NATA Mock Test - 8 - JEE MCQ

The word APPLE contains 5 letters, which can be arranged in 5! ways, but the letter P is repeated twice.
Thus, the required number of ways = 5! / 2! = 60.
Hence, the correct answer is 60.

The centre of the circle is (-a, -b) and the radius is √(a² - b²).
So, the equation of the circle is (x + a)² + (y + b)² = (√(a² - b²))².
⇒ x² + y² + 2ax + 2by + 2b² = 0
Hence, the correct answer is A: x² + y² + 2ax + 2by + 2b² = 0.

To find: The principal value of cosec⁻¹(−√2)
Let the principal value be given by x.
i.e. x = cosec⁻¹(−√2)
⇒ cosec x = −√2
⇒ cosec x = −cosec(π/4) [∴ cosec(π/4) = √2]
∴ cosec x = cosec(−π/4) [∴ −cosec(π/4) = cosec(−x)]
Taking cosec⁻¹ on both sides:
x = −π/4
Hence, the principal value is −π/4.

Let 

Let, x⁶ = t
Differentiate w.r.t.  x,

Using formula

Now, 

Hence, correct option is (A)

Given, r = 0.8 and bᵧₓ = 0.2
∴ r² = bₓᵧ * bᵧₓ⇒ (0.8)² = bₓᵧ * (0.2)
⇒ 0.64 = bₓᵧ * 0.2
⇒ bₓᵧ = 0.64 / 0.2 = 3.2
Hence, the regression coefficient bₓᵧ = 3.2.

If log₁₀a, log₁₀b, log₁₀c are in A.P.,
Then, by the formula:
y = (x + z) / 2,
where:
x = log₁₀a,
y = log₁₀b,
z = log₁₀c.

This leads to:
log₁₀b = (log₁₀a + log₁₀c) / 2
⇒ 2log₁₀b = log₁₀a + log₁₀c
⇒ log₁₀(b²) = log₁₀(ac)
⇒ b² = ac

This is the condition for the variables to be in G.P.

Hence, the correct answer is B.

Checking by option one by one:

(i) For n = 1, the value of the expression 47^n + 16^n - 1 is 62, which is not divisible by 4. Hence, this option is discarded.

(ii) For n = 1, the value of the expression 2(42^n + 1) - 33^n + 1 is 47, which is not divisible by 9. Hence, this option is discarded.

(iii) For n = 2, the value of the expression 4^n - 3^n - 1 is 9, which is not divisible by 11. Hence, this option is discarded.

(iv) For any value of n, this option always satisfies the condition for divisibility by 17, and hence this is the correct option.

using the properties


= 9 + 36 − 343 = −298.

x² + bx + c = 0 ...(i)

Roots are α, β.

Given that α - 2 = 1/α and β - 2 = 1/β

⇒ α² - 2α - 1 = 0 & β² - 2β - 1 = 0 ...(ii)

This means that α, β are the roots of x² - 2x - 1 = 0 ...(ii)

Comparing (i) and (ii), we get:

b = -2, c = -1

⇒ b² + c² = 5

Hence, the correct answer is 5.

Given,


Vectors  and  are parallel in the same direction and vectors  and  are also parallel but are in the opposite direction.
Hence,  and  are in opposite directions.
So, the angle between them is π.

Assuming, if today is x−day, it will repeat after 7 days.
Example, let us say today is Thursday, so after 7 days it will occur again.
For further occurrence, this day will occur also after 14, 21, 28,... days.
Or we can say that after multiples of 7 days, the day will repeat itself.
So, according to the question: 50 / 7 = 7 (remainder = 1)
Hence, after 49 days Thursday will occur, and on the 50^th day it will be Friday!

As per the question figure, when the block are numbered, when folded cube should not have any visible shaded block. (as shown below)

Therefore,
In option A, we have only 2 shaded sides, in this pic the shaded sides are located in invisible side.
In option B, while folding the two shaded side are visible.
In option C, while folding the two shaded side are visible.
In option D, while folding the two shaded side are visible.
Thus, option A is correct answer.

In the given question we have to find the relation between N and P.

• M’s son is Q’s brother
• P and Q are sisters

It means M is the father of P. 
M and N are brothers
Thus, N is the uncle of P.
So, the correct answer is option (B).

In the given figure series
An element is moving 90ºClock-wise and every time a new element is getting added alternately. Then newly added element is moved clockwise, and new elements is added. 

• In figure 2, square is moves clockwise in figure and new element circle is added.

Similarly,

• In figure 3, circle moves clockwise and triangle is added.
• In figure 4, triangle moves clockwise and a plus sign is added.

To complete the sequence , in option figure plus sign should be moved clockwise from its current position and a new element is to be added.

• In option B, plus sign move clockwise, but the element added i.e triangle is a repeated element.
• In option C,  both the elements are not as per the description 
• In option D, plus sign moves clockwise but two places clockwise and triangle is repeated element.

In option A. plus sign moves clockwise and new element a shaded star is added. Thus, it fulfils the requirement to complete the series. 

Hence, the answer is option .

Total number of members: Seven
R likes Orange and his favourite sport is Cricket. The one who likes Pink does not like Chess. Therefore, his favourite sport is Football.
Q's favourite sport is shooting, and he likes Black. S likes Red. W likes Basketball. P likes Volleyball. T likes Pink.

