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NATA Mock Test - 2


50 Questions MCQ Test NATA - Sample Paper & Mock Tests | NATA Mock Test - 2


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Attempt NATA Mock Test - 2 | 50 questions in 90 minutes | Mock test for JEE preparation | Free important questions MCQ to study NATA - Sample Paper & Mock Tests for JEE Exam | Download free PDF with solutions
QUESTION: 1

The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is

Solution:

Let the equation of the circle is

(x-1)2 + (y-k)2  = k2

It passes through (2, 3)

⇒ (2-1)2 + (3-k)2 = k2

⇒ 1+9+k2-6k = k2

⇒ 10-6k=0

⇒ k=-10/-6

⇒ k = 5/3

⇒ diameter = 10/3

QUESTION: 2

The value of ii is :

Solution:

Let A=ii

⇒ log A = i log i

∵ ei θ = cos θ + i sin θ

∴ eiπ/2 = i

∴ i . π/2 = log i

∴ log A = i · i π/ 2 = - π / 2

⇒ A = e-π/2

QUESTION: 3

If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex is

Solution:

Let the third vertex C be (x1 , y1) since O(0, 0) is the orthocenter

mCO × mAB = – 1

⇒ y 1 - 0 x 1 - 0 · 3 - - 1 - 2 - 5 = - 1

⇒ y 1 x 1 · 4 7 = 1

⇒ 7 x 1 = 4 y 1

Also mBO × mAC = – 1

⇒ 3 - 2 × y 1 + 1 x 1 - 5 = - 1

⇒ 3 y 1 + 3 = 2 x 1 - 1 0

⇒ 3 × 7 4 x 1 + 3 = 2 x 1 - 1 0

⇒ x1 = – 4

y1 = – 7

Hence, the third vertex is (– 4, – 7)

QUESTION: 4

If a < 0, the function f(x) = eax + e- ax is a monotonically decreasing function for values of x

given by :
Solution:

f(x) = eax + e- ax

But a < 0

∴ e ax - e - ax > 0

⇒ e ax > e - ax

⇒ ax > - ax ⇒ 2 ax > 0

∴ ax > 0, then x < 0 (∴ a < 0)

QUESTION: 5

How many three-digit numbers can be formed without using the digits 0, 2, 3, 4, 5 and 6 ?
Solution:

Three-digit numbers are to be formed by using the digits 1, 7, 8 and 9.

To form a number of three digits, we are to fill up three places : the hundred's, the ten's and the unit's. The hundreds place can be filled in 4 different ways because anyone of 1, 7, 8 and 9 can fill up this place.

Similarly, ten's and unit's places can also be filled in 4 different ways each.

Accordingly, by FPC, the no. of three-digit numbers = 4 × 4 × 4 = 6 4

QUESTION: 6

For what value of 'a' is the area bounded by the curve y=a2 x 2+ax+1 and

the straight line y = 0, x = 0 & x = 1 the least ?
Solution:

QUESTION: 7

How many five digit numbers can be formed by using the digits 1,2,3,4,5 without repetition of digits?
Solution:

1,2,3,4,5

Number of given digits (=5) Number of Digits number

to be formed (=5) Number of such numbers

QUESTION: 8

A particle is moving in a circular motion of radius R. Its tangential retardation at any time is equal to the centripetal acceleration. If it starts with speed v0, then the speed after one revolution is
Solution:

Hence, speed after one revolution

QUESTION: 9

A particle starts moving with velocity from origin, where k is a constant. The general equation for its path is
Solution:

Comparing vx = ky2

vy = kx

and slope

QUESTION: 10

A stationary body of mass 3 kg explodes in to three pieces of equal mass. Two of the piece fly off along x-axis and yaxis with equal speed 2 m/s and time of explosion is 10–3 s, then average force on the third piece
Solution:

By conservation of angular momentum

and average force on third particle

QUESTION: 11

Two particles of equal mass are moving along x-axis and y-axis respectively, if initial velocity of 1st particle is zero but acceleration is constant whereas 2nd particle acceleration is zero, then path of centre of mass
Solution:

x ∝ y2, path is parabolic.

QUESTION: 12

Find the P – O bonds are present in P4O6?
Solution:

QUESTION: 13

When hydrogen peroxide is added to acidified potassium dichromate, a blue colour is produced due to the formation of
Solution:

QUESTION: 14

If B.O.D. of a river is high, it means that the river is
Solution:
QUESTION: 15

Which of the following has unstable enol form?
Solution: Enol of has anti-aromatic character which is least stable i.e. unstable enol forms of others are stable due to aromatic character and H-bonding.
QUESTION: 16

Red, Yellow and _________ form a primary colour scheme
Solution:

Any of a group of colours from which all other colours can be obtained by mixing.Red, Yellow and Blue form a primary colour scheme

QUESTION: 17

Identify the structure
Solution:

The Rashtrapati Bhavan is the official home of the President of India located at the Western end of Rajpath in New Delhi, India.

QUESTION: 18

What is the finish of sanitary fittings
Solution:

The following sanitary fittings are commonly used in buildings, for efficient collection and removal to the house drain: 1. Wash basins 2. Sinks 3. Bath tubs 4. Water closets 5. Urinals 6. Flashing cisterns

QUESTION: 19

A 3-D problem figure is given below. Identify the correct front view from the options
Solution:
QUESTION: 20

A 3-D problem figure is given below. Identify the correct top view from the options
Solution:
QUESTION: 21

Identify the structure
Solution:

The Statue of Liberty is a colossal neoclassical sculpture on Liberty Island in New York Harbor in New York, in the United States. The copper statue, a gift from the people of France to the people of the United States, was designed by French sculptor Frédéric Auguste Bartholdi and its metal framework was built by Gustave Eiffel. The statue was dedicated on October 28, 1886.

