NATA Mock Test - 6 - JEE MCQ

Given the point P(α,β,γ) and the point on the y-axis (0,β,0).

The distance between two points (a,b,c) and (p,q,r) is given by the formula:

Substituting the values of the given points:

Required distance =

Given: (3x − 5/y) raised to the power of 10
The number of terms in the expansion of (a + b) raised to the power of n is n + 1 terms.
Here, n = 10
So, n + 1 = 10 + 1 = 11
Therefore, the number of terms in the expansion of (3x − 5y) raised to the power of 10 is 11.
Thus, the correct answer is B) 11.

As we know, sin⁻¹(x) = θ ↔ sin(θ) = x, -1 ≤ x ≤ 1 & -π/2 ≤ θ ≤ π/2,
cos⁻¹(x) = θ ↔ cos(θ) = x, -1 ≤ x ≤ 1 & 0 ≤ θ ≤ π.
Therefore,
cos⁻¹(1/2) + 2sin⁻¹(1/2) = π/3 + 2π/6 = 2π/3.

The given function is y = 2sin(x)
We need to find dy/dx.
We know,

Now, on differentiating both sides with respect to x, we get,
 (using equation (2))
 (using equation (3))

Given that, the trigonometric equation is tan θ = 0
⇒ (sin θ / cos θ) = 0
⇒ sin θ = 0
The principal values of sin θ = 0 are: 0, π, 2π, ...
⇒ θ = nπ, n ∈ ℤ
Thus, the general solution of the given trigonometric equation is:
θ = nπ, n ∈ ℤ

Given p₁ + p₂ + p₃ = 0.8......(i) and p₂ + p₃ + p₄ = 0.9......(ii)
We know that the sum of the probabilities in a probability distribution is always 1
⇒ p₁ + p₂ + p₃ + p₄ = 1
⇒ 0.8 + p₄ = 1  { from (i) }
⇒ p₄ = 0.2
And p₁ + 0.9 = 1  { from (ii) }
⇒ p₁ = 0.1

So, p₁ + p₄ = 0.1 + 0.2 = 0.3
And p₂ + p₃ = 1 − 0.3 = 0.7

Given that,
z³ + iz - 1 = 0
Let one real root of the given cubic equation be z
Let z = α, (α ∈ R)

⇒ α³ + iα - 1 = 0
⇒ (α³ - 1) + iα = 0 + 0i
Comparing real and imaginary parts, we get
α³ - 1 = 0 and α = 0
⇒ α = 1 and α = 0, which is not possible simultaneously.
So, the given equation has no real roots.

Let R be a relation on N defined by x + 2y = 8, which gives x = 8 - 2y.
Substituting values for y = 1, 2, 3, we get the corresponding values of x = 6, 4, 2.
Thus, R = {(2, 3), (4, 2), (6, 1)}.
Hence, the domain of R is {2, 4, 6}.

Required Area = 
= 
= 1/2 - 1/3
= 1/6

We have:
∑x = 15, ∑y = 36, ∑xy = 110, n = 5
and x̄ = (1/5) ∑x = 15/5 = 3, ȳ = (1/5) ∑y = 36/5 = 7.2

We know,
Cov(x, y) = (1/n) ∑xy - x̄ȳ

= 2/5

Let us first calculate the number of days from January 1^st to February 4th, 2004.
Since the whole of January will be considered as we have to find the day on 1^st Jan, the number of days in Jan is 31 days.
In Feb, since we have to calculate to 4th Feb, there are only 3 days before 4th Feb.
Therefore, the number of days between 1st Jan To 4th Feb will be =  31 + 3 = 34 days. 
To calculate the number of odd days,
34 / 7 = 4 weeks and 6 days.
There are 6 odd days 
Therefore, calculate 6 days backwards from Monday = Tuesday
So, 1st January, 2004 was on Tuesday.

As we know, when an open cube is folded, the alternate faces of the open cube appear on the opposite faces of the cube.
Also, the side faces are opposite to each other.
The opposite faces are shown below:

Thus, the pair of opposite faces are:

From the options, the correct pair of opposite faces is + and @.
Therefore, the correct answer is + and @.

In this question, we have given some statements. Now, we have to deduce the answer as per the question asked for.
Given that,
L − M + K ÷ F
According to the above condition,
'L − M' means LL is the wife of M.
'M + K' means MM is the brother of K.
'K ÷ F' means KK is the brother of F.
Gender of FF cannot be determined. FF is either son or daughter.
So, we cannot determine the answer.
Hence, the correct answer is option D.

In the figure given for reference, 'T' shaped is added in the latter and rest are aligned as if they are forming a triangle. 
Now, apply the same to get the answer
'Arrow' shaped should be added and rest should be aligned as given above.

