NATA Mock Test - 1 - JEE MCQ

If α, β, and γ are the angles made by a line with the positive direction of the x, y, and z axes respectively, then their direction cosines are given by cos(α), cos(β), and cos(γ).

In this case, the direction cosines of the x-axis are asked. The line is along the x-axis, which makes angles α = 0°, β = 90°, and γ = 90° with the x, y, and z axes respectively.

Therefore, the direction cosines are: (l, m, n) = (cos(0°), cos(90°), cos(90°)) = (1, 0, 0).

Hence, the correct answer is B.

Arithmetic mean, x = (a + b) / 2
Geometric mean, y = √(ab)
Harmonic mean, z = 2ab / (a + b)
Now, let's calculate:
xz = (a + b) / 2 × 2ab / (a + b) = ab
This gives y² = xz
Hence, option B is the correct answer.

A compound sentence formed by two simple statements p and q using connective 'or' is called a disjunction.

Consider  (0/0 form)
Apply L'Hospital's Rule,

 
  [∵sin(π − θ) = sinθ]
= π/3  which lies in the range 
Note: sin⁻¹(sinθ) = θ is only when .

Given equation of the circle is 2x² - ky² - 6x + 4y - 1 = 0
The condition for the equation ax² + by² + 2gx + 2fy + c = 0 to be a circle is a = b ≠ 0.
Therefore, we have -k = 2 ⇒ k = -2.

According to the function given in the problem,
y = sin(t²)
Differentiating both sides with respect to t using the chain rule,

Again differentiating both sides with respect to t using the chain rule,

= 2 cost² + 2t(−sint²)2t
= 2 cos(t²) − 4t²sin(t²)

Given,

⇒ (t³/3 - 8t²/2 + 13t)ᵡ = x sin(a/x)
⇒ (t³/3 - 4t² + 13t) = x sin(a/x)
⇒ (t³/3 - 4t² + 13) = sin(a/x)
⇒ (1/3) (x - 6)² + 1 = sin(a/x)
As the maximum value of the right-hand side is 1 and the minimum value of the left-hand side is 1, equality will hold only if x = 6.
Now, putting x = 6,
sin(a/6) = 1.

Let AB be the pole and AC be its shadow.
Now, AB = AC.
If θ is the angle of elevation of the sun, then:
tan(θ) = AB / AC = AB / AB = 1 = tan(45°)
⇒ θ = 45°

Hence, the angle of elevation of the sun is 45°.

Now,
Domain of R = {2, 4, 7} = B
Range of R = {3, 5, 8} = C
B∩C = {2, 4, 7} ∩ {3, 5, 8} = ∅

The first equation is x + 3 > 0.
⇒ x > −3 ….. (i)
The second equation is 2x < 14.
⇒ x < 7 ….. (ii)
On combining (i) and (ii), we get −3 < x < 7.
⇒ x ∈ (−3, 7)
So, the correct answer is C) (−3, 7).

Given: y = |x − 1|, x = 1, x = 3 & x - axis

Required area = 

= (4 − 2)
= 2 sq.unit.

The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean. Variance tells us the degree of spread in your data set. The more spread the data, the larger the variance is in relation to the mean.
The square root of variance((σ²) is known as standard deviation(σ).

In the given options, 
For option (A),
Required number = 
For option (B),
Ascending order
8, 9, 17, 19, 25, 71, 85
For option (3),

For option (D),
Required numbers = = 2.8 or 2.9 or  3.0,3.5 etc.
There can be infinite numbers that are greater than 2.7.
Hence, ''Write any four numbers greater than 2.7'' is the correct answer.

There are 6 persons namely:
Geeta, Sadhana, Shilpa, Deepa, Meeta and Sunita.
According to the question.
Geeta > Shilpa and Deepa > Meeta
From statement I: Sadhana is taller than Sunita.
Sadhana > Sunita
Therefore, Sadhana > Sunita, Geeta > Shilpa and Deepa > Meeta
From statement II: Sadhana is taller than Shilpa and Meeta as well as Deepa.
Sadhana > (Shilpa, Meeta, Deepa).
From both the statements, we have
Sadhana > (Shilpa, Deepa > Meeta, Sunita)
But, also Geeta > Shilpa.
Therefore, Sadhana/Geeta > (Shilpa, Deepa > Meeta, Sunita).
So, either Sadhana or Geeta may be tallest.

