NATA Mock Test - 5 - JEE MCQ

Given, 

To find - A−B

Given integral is .

We know that 

Using the above property,

Given that,
sinθ + cosecθ = 2
We know that:
cosecθ = 1/sinθ ...(1)
Substitute (1) into the equation:
⇒ sinθ + 1/sinθ = 2
Take LCM on the left-hand side:
⇒ (sin²θ + 1)/sinθ = 2
Now cross-multiply:
⇒ sin²θ + 1 = 2sinθ
⇒ sin²θ − 2sinθ + 1 = 0
⇒ (sinθ − 1)² = 0
⇒ sinθ = 1 ...(2)
From (2),
cosecθ = 1/sinθ = 1/1 = 1
Now compute:
sin⁵θ + cosec⁵θ = (1)⁵ + (1)⁵ = 1 + 1 = 2

We have

= 
= .

A finite set is a set where finite number of elements are present. But the numbers of prime numbers are not finite. So, the set of all prime numbers is not a finite set.
A singleton set is a set where only one element is present and null set is a set where no element is present.
Assume A is a set of all prime numbers. So,
A={2,3,5,7,....}
So, the first prime number is 2 and the next prime number is 3.
So, the set of all prime numbers is not a null set or a singleton set.
In the set of all prime numbers infinite numbers of elements present.
So, the set of all prime numbers is an infinite set.

The general equation of a circle is given by x² + y² + 2gx + 2fy + c = 0 with center at (-g, -f) and radius √(g² + f² - c).
So, the given equation x² + y² + 2x - 4y + 5 = 0 represents the circle equation. The radius of the given circle is √(1² + (-2)² - 5) = √(1 + 4 - 5) = √0 = 0.
Thus, the given equation is a circle equation with the radius equal to 0, which represents a point.
Since it represents a point, the equation will not represent a pair of straight lines which contains infinitely many points.
Hence, the correct answer is A: a point.

Let 
= 
= 

= 2

We have, .
As we know .
Therefore, n(3)ⁿ⁻¹ = 108 = 4(27) = 4(3)⁴⁻¹
On comparing, we get n = 4.

f(x) = Max {x², (1 − x)², 2x(1 − x)}

The coordinate of A:
(1 − x)(1 − x − 2x) = 0
⇒ x = 1/3, A(1/3, 0) is the coordinate of B.

Now,
2x(1 − x) = x², 2(1 − x) = x, 2 − 3x = 0, x = 2/3.

= 17/27

Let one number be x, then the other number is x + 2.
According to the question:
x + (x + 2) > 20
⇒ 2x + 2 > 20
⇒ 2x > 18
⇒ x > 9 … (i)
Also, given that both numbers are smaller than 18:
x < 18 … (ii)
From equations (i) and (ii), we get:
9 < x < 18
Now, the consecutive odd positive integers are: x = 11, 13, 15, 17.
Hence, the required pairs are (11, 13), (13, 15), (15, 17).
So, the correct answer is C) (11, 13), (13, 15), (15, 17).

Let AB be the pole =12 m and let AC be its shadow = 4√3 m
If θ is the angle of elevation of the sun, then

⇒ θ = 60°

Given,

• A, B, C, D, E, F, G and H are sitting around a rectangular table in such a way that two persons sit on each of the four sides of the table facing the centre.
• Persons sitting on opposite sides are exactly opposite to each other.
• D faces North and sits exactly opposite H.
• E is on the immediate left of H. A and G sit on the same side.
• G is exactly opposite B, who is on the immediate right of C.
• A is next to the left of D.

Representing the sitting arrangement pictographically:

From the above given seating arrangement, we can conclude that B is sitting next to E in clockwise direction.

From the given information, we can understand that the question has a missing number.
To find the missing number, we need to identify the logic of the series.
After careful observation, we can observe that the series should be solved in a vertical direction.
The summation of all numbers in a vertical direction is 25.
From the logic observed:
1^st row: 12 + 4 + 9 = 25
3^rd row: 6 + 13 + 6 = 25
Let the missing number be x.
Similarly, for the 2^nd row:
7 + 8 + x = 25 
15 + x = 25 
x = 25 − 15 
x = 10
Which is the missing number.
Therefore, 10 is the correct answer.

