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NATA Mock Test - 9 - JEE MCQ


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50 Questions MCQ Test NATA Sample Papers & Mock Tests 2024 - NATA Mock Test - 9

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NATA Mock Test - 9 - Question 1

A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration 'a' directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration 'a' vertically.The tension in the string is equal to :

Detailed Solution for NATA Mock Test - 9 - Question 1


(Force diagram in the frame of the car)
Applying Newton's law perpendicular to strin
mg sin θ = ma cos θ
tan  θ = a/g
Applying Newton's law along string

NATA Mock Test - 9 - Question 2

A uniform sphere has a mass M and radius R. Find the pressure p inside the sphere, caused by gravitational compression, as a function of the distance r from its centre. (γ is universal gravitational constant)

Detailed Solution for NATA Mock Test - 9 - Question 2

We consider a spherical concentric shell of radius x and thickness dx.
The mass of considered element is dm = (4π x2dx)ρ.
Gravitational field at a point in the shell is

∴ 

The pressure in the element is 

∴ 
But 
By putting the value of ρ, we get, 

NATA Mock Test - 9 - Question 3

A 220 volt input is supplied to a transformer. The output circuit draws a current of 2.0 ampere at 440 volts. If the efficiency of the transformer is 80%, the current drawn by the primary windings of the transformer is

Detailed Solution for NATA Mock Test - 9 - Question 3

Here,
Input voltage, Vp = 220 V
Output voltage, Vs = 440 V
Input current, Ip = Ip
Output current, Is = 2A
Efficiency of the transformer,  η = 80%

Efficiency of the transformer, 

NATA Mock Test - 9 - Question 4

A stone is dropped from a height of 45 m on a horizontal level ground. There is horizontal wind blowing due to which horizontal acceleration of the stone becomes 10 m/s2.(Take g = 10 m/s2).
The time taken (t) by stone to reach the ground and the net horizontal displacement (x) of the stone from the time it is dropped and till it reaches the ground are respectively

Detailed Solution for NATA Mock Test - 9 - Question 4

Taking motion in vertical direction, 

 u = 0, g = 10 m/s, h = 45 m

⇒ h = 0 + (1/2) gt 2
⇒ t =  √(2h/g) = √[(2× 45)/10]
⇒ t = 3 sec.
(b) Taking motion in horizontal direction,

NATA Mock Test - 9 - Question 5

The combination of 'NAND' gates shown here (in figure), are equivalent to

Detailed Solution for NATA Mock Test - 9 - Question 5

   (if a NAND is given only 1 input it s behaves as NOT gate, as it is  (one input is divided in two and then passed through NAND)

i.e. OR gate.
For second circuit C = Not of (A NAND B)
i.e. AND only

NATA Mock Test - 9 - Question 6

If helium and methane are allowed to diffuse out of the container under the similar conditions of temperature and pressure, then the ratio of rate of diffusion of helium to methane is .

Detailed Solution for NATA Mock Test - 9 - Question 6

NATA Mock Test - 9 - Question 7

For a monatomic gas kinetic energy = E, the relation with rms velocity is

Detailed Solution for NATA Mock Test - 9 - Question 7

For a monatomic gas with only Translational degrees of freedom
E⁡a = 3/2 kbT⁡ (Avg K E per molecule)

NATA Mock Test - 9 - Question 8


In this balanced equartion x, y, z are

Detailed Solution for NATA Mock Test - 9 - Question 8



eqn (2) multiply with 3 and adding with eqn (1) we get



So x = 1
y = 3
z = 6

NATA Mock Test - 9 - Question 9

Propyne and propene can be distinguished by

Detailed Solution for NATA Mock Test - 9 - Question 9

The terminal hydrogen is acidic in 
H3C - C ≡ CH
(propyne) and it reacts with ammoniacal AgNO3. In propene, CH3CH = CH2 there is no acidic hydrogen.

