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NATA Mock Test - 4 - JEE MCQ

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30 Questions MCQ Test - NATA Mock Test - 4

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NATA Mock Test - 4 - Question 1

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A planet of core density 3ρ and outer curst of density ρ has small tunnel in core. A small Particle of mass m is released from end A then time required to reach end B :

Detailed Solution for NATA Mock Test - 4 - Question 1

At some distance from centre inside core

Now time for A to B =

NATA Mock Test - 4 - Question 2

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A small circular wire loop of radius a is located at the centre of a much larger circular wire loop of radius b as shown above (b> >a). Both loops are coaxial and coplanar. The larger loop carries a time (t) varying current I = I₀ cos ωt where I₀ and ω are constants. The large loop induces in the small loop an emf that is approximately equal to which of the following.

Detailed Solution for NATA Mock Test - 4 - Question 2

Magnetic flux passing through inner loop due to current in outer loop-

So, emf developed,

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NATA Mock Test - 4 - Question 3

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A spring mass system is placed on a frictionless horizontal surface as shown in the figure. The spring is expanded by 1/10m and the blocks are given velocities as shown, then maximum extension of spring is :

Detailed Solution for NATA Mock Test - 4 - Question 3

As there is no loss of energy
Initial mechanical energy = Final mechanical energy
For initial Mechanical energy

Where and v_relative =5 m/s

= 25 + 25 = 50
For final Mechanical energy
When there is maximum extension relative velocity between block = 0

NATA Mock Test - 4 - Question 4

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An electromagnetic wave of frequency f = 7.3MHz passes from a vacuum into a dielectric medium with permittivityε = 9. Then,

A.
Frequency of the wave will remains same but wavelength will become thrice
B.
Frequency remains same but the Velocity and wavelength both will become 3 times of the original value
C.
Velocity and frequency both will become 1/3 times of the original value
D.
Frequency remains same but the Velocity and wavelength both will become 1/3 times of the original value

Detailed Solution for NATA Mock Test - 4 - Question 4

As permittivity is greater than the permittivity of free space so the refractive index of medium is

Wavelength of the electromagnetic wave in medium will be
Velocity of wave will be.

NATA Mock Test - 4 - Question 5

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A particle is projected from point A towards a building of height h as shown at an angle of 60 ° with horizontal. It strikes the roof of building at B at an angle of 30 ° with the horizontal. The speed of projection is

A.
√gh
B.
√2gh
C.
√3gh
D.
2√gh

Detailed Solution for NATA Mock Test - 4 - Question 5

Let u be the speed of projection and v be the speed at B

Applying law of conservation of energy,

Using equation (i) in equation (ii),
we have

NATA Mock Test - 4 - Question 6

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Consider the following equilibrium
N₂O₄ (g) ⇔ 2NO₂(g)
Then select the correct graph: (graph represent relation between concertation of NO₂ and N₂O₄ at equilibrium)

Detailed Solution for NATA Mock Test - 4 - Question 6

Keq =
[NO₂]² = keq [N₂O₄]
It resembles graph of y² = 4 ax
So option (b) is correct

NATA Mock Test - 4 - Question 7

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If two different non-axial d-orbitals having XZ nodal plane form π bond by overlapping each other, then internuclear axis will be;

A.
X
B.
Y
C.
Z
D.
No π-bond will form

Detailed Solution for NATA Mock Test - 4 - Question 7

Two different non-axial d-orbitals will lie in planes perpendicular to each other, such d-orbital will not formed
Hence, (d) option is correct.

NATA Mock Test - 4 - Question 8

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The given osazone can be formed by

A.
D-glucose
B.
D-fructose
C.
D- Idose
D.
Both a and b

Detailed Solution for NATA Mock Test - 4 - Question 8

Formation of osazone involves only C₁ and C₂ carbon atoms. The rest of the carbon atoms remains uneffected.
Glucose and fructose differ only in the configurations of first and second carbon atoms remaining positions are similar. So they form same osazone.

NATA Mock Test - 4 - Question 9

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The cyclotrimetaphosphoric acid is

A.
(HPO₃)₃ and contains 9 σ – bonds
B.
H₃P₃O₆ and contains 12 σ – bonds
C.
(HPO₃)₃ and contains 15 σ – bonds
D.
H₃P₃O₉ and contains 18 σ – bonds

Detailed Solution for NATA Mock Test - 4 - Question 9

Hence, option (C ) is correct.