The sequence in numerators is +5, +10, +20,.
The sequence in denominator is +11, +22, +44,..
So, numerator of missing fraction = 9 + 10 = 19
Denominator of missing fraction =20 + 22 = 42
So, the missing fraction is 19/42.

According to the question cost of one apple is Rs. 7, cost of mango is Rs. 5 each and total of Rs. 38 are spend on fruits so the purchase of apply will be
Let number of apples and mangoes is x and y.

Y is a whole number if  38 − 7x is divisible by 5 5
It will be possible when x = 4
Therefore, the correct answer is 4

Given:
Rajan is tenth from the right and Suraj is tenth from the left.
It can be represented as,

From the above picture, As the position of boys is equal from both ends, Rajan will also be 27th from the right after changing positions.
Thus, the answer is none of these.

The correct option is D.
From the question figure it can be seen that the dots at the triangular part are in the opposite face.
In th given option A, B And C, dot in the triangle are in adjacent faces. 
In the given option D, only single dot is visible which means that other dot is in the face opposite to it, which can not be seen in the given view.
As shown below.

Therefore, correct option is 'D'.

• Sir Isaac Newton, a physicist and mathematician, experimented with sunlight and prisms.
• To understand the rainbow, he refracted white light with a prism, resolving it into 77 different colours.
• He demonstrated that clear white light was composed of seven visible colours which were known as ROYGBIV colours (red, orange, yellow, green, blue, indigo, and violet).

In the given figure, we can see that the position of the arrow and the circle on either side with dotted line running through the centre of the sheet. The sheet is divided equally on both sides forming a "V" figure.
Hence, after folding from the centre arrow and circle should  overlap.
In the given figures 1 and 3 when the sheet is folded along the dotted line then, the circle and arrow are not overlapping each other.
In figure 4, circle and arrow are overlapping, but the lines are form a 'X' shape instead of 'V' as question figure.
In figure 2, circle and arrow are overlapping each other , forming 'V shaped figure.
Thus, the option B is correct answer.

Grey colour creates a dull, moody and sad effect on our mind and body.
Gray is considered an unemotional colour as it can make one feel detached or neutral.
It evokes feelings of sadness or depression, loneliness and isolation. 

A building envelope is the physical separator between the conditioned and unconditioned environment of a building including the resistance to air, water, heat, light and noise transfer.
The many functions of the building envelope can be separated into three categories: 

• Support (to resist and transfer structural and dynamic loads)
• Control (the flow of matter and energy of all types)
• Finish (to meet desired aesthetics on the inside and outside.

'Exaggerate' means to overstate or to describe more than is fact,
For example:
a) I've told you a billion times not to exaggerate! Why can't you ever take things as they are! What is the need for this exaggeration!
b) He said he had a lot of girlfriends in college, but I know he's exaggerating. The real number is about ten.
Hence, the correct option is "exaggerate".

Texture is defined as are the patterns of variations upon a solid surface.
The actual way a surface feels when it is felt or touched, such as rough, smooth, soft, hard, silky, slimy, sticky, etc. 3-D art such as sculpture, paintings and architectural structures are tactile because they can be felt.

Goethe was a scientist who did not agree with newton and discovered his own colour wheel with 12 colours.
He became the first person who explored colour and colour theory.
His statement was:
''Light and darkness, brightness and obscurity, or if a more general expression is preferred, light and its absence, one necessary to the production of colour. . . Colour itself is a degree of darkness.''
Below is the image of colour wheel that he drew according to his research. 

In the given Series, 

1. In the first figure, the dot and arrowheads are approaching the same point.
2. In the second figure, they are travelling in the opposite direction with inward segment.
3. In the third Step, they are travelling in the same direction with inward segments.
4. In the fourth step, they will travel in the same direction with outward segment.

The Complete Series will look like the following.

Hence, Option D is correct

The world's first ever thermal battery plant was established in Andhra Pradesh. The largest source of energy is the thermal energy which  has been contributing almost 71% of electricity and 85% of which is coal-based.
Hence, the correct answer is Andhra Pradesh.

The visual appearance and characteristic of the object given by the size, shape and density of the element.
In design texture is associated with the sense of feel of the element.
Texture can also be described as the way three-dimensional work actually feels when touched or visual feel of a two-dimensional work. 
Example of different textures.

• Rainbow appear in seven colours when water droplets break white light into seven colours.
• The rainbow spectrum is called ROYGBIV.
• They are red, orange, yellow, green, blue, indigo and violet.