NATA Mock Test - 9 - Question 10

A piston is cleverly designed so that it extracts the maximum amount of work out of a chemical reaction, by matching Pexternal to the Pinternal at all times. This 8cm diameter piston initially holds back 1 mol of gas occupying 1 L, and comes to rest after being pushed out a further 2 L at 25oC .After exactly half of the work has been done, the piston has travelled out a total of

Detailed Solution for NATA Mock Test - 9 - Question 10




Piston change in volume  

V = of cylinder = πr2h

NATA Mock Test - 9 - Question 11

A vector of magnitude 9 and perpendicular to both the vectors 

Detailed Solution for NATA Mock Test - 9 - Question 11


Hence a unit vector perpendicular to 

Hence the required vector is

NATA Mock Test - 9 - Question 12

If x = 9 is the chord of contact of the hyperbola x2 - y2 = 9, then the equation of the corresponding pair of tangents is

Detailed Solution for NATA Mock Test - 9 - Question 12

Let (h, k) be point whose chord of contact with respect to hyperbola x2 - y2 = 9 is x = 9.
W e know that, chord of contact of (h, k) with respect to hyperbola x2 - y2 = 9 is T = 0 

But it is the equation of the line x = 9.
This is possible when h = 1, k = 0 (by comparing both equations).
Againe quation of pair of tangents is T2 = SS1
 

NATA Mock Test - 9 - Question 13

Detailed Solution for NATA Mock Test - 9 - Question 13


Roots of the corresponding equation are 
∴ by sign - scheme :


NATA Mock Test - 9 - Question 14

If α, β and γ are the angles which a directed line makes with the positive directions of the co-ordinates axes, then find the value of  sin2α + sin2β + sin2γ.

Detailed Solution for NATA Mock Test - 9 - Question 14

The direction cosines of the line are 

NATA Mock Test - 9 - Question 15

In an acute - angled triangle ABC, points D, E and F are the feet of the perpendiculars from A, B and C onto BC, AC and AB, respectively. H is the orthocentre of ΔABC. If sin A = 3/5 and BC = 39, then the length of AH is

Detailed Solution for NATA Mock Test - 9 - Question 15

NATA Mock Test - 9 - Question 16

The below question consists of problem figures and followed by four answer figures (A), (B), (C) and (D). Find out the figure from the answer figures which will continue the given series.

Explanations:

NATA Mock Test - 9 - Question 17

The below question consists of problem figures and followed by four answer figures (A), (B), (C) and (D). Find out the figure from the answer figures which will continue the given series.

Explanations: Circle and square are rotating in clockwise direction at an angle of 90∘

.Triangle is rotating in anticlockwise direction at an angle of 90∘

NATA Mock Test - 9 - Question 18

Choose the correct alternative in which only specified components of the key figure (X) are

Found.

Explanations:

NATA Mock Test - 9 - Question 19

Which one of the given set of figures violates the given rule?

Rule: Black elements are decreasing and white elements are increasing.

Explanations:

NATA Mock Test - 9 - Question 20

The below question consists of a related pair of figures (problem pair) and followed by four answer pairs marked as (A), (B), (C) and (D). Out of these four, three have relationship similar to that in the problem pair. Only one pair of figures does not have similar relationship. You have to select that pair of figures which does not have a relationship similar to that in the problem pair.

Explanations: The outermost element has changed its position to become the innermost element, and similarly, all the elements have changed their respective positions.

NATA Mock Test - 9 - Question 21

A clock is attached to a wall. Below the clock a mirror is placed. When seen through a mirror, the clock shows 6 : 45. The correct time is

Explanations: The correct time is 5:15

Detailed Solution for NATA Mock Test - 9 - Question 21

When you view a clock in a mirror, the reflection shows a reversed image of the actual time.

To find the correct time when the mirrored image shows 6:45:

  • Subtract the minutes shown from 60 to find the actual minutes. 60−45=15
  • Subtract the hour shown from 12 to find the actual hour. 12−6=6 Since 6:45 is being viewed in a mirror, it actually means: 6−1=5

So, the mirrored image of 6:45 corresponds to the actual time of 5:15.

Therefore, the correct answer is:

2. 5:15

NATA Mock Test - 9 - Question 22

The below question consists of a question figure and followed by four figures (1), (2), (3) and (4), which show the possible water images of the question figure. Choose one out of these four figures which shows the correct water image of the question figure.

Explanations:

NATA Mock Test - 9 - Question 23

The below question consists of a question figure and followed by four figures (a), (b), (c) and (d). Choose one out of these four figures that can replace ‘?’ to complete the question figure.