QUESTION: 22

If a colour is made darker by adding black, the result is called a __________.
Solution:

If a colour is made darker by adding black, the result is called a Shade

QUESTION: 23

Complete the series of the problem figures by choosing the correct answer from the options given below
Solution:
QUESTION: 24

CN Tower is also known as
Solution:

Its name "CN" originally referred to Canadian National, the railway company that built the tower. Following the railway's decision to divest non-core freight railway assets prior to the company's privatization in 1995, it transferred the tower to the Canada Lands Company, a federal Crown corporation responsible for real estate development.

QUESTION: 25

Higher the purity of a colour, higher the ______.
Solution:

Chroma: the quality of a color's purity, intensity or saturation. For example: A gray color is a neutral -- an extreme low chroma. Fire-engine red may be a hi chroma red.

QUESTION: 26

Identify the building
Solution:

LIC Building is a 15-storied building in Chennai, India, serving as the southern regional headquarters of the Life Insurance Corporation of India

QUESTION: 27

Find the correct 3-D figure from the options, which has the same front view as given in the problem figure, looking in the direction of the arrow

A.

B.

C.

D.


Solution:
QUESTION: 28

Identify the building
Solution:

The Petronas Towers, also known as the Petronas Twin Towers, are twin skyscrapers. According to the Council on Tall Buildings and Urban Habitat (CTBUH)'s official definition and ranking, they were the tallest buildings in the world from 1998 to 2004 and remain the tallest twin towers in the world.

QUESTION: 29

In the given problem figure, find out the total number of surfaces of objects
Solution:
QUESTION: 30

TEOTIHUACAN is famous for ___________
Solution:

TEOTIHUACAN is an ancient Mesoamerican city located in a sub-valley of the Valley of Mexico, located in the State of Mexico 40 kilometres (25 mi) northeast of modern-day Mexico City, known today as the site of many of the most architecturally significant Mesoamerican pyramids built in the pre-Columbian Americas.

QUESTION: 31

A sheet of paper is folded & cut in the given steps. Select the correct answer from the options given below which resembles the pattern paper acquires when it is unfolded
Solution:
QUESTION: 32

Why India Gate was built ?
Solution:

This monument is regarded as the heritage of India and is located on RajPath in New Delhi. India Gate was designed by Sir Edwin Lutyens and was built in 1931 and initially named as 'All India War Memorial'. ... India Gate was built to honor these soldiers.

QUESTION: 33

Identify the structure
Solution:

The Louvre Pyramid is a large glass and metal pyramid designed by Chinese-American architect I. M. Pei, surrounded by three smaller pyramids, in the main courtyard ) of the Louvre Palace in Paris

QUESTION: 34

Why was Statue Of Liberty Built?
Solution:

1865 - 1886. In 1865, a French political intellectual and anti-slavery activist named Edouard de Laboulaye proposed that a statue representing liberty be built for the United States. This monument would honor the United States' centennial of independence and the friendship with France.

QUESTION: 35

Which of the following dices is identical to the unfolded figure shown below
Solution:
QUESTION: 36

Why is Statue Of Liberty green in colour ?
Solution:

When the Statue was unveiled in 1886, it was a shiny brown color, like a penny. By 1906, the color had changed to green. The reason the Statue of Liberty changed colors is that the outer surface is covered with hundreds of thin copper sheets. Copper reacts with the air to form a patina or verdigris.

QUESTION: 37

Understand the relationship between a & b. Choose the missing figure from the options given such that a similar relationship is established between c & d
Solution:
QUESTION: 38

In the given problem figure, find out the total number of surfaces of objects
Solution:
QUESTION: 39

Identify the structure
Solution:

The Taj Mahal meaning "Crown of the Palaces" is an ivory-white marble mausoleum on the south bank of the Yamuna river in the Indian city of Agra

QUESTION: 40

____________ is a tint of red.
Solution: Pink is a tint of red.

QUESTION: 41

Identify the material
Solution:

The material in the image is Glass.

QUESTION: 42

A sheet of paper is folded & cut in the given steps. Select the correct answer from the options given below which resembles the pattern paper acquires when it is unfolded
Solution:
QUESTION: 43

Understand the relationship between a & b. Choose the missing figure from the options given such that a similar relationship is established between c & d
Solution:
QUESTION: 44

If Orange : Juice, then Mango : ________
Solution:

Mango pulp is the inner fleshy yellow, sweet part of the mango. Pulp of mango can be easily extracted by peeling any variety of mango and then crushing it. In order to extract mango pulp, crush using your hands or put the pieces in a mixer or food processor and blend to a pulp.

QUESTION: 45

Understand the relationship between a & b. Choose the missing figure from the options given such that a similar relationship is established between c & d
Solution:
QUESTION: 46

Violet, indigo, blue, green, yellow, orange, red form the ____________.
Solution:

There are seven wavelength ranges within the visible spectrum that each correspond to a different color. The colors fall in an order commonly referred to with the acronym ROYGBIV. ROYGBIV can aid in remembering the order of the colors: red, orange, yellow, green, blue, indigo, and violet.

QUESTION: 47

Assuming the question figure to be a transparent sheet with a given pattern. Find out the

correct figure from the options which would appear when the problem figure is

folded along the dotted line
Solution:
QUESTION: 48

A 3-D problem figure is given below. Identify the correct front view from the options.
Solution:
QUESTION: 49

In the given problem figure, find out the total number of surfaces of objects
Solution:
QUESTION: 50

Complete the series of the problem figures by choosing the correct answer from the options given below
Solution:
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