NATA Mock Test - 4 - Question 10

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In a face centered cubic lattice of edge length 'a' number of next to next nearest neighbor to corner atom and distance of corner atom to next to next nearest atom is respectively-

A.
B.
6, a
C.
D.

Detailed Solution for NATA Mock Test - 4 - Question 10

Nearest neighbor
Next nearest neighbor = a
Next to next nearest neighbor

No of such neighbors = 24
Hence, correct answer is (c)

NATA Mock Test - 4 - Question 11

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There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white is

A.
1/4
B.
1/3
C.
2/3
D.
1/6

Detailed Solution for NATA Mock Test - 4 - Question 11

Let E_i(0 < i < 2) denote the event that urn contains 'i' white and '(2 – i)' black balls.
Let A denote the event that a white ball is drawn from the urn.
We have P(E_i) = 1/3 for i = 0, 1, 2
P (A|E₁) = 1/3, P(A|E₂) = 2/3, P(A|E₃) = 1.
By the total probability rule,
P(A)= P(E₁)P(A|E₁) + P(E₂)P(A|E₂) + P(E₃)P(A|E₃)

NATA Mock Test - 4 - Question 12

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The plane passing through the point (−2, −2, 2) and containing the line joining the points
(1, 1, 1) and (1, −1, 2) makes intercepts on the coordinates axes the sum of whose lengths is

A.
3
B.
4/3
C.
4
D.
16/3

Detailed Solution for NATA Mock Test - 4 - Question 12

Equation of any plane passing through (−2, −2, 2) is
a(x + 2) + b(y + 2) + c(z – 2) = 0
Since it contains the line joining the points (1, 1, 1) and (1, −1, 2), it contains these points as well
so that
3a + 3b – c = 0
and 3a + b + 0 = 0
Solving we get

and thus the equation of the plane is
(x + 2) - 3(y + 2) = 0
x+3y-4=0

Intercepts on axes = 4, 4/3
The required sum= 4+(4/3)=16/3

NATA Mock Test - 4 - Question 13

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If a, b, c are in GP and are in AP, then a, b, c are the lengths of the sides of a triangle which is

A.
acute angled
B.
obtuse angled with ∠A being obtuse
C.
right angled with ∠A being 90°
D.
equilateral

Detailed Solution for NATA Mock Test - 4 - Question 13

a, b, c are in GP b² = ac
are in AP.
2(log 2b – log 3c) = log a – log 2b + log 3c – log a
log 2b = log 3c 2b = 3c
∴ b² = ac & 2b = 3c
b = 2a/3 and c = 4a/9
Since (a+b) = 5a/3 > c, (b+c) = 10a/9 > a and
(c + a) = 13a/9 > b, therefore, a, b, c are the sides
of a triangle. Also, as ‘a’ is the greatest side, let us
find angle A of ΔABC

Hence ΔABC is an obtuse angled triangle.

NATA Mock Test - 4 - Question 14

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Sum of the series
1 + 3 + 6 + 10 + 15 + ……………………….n terms is

Detailed Solution for NATA Mock Test - 4 - Question 14

NATA Mock Test - 4 - Question 15

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The solution of the equation (2x + y + 1) dx + (4x + 2y – 1) dy = 0 is

A.
log (2x + y – 1) = C + x + y
B.
log (4x + 2y – 1) = C + 2x + y
C.
log (2x + y + 1) + x + y = C
D.
log (2x + y – 1) + x + 2y = C

Detailed Solution for NATA Mock Test - 4 - Question 15

Put 2x + y = X ⇒Therefore, the given equation is reduced to

= x + constant
2(2x + y) + log (2x + y – 1) = 3x + constant
x + 2y + log (2x + y – 1) = C

NATA Mock Test - 4 - Question 16

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Which one of the answer figures shows the correct view of the 3-D problem figure after the problem figure is opened up ?

A.
1
B.
2
C.
3
D.
4

Detailed Solution for NATA Mock Test - 4 - Question 16

Correct Answer is option (B)

NATA Mock Test - 4 - Question 17

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Which one of the answer figures shows the correct view of the 3-D problem figure after the problem figure is opened up ?

A.
1
B.
2
C.
3
D.
4

Detailed Solution for NATA Mock Test - 4 - Question 17

Correct Answer is (A)

NATA Mock Test - 4 - Question 18

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Which one of the answer figures shows the correct view of the 3-D problem figure after the problem figure is opened up ?