In the given questions, 

The given letters are arranged according to there number value. Then the corresponding letters of the words in the code are decreases by 3.

P(16 )− 3 = M(13)
Similarly:

Therefore, DIG is the code for AFD word.

In the given question,
Tall, Huge and Thin are dimensions while Sharp is not a dimension.
Sharp is property of some tool or defines a tangible property of an article.

When the question figure has been rotated clockwise by 180°angle ,the answer figure gets inverted
The given question figure contains the shape of a circle with the triangles inside it with one dot on the top right side of the circle when rotated will give an inverted figure with given dot will get shifted to the bottom left side of the circle. 
In option A, when the question image is rotated at 180 we get figure with dot on the left corner of the circle.(as shown below)

Hence, the option A is correct answer.

• Santiago Calatrava Valls (born 29 July 1951) is a Spanish architect, structural engineer, sculptor and painter.
• He is known for his bridges supported by single leaning pylons, and his railway stations, stadiums, and museums, whose sculptural forms often resemble living organisms.
• His best-known works include
• The Olympic Sports Complex of Athens,
• The Milwaukee Art Museum,
• The Turning Torso tower in Malmö, Sweden,
• The World Trade Center Transportation Hub in New York City
• The Auditorio de Tenerife in Santa Cruz de Tenerife. 

• It is Designed by Kenzo Tange and built between 19611and 1964.
• it hosted swimming and diving events at the 1964 Summer Olympics.
• During these games, different extensions were used for basketball competitions. We will also hold a handball tournament at the  2020 Summer Olympics.
• This design influenced Frei Otto's arena design at the Olympic Stadium in Munich. 

Hence,Option A is correct.

A vanishing point is a point on the image plane of a perspective drawing where the two-dimensional perspective projections of mutually parallel lines in three-dimensional space appear to converge.
A vanishing point is placed on the horizon line, before basics shapes are drawn.
zero-point perspective is used to draw a non-linear scene in which there are no parallel lines appearing to meet off in the distance somewhere. Thus, no vanishing point.

Contrast is the practice of making design elements look different from each other such that stand out.
A high contrast image has a wide range of tones full of blacks and whites with dark shadows and bright highlights. 
These images will have intense colors and deep textures, creating very profound end results.

The World Bank is not a principal organ of the United Nations.
The World Bank is an international financial institution that provides loans and grants to the governments of low-and middle-income countries for the purpose of pursuing capital projects.
The United Nations has six principal organs: the General Assembly, the Security Council, the Economic and Social Council, the Trusteeship Council, the International Court of Justice, and the Secretariat.

The correct article that should be used here is 'an'.
The reason for that is, we always use 'an' as an article before vowels.
Here, 'Interesting' is a vowel.
Hence the correct sentence is "I saw an Interesting film last week."

The correct article that should be used here is 'an'.
The reason for that is, we always use 'an' as an article before vowels.
Vowels are words that sound like they begin with a,e, i,o,u.
Hence the correct sentence is "She is an American."

The colours which are created by combining two primary colours are called secondary colours.
They are located between the primary colours on the colour wheel.
Example of Secondary colour :-  
Red +Green = Yellow
Green+ Blue = Cyan
Blue+ Red = Magenta

A bay window is a window space that is projecting outward from the main walls of a building and forms a bay in a room.
It is Originated from houses in San Francisco having windows that are overlooking the bay.

Hence, Option D is correct answer.

Absolute dating is the process of determining an age on a specified chronology in archaeology and geology. Some scientists prefer the terms chronometric or calendar dating, as use of the word "absolute" implies an unwarranted certainty of accuracy. 
A relative date is a period of time that is relative to the current date.

The Nuclear Suppliers Consortium (NSG) is a multilateral export control system and a group of nuclear supplier countries whose goal is to prevent nuclear proliferation by limiting the export of materials, equipment, and technology that can be used to make nuclear weapons.
In 1974, the Nuclear Supplier Group was formed with the goal of preventing nuclear proliferation. 
It now has 48 countries as members.
Hence, the correct answer is 1 and 2.

The minimum width of the landing is equal to the width of the stairs.
The size of the tread generally ranges from 270 mm for residential buildings and 300 mm for public buildings.
The greater size allows easier moveability.

Pigment colours are defined as a substance that imparts black or white or a colour to other materials.They are also called colourants.
It is a powdered substance that is mixed with a liquid and are completely insoluble 
There are ten pigment codes that refer to the ten basic categories of pigments:
PY = Pigment Yellow.
PO = Pigment Orange.
PR = Pigment Red.
Examples - Cadmium pigments, Chromium pigments.