The one who likes Volleyball does not like Brown and Green. Therefore, he likes blue.
The one who likes Basketball does not like Green. Therefore, he likes brown.
V's choice of colour is neither Blue nor Black. Therefore, he likes green. T's favourite sport is neither Hockey nor Basketball. 
The final arrangement is:

Therefore, V likes green colour.
Hence, 'green' is the correct answer.

According to the question, the given figure:

In the first figure, the hexagon is inscribed in a circle and in the second figure the circle is inscribed in the hexagon.
Similarly,
In the third circle, the pentagon is inscribed in a triangle and in the fourth figure the triangle must be inscribed in a pentagon.
Hence, Option D is the correct option.

Warm humid climates are characterised by long periods of warm weather in which outdoor and semi-outdoor environments are considered more conducive than indoor environments especially when there is no air-conditioning.
Design ideas to build in Warm humid climate
1) Make smart use of air conditioning
2) Consider position of the sun while designing.
3) UV deflecting glass for windows and doors
4) Waterproof material for roof.
5) Insulating materials for the walls.

Red is used in depicting many things, all of them are potent.
Red is popularly used to specify romantic love, and its physical passion ,at the same time it even depicts violence, anger, and aggression, that indicates danger.
Paradoxically–for a colour associated with action and energy–red is universally used as the colour that means "stop."

• A bay window is a window space projecting outward from the main walls of the building and forming a bay in a room.
• It is a multi-panel window set in a wall that projects out from the rest of the house.
• A bay window is also known as an oriel or oriel window when it projects from an upper story and is supported by corbels.

The Exterior and interior look of the window is shown below.

Earthquakes contribute to environmental pollution by rendering a large number of dust particles into the air while the automobiles and industries contribute to pollution by the emission of harmful gases and chemicals into the air and water bodies. Sewage also is responsible for the pollution of water bodies.
All these sources, other than Earthquake are artificial sources of pollution while the earthquake is a natural source.

The Visual Elements of art are Line, Shape, Tone, Colour, Pattern, Texture and Form. When we analyse any drawing, painting, sculpture or design, we examine these component parts to see how they combine to create the overall effect of the artwork.

Example- 

• Lines cross over one another to form shapes.
• Shapes can be filled with tone and Colour, or repeated to create pattern
• A shape may be rendered with a rough surface to create a texture.

The indefinite article 'a' is should be used here.
They are used to refer to a person or a thing that needs to be represented as a group or a single entity even though the group is formed up using singular individuals.
As in this example, we refer to a dozen of oranges as a group or single entity.
The article 'a' connects the noun (a dozen oranges) to the verb (bought).

Colour theory was first given by Aristotle.

• He believed that it was sent by God from Heaven through celestial rays.
• According to him, all colours came from lightness and darkness and related them to water, earth, fire and air. 
• A formalization of "colour theory" began in the 18th century, initially within a partisan controversy over Isaac Newton's theory of colour.

A retarder is used to increase the initial setting time of the cement.
The substance added as a retarder usually slow down the rate of a chemical change.
Gypsum retarder contain 4 types-

1. Organic acids
2. Phosphates
3. Proteins
4. Composite retarder

• Shape refers to a structure that can plainly be reflected on a plain sheet of paper in just two dimensions.
• Certain examples are circle, rectangle, square, etc.
• Form refers to the structure happens to be a three-dimensional one and cannot be painted on a plain sheet.
• It contains the length, width, and depth of certain objects, and it cannot be reflected on the plain sheet of paper
• These two are separate from each other in terms of perception and point of view as well.

Nitrogen dioxide (NO₂), sulphur dioxide (SO₂), and carbon monoxide gas are important ambient air pollutants. High-intensity, confined space exposure to NO₂ Has caused catastrophic injury to humans, including death. Sulfur dioxide (SO₂) Contributes to respiratory symptoms in healthy patients and people with the underlying pulmonary disease; chronic exposure to carbon monoxide gas is related to an increased risk for adverse cardiopulmonary events, including death.
So, option C is the correct answer.

Vincent Willem van Gogh was a Dutch Post-Impressionist painter who posthumously became one of the most famous and influential figures in Western art history.
The Starry Night is an impressionist style of oil-on-canvas painting, painted in June 1889.
The painting was painted in the year 1889 during his stay in Saint-Paul asylum in Saint-Remy, France during his breakdown and the mutilation of his left year.
The painting is a scene showing just before sunrise, with the addition of an imaginary village.

The Finger Plan is an urban plan from 1947 which provides a strategy for the development of the Copenhagen metropolitan area, Denmark.

• According to the plan, Copenhagen is to develop along five 'fingers', centered on S-train commuter rail lines, which extend from the 'palm', that is the dense urban fabric of central Copenhagen. In between the fingers, green "wedges" are intended to provide land for agriculture and recreational purposes.
• The Finger Plan for Greater Copenhagen was introduced in 1947 when a group of town planners realized that Greater Copenhagen was beginning to spread uncontrollably.

Hatching and cross-hatching are linear drawing techniques that can be used to create texture, value, and the illusion of form and light.

• Hatching is created when non-crossing lines are used to indicate the value on or around an object.
• The value added to the object is dependent on the location of a light source. 
• When cross-hatching is used, artist is adding value as hatching, by allowing the lines to cross over each other.  
• The more that the lines cross over each other, the darker the value becomes. 

Any colour that is vivid or bold in nature is termed as warm colour.

• They contrast with cool colours.
• They tend to be advanced in space.
• Warm colours are stimulating and they heighten emotions.
• They are used to conveying messages of happiness, sociability and energy.