Explanations:

NATA Mock Test - 9 - Question 24

In the below question, one or more dots are placed in the problem figure (X) followed by four alternatives (a), (b), (c) and (d). One out of these four alternatives contain region(s) common to the circle, square, triangle and rectangle similar to that marked by the dot in figure (X).

Explanations:

NATA Mock Test - 9 - Question 25

The below question consists of a unfolded dice in the left side and four choices (a), (b), (c) and (d) are given in the form of complete dices in the right side. You are required to select the correct answer choice which is formed by folding the unfolded dice.

Explanations:

NATA Mock Test - 9 - Question 26

A Clock is attached to a wall. Above the clock a mirror is placed. Looking into a mirror, the clock shows 3 : 20. The correct time is

Explanations:

NATA Mock Test - 9 - Question 27

The below question consists of a combination of alphabets and followed by four alternatives (a), (b), (c) and (d). Choose the alternative which is closely resembles the mirror image of the given combination.

Explanations:

NATA Mock Test - 9 - Question 28

Find the number of triangles in the given figure.

Explanations:

14 (small triangles) + 11(medium triangles) + 4(big

triangles) = 29

NATA Mock Test - 9 - Question 29

The below question consists of four figures a, b, c and d followed by a set of four alternatives A, B, C and D. Which of the combinations given below when fitted into each other would form a complete square?

Explanations:

NATA Mock Test - 9 - Question 30

The below question consists of a set of three figures K, L and M showing a sequence of folding of a piece of paper. Figure M shows the manner in which the folded paper has been cut. These three figures are followed by four figures (1), (2), (3) and (4) from which you have to choose a figure which would most closely resemble the unfolded form offigure M.

Explanations:

NATA Mock Test - 9 - Question 31

The below question consists of a figure matrix with one or more missing terms and followed by four answer figures (1), (2), (3) and (4). Find the correct answer figure that will replace '?'

Explanations:

NATA Mock Test - 9 - Question 32

The below question consists of a four figures. Three are similar in a certain way and so form a group. Find out which one of the figures does not belong to that group.

Explanations:

In all figures, the first element is rotating in

anticlockwise direction and second element is rotating in

clockwise direction except in fourth figure.

NATA Mock Test - 9 - Question 33

The below question consists of a question figure and followed by four figures (1), (2), (3) and (4), which show the possible water images of the question figure. Choose one out of these four figures which shows the correct water image of the question figure.

Explanations:

NATA Mock Test - 9 - Question 34

The below question consists of problem figures followed by answer figures marked as (1), (2), (3), (4) and (5). You have to select that figure from the set of answer figures which would come in the place of question mark (?) in the problem figure.

Explanations:

The arrows rotate 135∘CW and the remaining part of

the figure rotates 90∘ ACW.

NATA Mock Test - 9 - Question 35

Choose the correct alternative which is embedded in the question figure.

Explanations:

NATA Mock Test - 9 - Question 36

Indian Cancer Research institute is located at

Explanations: IACR's Head Office was located at the Cancer Research Institute, Tata Memorial Centre, Dr. E. Borges Marg, Parel, Mumbai.The Cancer Research Institute has

moved to Kharghar, Navi Mumbai, and is now called the Advanced Centre for Treatment, Research and Education in Cancer (ACTREC).

NATA Mock Test - 9 - Question 37

Central Drug Research Institute is located at

Explanations:

The Central Drug Research Institute is a

multidisciplinary research laboratory in Lucknow, India,

employing scientific personnel from various areas of

biomedical sciences.

NATA Mock Test - 9 - Question 38

Ajanta-Ellora caves are situated near

Explanations:

The Ajanta Caves are 30 (approximately) rock-cut Buddhist cave monuments which date from the 2nd century BCE to about 480 CE in Aurangabad district of Maharashtra state of India.

NATA Mock Test - 9 - Question 39

National School of Mines is located in ?

Explanations:

The Indian Institute of Technology (ISM), Dhanbad (abbreviated as IIT (ISM) is a public engineering and research institution located in Dhanbad, India. It was formerly known as Indian School of Mines and was a Central University before it was converted into an Indian Institute of Technology (IIT) and an Institute of National Importance.

