NATA Mock Test - 6 - JEE MCQ

If the terms a, b, c are in H.P., then
2b = 1/a + 1/c.

Now, substitute the value of 1/b in the line equation and equate the coefficients. This will give the required solution.

The correct point is (1, −2).
Hence, the correct answer is B.

If we treat the two L's as one letter, then there will be 10 letters, of which there are two A's and two E's. Also, the two L's, which are together, can be arranged in just one way.
The number of ways of arranging n things in which p are alike of one type and q are alike of another type is given by:
Total number of arrangements = n! / (p! × q!)
In this case, the total number of arrangements = 10! / (2! × 2!).
Hence, the correct answer is 10! / (2! × 2!).

Given, 
= 
= 
= n
Hence, the required answer is n.

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.

S₁₁ = -16
1 + 36 + 4 - 36 - a = -16
a = 5 + 16 = 21
Hence, the correct answer is D: 21.

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

The integration formula,
∫sinx dx = −cosx + C

Let AB be the pole and let AC be its shadow.

Let the length of the shadow be x meters.

Then, the height of the pole = √3 * x meters.

If θ is the angle of elevation of the sun, then:

tan(θ) = (√3 * x) / x = √3 = tan(60°)

∴ θ = 60°

Hence, the angle of elevation of the sun is 60°.

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}.

= 
= 2 - 2
= 0

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

The y-axis divides the line joining (-3, -4) and (1, -2) in some ratio m : n. Using the section formula, the x-coordinate of the dividing point is given by:
0 = (m × 1 + n × (-3)) / (m + n)
0 = (m - 3n) / (m + n)
m - 3n = 0
m = 3n
m/n = 3/1
The required ratio is 3:1.
Correct answer: Option C: 3 : 1.

Based on the information given, we can understand that a letter can be represented by a couple of numbers.
But the same letter can also have many couple of numbers by which it can be represented.
The representation should be the number of the row as 1^st digit and the number of the column as 2^nd digit.
MANGO is to be represented by numbers from the matrices.
Following is the representation of the letters:
M: 75, 20
A: 03, 34, 86, 97
N: 12, 21, 40, 42, 58, 65, 79, 95
G: 00, 13, 59,
O: 11, 30, 57, 78, 89
The set of numbers that correctly represent all the letters are  75, 34, 58, 13, 30.
Hence, 75, 34, 58, 13, 30 is the correct answer.

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 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. 

The President position is voted by the United Nations General Assembly (UNGA) representatives on a yearly basis. He presides over the sessions of the General Assembly. The Nigerian Tijjani Muhammad-Bande was elected as the President of the 74th session of the UN General Assembly on 4th June 2019 and later succeeded María Fernanda Espinosa.
Hence, the correct answer is 'Tiijani Muhammad-Bande'.

• 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.

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 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

Caryatid is the sculpted female figure supporting an entablature on her head.
They are used in the place of the column as the support on a building.
They were especially used in the Ionic tower.

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.

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.