A.
1
B.
2
C.
3
D.
4

Detailed Solution for NATA Mock Test - 4 - Question 18

NATA Mock Test - 4 - Question 19

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Which one of the answer figures shows the correct view of the 3-D problem figure after the problem figure is opened up ?

A.
1
B.
2
C.
3
D.
4

Detailed Solution for NATA Mock Test - 4 - Question 19

NATA Mock Test - 4 - Question 20

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Which one of the answer figures shows the correct view of the 3-D problem figure after the problem figure is opened up ?

A.
1
B.
2
C.
3
D.
4

Detailed Solution for NATA Mock Test - 4 - Question 20

NATA Mock Test - 4 - Question 21

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What is the increased percentage rate of social media fraud in 2018?

A.
50%
B.
38%
C.
43%
D.
52%

Detailed Solution for NATA Mock Test - 4 - Question 21

A study has found that social media fraud increased by 43% in 2018. The cybercriminals are increasingly relying on Facebook, Instagram, WhatsApp, and other legitimate social media and messaging platforms to sell stolen identities, credit card numbers and other ill- gotten gains. The name of the report is Current State of Cybercrime - 2019, released by RSA security.

NATA Mock Test - 4 - Question 22

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Find the total number of surface of the object given below in the problem

A.
10
B.
12
C.
14
D.
15

Detailed Solution for NATA Mock Test - 4 - Question 22

In the given question 13 surfaces are clearly shown which are labelled 1 to 13.
In addition to this, there is 1 surface at the bototm and 1 surface is not visible
So, there are 13 + 1 + 1 = 15 surfaces
Hence, the correct option will be (D)

NATA Mock Test - 4 - Question 23

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Find out the total number of surfaces of the object given below in the problem figure.

A.
10
B.
11
C.
2
D.
9

Detailed Solution for NATA Mock Test - 4 - Question 23

Surfaces visible from the top are: 1, 7, 5, 2
Surfaces visible from the front are: 8, 4
Surfaces visible from the left side are: 9
Surfaces visible from the right side are: 3, 6
Surfaces visible from the back are: 10
Surfaces visible from the bottom are: 11
Hence, there are total 11 surfaces.

NATA Mock Test - 4 - Question 24

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Find out the total number of surfaces of the object given below in the problem figure.

A.
14
B.
15
C.
16
D.
13

Detailed Solution for NATA Mock Test - 4 - Question 24

Surfaces visible from the top are: 1, 2, 10, 4, 5
Surfaces visible from the front are: 3, 6, 8
Surfaces visible from the left side are: 12
Surfaces visible from the right side are:9, 7
Surfaces visible from the back are: 11
Surfaces visible from the bottom are: 13
Hence, there are total 13 surfaces.

NATA Mock Test - 4 - Question 25

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One of the following answer figure is hidden in the problem figure in the same size and direction. Select the correct one.

A.
1
B.
2
C.
3
D.
4

Detailed Solution for NATA Mock Test - 4 - Question 25

NATA Mock Test - 4 - Question 26

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One of the following answer figure is hidden in the problem figure in the same size and direction. Select the correct one.

A.
1
B.
2
C.
3
D.
4

Detailed Solution for NATA Mock Test - 4 - Question 26

NATA Mock Test - 4 - Question 27

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One of the following answer figure is hidden in the problem figure in the same size and direction. Select the correct one.

A.
1
B.
2
C.
3
D.
4

Detailed Solution for NATA Mock Test - 4 - Question 27

NATA Mock Test - 4 - Question 28

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The problem figure shows the top view of objects. Looking in the direction of the arrow, identify the correct elevation, from amongst the answer figures.

A.
1
B.
2
C.
3
D.
4

Detailed Solution for NATA Mock Test - 4 - Question 28

NATA Mock Test - 4 - Question 29

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The problem figure shows the top view of objects. Looking in the direction of the arrow, identify the correct elevation, from amongst the answer figures.

A.
1
B.
2
C.
3
D.
4

Detailed Solution for NATA Mock Test - 4 - Question 29

NATA Mock Test - 4 - Question 30

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The problem figure shows the top view of objects. Looking in the direction of the arrow, identify the correct elevation, from amongst the answer figures.

A.
1
B.
2
C.
3
D.
4

Detailed Solution for NATA Mock Test - 4 - Question 30

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