒ c = 0
⇒ x2 - y2 = 1

AMU B.Tech Entrance Exam Mock Test- 2 - Question 28

∫ (2x¹² + 5x⁹) / (x⁵ + x³ + 1)³ dx is equal to

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 28

Let I = ∫ (2x¹² + 5x⁹) / (x⁵ + x³ + 1)³ dx

= ∫ (2/x³ + 5/x⁶) / (1 + 1/x² + 1/x⁵)³ dx

Put 1 + 1/x² + 1/x⁵ = t

⇒ (-2/x³ - 5/x⁶) dx = dt

Then, I = -∫ dt / t³ = 1 / 2t² + c

= 1 / 2(1 + 1/x² + 1/x⁵)² + c

= x¹⁰ / 2(x⁵ + x³ + 1)² + c

AMU B.Tech Entrance Exam Mock Test- 2 - Question 29

In a triangle ABC, the angle B is greater than angle A. If the values of the angle A and B satisfy the equation 3 sin x - 4 sin3 x - k = 0, 0 < k < 1, then value of C is

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 29

AMU B.Tech Entrance Exam Mock Test- 2 - Question 30

The number of values of k for which the system of linear equations (k + 2)x + 10y = k and kx + (k + 3)y = k - 1 has no solution is

Detailed Solution for AMU B.Tech Entrance Exam Mock Test- 2 - Question 30

For no solution,

k + 2 / k = 10 / k + 3 ≠ k / k - 1
(k + 2)(k + 3) = 10k
k2 - 5k + 6 = 0
 k = 2, 3
 2 as for k = 2, both lines are identical.
So, k = 3 only
So, the number of values of k is 1.

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