NATA Mock Test - 10 - JEE MCQ

The line equation is given by x/6 = y/3 = z/2, so the direction ratios of the line are <6, 3, 2>.

We know that if a line is perpendicular to a plane, then their direction ratios are proportional.

The equation of a plane passing through a point (x1, y1, z1) and having direction ratios <a, b, c> is:

a(x - x1) + b(y - y1) + c(z - z1) = 0.

For the plane passing through the origin (0, 0, 0) and perpendicular to the line, we use the direction ratios <6, 3, 2>:

6k(x - 0) + 3k(y - 0) + 2k(z - 0) = 0
⇒ 6x + 3y + 2z = 0.

Therefore, the correct answer is A) 6x + 3y + 2z = 0.

Let the three terms be x/y, y/z, and z/x.
The arithmetic mean (AM) of the three terms is 
GM of 3 terms = 
As AM ≥ GM

We know that the symbol ⇔ is used for the connective word "if and only".
Hence, the symbolic form of the statement " ABC is an equilateral triangle if and only if its every interior angle is 60° is p ⇔ q.

Given, 
From direct substitution of the value of x.
= 
= 2

The given equation can be written as
AX = B ⇒ X = A⁻¹ B
Where, 

= (0 + 9)−2(0 − 6) + 1(−3 − 0)
= 9 + 12 − 3 = 18 ≠ 0
∴  A⁻¹  exists
∴  A⁻¹

∴ X = A⁻¹

Differentiate using the chain rule.

Let sinx = t

Substituting the value of  t,

Given: tan 3x = 1
⇒ tan 3x = tan(π/4) ...(i)
Then, the general solution of equation (i) is:
3x = nπ + π/4, n ∈ ℤ
⇒ x = nπ/3 + π/12, n ∈ ℤ
Correct Answer: B. x = nπ/3 + π/12, n ∈ ℤ

Only one out of five horses can win and hence rest four horses lose.
So, the probability that Mr. A has selected the loosing horse 
= 
Therefore, the probability that Mr. A  selected the winning horse = 1 - 3/5 = 2/5

When a complex number z is rotated by an angle θ in the anticlockwise direction, the resultant complex number is given by
z × e^(iθ)
Similarly, here the resultant complex number is given by (iz) × e^(iπ/2) = (iz) × (cos(π/2) + i sin(π/2)) = (iz) × i = -z
Therefore, the complex number representing the new position after rotating iz by an angle π/2 through the origin is -z.

Let the length of the ladder be AC and the height of the wall be AB.

Given:
AC = 10 m and AB = 5 m.

To find θ, we have:

⇒ sin(θ) = AB / AC = 5 / 10 = 1/2

We know that sin(30°) = 1/2.

∴ θ = 30°

Hence, the angle θ made with the horizontal is 30°.

Number of relations on the set A = Number of subsets of A × A = 2ⁿ², thus n(A × A) = n².

Assume the commission received is ₹y.
We can write it as:
Sales: 1000 → 100
Commission: 73 → y
Since more sales lead to more commission, this is a case of direct proportion.
Thus,
1000/73 = 100/y
So,
1000 × y = 73 × 100
y = (73 × 100) / 1000
y = ₹7.30
Hence, the commission he will get on a sale of ₹100.00 is ₹7.30.
The correct answer is A) ₹7.30.

Required Area = 

Mode can be computed by histogram that is mode means the data that repeat mostly
for example 23,23,24,25,26,45,67,34.....(1)
here mode is 23 because it is repeating twice.
Median will be changed if data are changed so (2) is correct.
for example- median of data used in above example(1) is 23,23,24,25,26,34,45,67
is  = 25 + 26 / 2 = 25.5  it can be changed if data is changed.
Variance depends on change of scale so (3) is not correct.

We know, 
100 years contain 5 odd days.
Therefore, last day of the 1st century is Friday.
200 years contain (5 x 2) = 10 extra days = (10 - 7 =  3) odd days.
Therefore, last day of the 2nd century is Wednesday.
300 years contain (5 x 3) = 15 extra days = (10 - 90 = 1) odd day.
Therefore, last day of the 3rd century is Monday.
400 years contain 0 odd day.
Therefore, last day of the 4th century is Sunday.
Since this order is repeat in successive cycles, we see that the last day of a century is not a Tuesday, Thursday or Saturday.

From the given question figure, we get cubes when folded and seen from direction of the arrow, we get two different views for the same cube. (as shown below) 

In option A, the unfolded cube is folded along the number and seen from the direction of the arrow. In this case the dot is visible on the top.
In option C, similarly the unfolded cube is folded along the number and seen from the other direction of the arrow. In this case shaded area is visible on the top.
Thus, the question figure can be folded in a cube and seen in two different views.
Hence, the option B is correct answer.