By analyzing each given figure we know that, 
In option A, a circle is divided into four parts.
In option C, a square is divided into four parts.
In option D, a triangle is divided into four parts.
But the figure in option B is made of two triangles.
Hence, the correct answer is 

Watches, scales, and thermometer all have some common quality.
All of them are used to measure some quantity.

• The watch is used to measure time.
• The scale is used to measure length.
• The thermometer is used to measure temperature.

Hence, this group has items with common quality.

If you overtake the last but one contestant, you will be head of last one but means third from the last. 

In the question figure, the mirror is placed on vertical to the figure.

• The reflection at a mirror is equivalent to an inversion.
• Image changes from the Left-hand side (real image) to the Right-hand side in the mirror image and vice versa.
• The top and bottom sides of the object remain the same.
• The letters having identical mirror images are A, H, I, M, O, T, U, V, W, X, Y.
• The number 1 and 8 are the only two numbers with their identical mirror images.

The circle on the top should be on left and the bottom one should be directed towards right. Also, the triangle within should have its base towards mirror.
Observing all the options of we found that

Option (B) is the correct answer.

Step 1: First go to A which is 30m due North (upward) of X.
Step 2: Then go to B which is 40m due West (left) of A.
Step 3: Then go to C which is 30m due North (upward) of B.
Step 4: Finally, reach school at Y which is 40m West (left) of C.

• Indira Gandhi Institute of Development and Research, Goregaon, Mumbai is designed by Ar. Uttam Jain, who was born in 1934 in Melwara, Rajasthan. 
• After establishing his own form in 1961, he involved in projects like, institutional buildings, commercial buildings, recreational facilities, theatres, hotels, university campus, etc. 
• The architect reflects back the heritage in his buildingsdesign. While designing IGIDR, the architect was inspired by Elephanta and Jogeshwari caves, thus lot of arches can be seen in the design.
• The campus was established in 1987.

•  colour is a darker shade of  colour.
• To find what  colour will become. According to the first comparison it has to be a darker shade.
• Thus  colour will be the darker colour of the given colour.
• As options A and C are lighter shades and option D shows a green touch in it. Thus, the options are incorrect.
• Hence, option B is the correct answer. 

Robotics is the field of science and technology which deals with the design, manufacture, and use of robots in various fields like engineering, medicine, etc.
A Robot is an automatically operating machine which replaces human by performing different operations for human.
Hence, the correct answer is 'Robotics'.

Front view of an object shows the width and height dimensions.
Horizontal plane of projection is the plane onto which the Top View of the multi-view drawing is projected. 
Top view of an object shows the width and depth dimensions. 

Indian Ballistic Missile Program is a two-tiered system consisting of two interceptor missiles that help in defence against ballistic missile attacks from enemies. Prithvi Air Defence (PAD) missile is for high altitude interception with an exo-atmospheric range that varies between 50 and 80 km approximately and the Advanced Air Defence (AAD) Missile for low altitude interception with endo-atmospheric range is up to 30 km approximately.
Hence, the correct answer is 'All of these'.

Harmony is a principle of art which refers to how well all the visual elements work together.
Elements which are in harmony should have some kind of logical progression or relationship. It should just look like it works.
Harmony uses the elements of art (color, line, shape, form, value, space, texture) as a vehicle to create a sense of togetherness amongst otherwise separate parts.

The difference is marked and shown below- 

Hence, Option A is correct.

Inspired by the French Gothic style of architecture, Notre Dame is famous for its Rose windows.

They are typical style of Gothic architecture i.e  

1. Flying Buttress.
2. Glass Art. 
3. Towers and The Spire

It also features ribbed vault ceiling and pointed arches.

The first Indian satellite,  Aryabhata named after the famous Indian astronomer Aryabhata. It was designed and fabricated in India but launched by the Kosmos-3M rocket in 1975.
The launch came from an agreement between India and USSR. The agreement allowed the USSR to use Indian ports for tracking ships.1
Therefore, the first Indian satellite, Aryabhata, was launched in the year in 1975.

A triadic colour scheme is comprised of three colours evenly spaced on the colour wheel.
It is used to balanced the colour scheme in a design by balancing between dominant colour and light colour.

A non-linear scene in which there are no parallel lines appearing to meet off in the distance somewhere. Use zero-point perspective when there are no parallel lines in an image to create a sense of depth.