NATA Mock Test - 9 - Question 40

Sun Temple is situated at?

Explanations:

Konark Sun Temple is a 13th-century CE sun temple at Konark about 35 kilometres (22 mi) northeast from Puri on the coastline of Odisha, India. The temple is attributed to king Narasingha deva I of the Eastern Ganga Dynasty about 1250 CE.

NATA Mock Test - 9 - Question 41

The 'Golconda Fort' is in which state?

Explanations:

Golconda, also spelled Golkonda or Golkonda, historic fortress and ruined city lying 5 miles (8 km) west of Hyderabad in western Telangana state, southern India. From 1518 to 1591 it was the capital of the Quṭb Shāhī kingdom (1518–1687), one of five Muslim sultanates of the Deccan.

NATA Mock Test - 9 - Question 42

Under Mother Teresa's guidance, the Missionaries of Charity built near Asansol, a lep er

colony is called

Explanations:

The Missionaries of Charity (Latin: Missionariarum a Caritate) is a Roman Catholic (Latin Church) religious congregation established in 1950 by Mother Teresa, now known in the Catholic Church as Saint Teresa of Calcutta. In 2012 it consisted of over 4,500 religious sisters.

Members of the order designate their affiliation using the order's initials, "M.C." A member of the congregation must adhere to the vows of chastity, poverty, obedience, and the fourth vow, to give "wholehearted free service to the poorest of the poor."Today, the order consists of both contemplative and active branches in several countries.Missionaries care for those who include refugees, former prostitutes, the mentally ill, sick children, abandoned children, lepers, people with AIDS, the aged, and convalescent. They have schools run by volunteers to

educate street children and run soup kitchens as well as other services according to the community needs. These services are provided, without charge, to people regardless of their religion or social status.

NATA Mock Test - 9 - Question 43

'Kanchipuram' is in which of the following states?

Explanations:

Kanchipuram, also known as Kānchi or Kancheepuram, is a city in the Indian state of Tamil

Nadu in Tondaimandalam region, 72 km (45 mi) from Chennai – the capital of Tamil Nadu.

NATA Mock Test - 9 - Question 44

The famous Meenakshi temple is located in It is dedicated to Meenakshi, a form of Parvati, and her consort, Sundareshwar, a form of Shiva. The temple is at the center of the ancient temple city of Madurai mentioned in the Tamil Sangam literature, with the goddess temple mentioned in 6th century CE texts.

Explanations:

NATA Mock Test - 9 - Question 45

'Tin Bhiga' lease by India to Bangladesh, was a part of

Explanations:

The Tin (or Teen) Bigha Corridor is a strip of land belonging to India on the West Bengal–Bangladesh border which, in September 2011, was leased to Bangladesh so that it can access its Dahagram– Angarpota enclaves.

NATA Mock Test - 9 - Question 46

Five persons with names, P, M, U, T and X live separately in any one of the following: a palace, a hut, a fort, a house or a hotel. Each one likes one or two different colours from among the following: blue, black, red, yellow and green. U likes red and blue. T likes black. The person living in a palace does not like black or blue. P likes blue and red. M likes yellow only. X lives in a hotel. M may lives in ?

Explanations:

NATA Mock Test - 9 - Question 47

From the given alternatives, select the word which cannot be formed using the letters of the given word. BANGALORE

Explanations:

There is only one ‘G’ in the given word. Therefore, the word GARBAGE cannot be formed.

NATA Mock Test - 9 - Question 48

Arrange the following in ascending order :

1. Centimeter

2. Kilometre

3. Decimetre

4. Metre

Explanations:

The correct order is Centimeter (0.01 meter )- Decimeter (0.1 meter )- Meter (1 meter )- Kilometer (1000 meter ). Hence, option (c) is the correct answer.

NATA Mock Test - 9 - Question 49

If B becomes A and P becomes O, what will K become in the English alphabet?

Explanations:

NATA Mock Test - 9 - Question 50

From the given alternatives, select the word which cannot be formed using the letters of the given word. ROTARY BLUES

Explanations:

there is only one ‘T’ in the given word. So, the word TABLET cannot be formed.

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