The codes of the letters are read in the manner of row first and then column.
Considering each option:
A)
55 – S
20 – A
56 – L
59 – E

B)
79 – S
13 – A
69 – L
75 – M

C)
96 – S
13 – A
76 – E
89 – M

D)
67 – S
21 – R
85 – L
97 – M
As can be seen from the codes and letters above, A), C), and D) cannot be the correct answer.
Hence, the correct answer is 79, 13, 69, 75.

According to the question
n = 5p + 2
⇒ n² = (5p + 2)² = (25p2 + 20p) + 4
Therefore dividing by n², 5 will result in a remainder of 4.
Hence, the correct answer is 4.

Nalanda university named after an ancient centre of learning in its vicinity, began its academic session in 2014. It is situated in Bihar. The first chancellor of this university was Amartya Sen who was a nobel laureate. After its completion, it will become the largest university of Asia.

The given image is the texture of the bark of a palm tree.

Coconut tree bark:

Neem tree bark:

Banyan tree bark:

Pisa Cathedral is best known for its campanile, the famous leaning tower of Pisa. 
The large marble church is a magnificent example of Romanesque architecture and filled with art.
Founded in 1064 and consecrated with great pomp on September 26th 1118, the Cathedral was built in two stages
1) Architect Buscheto, who created the original layout with the basilican body with four aisles and one nave, a transept with one nave and two aisles, and the dome on the cross vault,
2) Architect Rainaldo, who extended the building and the façade.

The Persian architecture makes use of abundant symbolic geometry, using pure forms such as the circle and square. Plans are often based on symmetrical layouts featuring rectangular courtyards and halls.
Hence, B option is correct.

• In 2550 BC, the first Giza pyramid project was built as a tomb for the Fourth Dynasty Egyptian pharaoh Khufu.
• Khufu was an ancient Egyptian monarch who was the second pharaoh of the Fourth Dynasty, in the first half of the Old Kingdom period.
• It is the largest pyramid in Giza (481 feet high) built above a plateau.
• The pyramid is made up of 2.3 a million stone blocks weight of 2.5 tons to 15 tons

Nagara or North Indian Temple Style: Nagara temples are characterized by:

• Curvilinear spiral roofs (Shikaras)
• Sanctum sanctorum (Garbagriha)
• Pillared hall (Mandapa). 

While the earliest temples had just shikhara, later temples had several. This style of temples is commonly found in the areas between the Himalayas and Vindhyas. Examples: Temple at Udaigiri, Temple at Sanchi.

There are different names for Nagara Style temple in different parts of India:

• Latina
• Phamsana
• Valabhi type

Basically, there are  kinds of temple architecture:

• Nagara Style
• Dravida Style
• Vesara Style

Note: The most striking feature of Dravida Style architecture is its pyramidal shikhara. They are found mainly in South India.

Hence, only statement 1 is correct regarding Nagara style of temple architecture.

Impression sunrise

• Impression, Sunrise is a painting by Claude Monet first shown at what would become known as the "Exhibition of the Impressionists" in Paris in April, 1874.
• Oscar-Claude Monet was a French painter and founder of impressionist painting who is seen as a key precursor to modernism, especially in his attempts to paint nature as he perceived it
• Impression, Sunrise depicts the port of Le Havre, Monet's hometown. Sunrise was the effects of the rising sun on a scene. The birth of a day affords him the opportunity to depict obviously cold effects in relation to the heat of the rising sun.
• Monet's Impression, Sunrise is considered to encapsulate the start of the impression movement, thus the name.

The definite article 'the' is used in the occasions where both the speaker and reader are familiar with the noun or adjective used in that particular sentence.
As in this example, one may assume that everyone is aware that the U.S.A. (United States of America) is a country.
Here the definite article joins the noun (U.S.A.) with the clause (living in).

The word 'hour' sounds like it starts with the letter 'o', but 'o' is a vowel, hence the most appropriate article that should be used here is 'an'
Hence correct sentence is "Tata Indica goes with a speed of hundred Kilometres an hour"

Ajanta caves are located in Aurangabad district of Maharashtra. It was declared as UNESCO world heritage in 1983. King Upendragupta had built Ajanta caves.

The capital of a column is not only responsible for supporting the upper portion of a structure, known as the entablature, but it also denotes the classical order.
 It mediates between the column and the load thrusting down upon it, broadening the area of the column's supporting surface.