NATA Sample Papers & Mock Test - 2 Free Online Test 2026

As,  lies in the plane of the vectors  and , So, 

Compare with 

Not in option
So, now consider 

Compare with 

Given function f(x) = x².Observe that as x takes value very close to 0, the value of f(x) also approaches to 0.
We say 
(i.e., the limit of f(x) as x tends to zero equals zero).

Given:
2 tan²θ = sec²θ
We know: sec²θ = 1 + tan²θ
So,
2 tan²θ = 1 + tan²θ
⇒ tan²θ = 1
⇒ tan²θ = (tan(π/4))²
⇒ θ = nπ ± π/4

Smallest angle is opposite to smaller side

⇒∠C = 30°

The formula to calculate the distance of a point (x, y, z) from the Y-axis is given by:
Distance = √(x² + z²).

For the point (4, 3, 5),
x = 4, y = 3, z = 5.

Thus,
Distance = √(4² + 5²) = √(16 + 25) = √41.

Therefore, the correct answer is C.

Given quadratic equations are:
(6k + 2)x² + rx + (3k - 1) = 0
(12k + 4)x² + px + (6k - 2) = 0
Quadratic equations a₁x² + b₁x + c₁ = 0 and a₂x² + b₂x + c₂ = 0 will have both roots common if a₁/a₂ = b₁/b₂ = c₁/c₂.
Applying the condition for both roots common, we get:
​​​​​​​

Mean of the height of the plants is:

Calculation for variance for the above data is as follows:

 

The formula to find variance for the given data is:

Hence, variance of the height of the plants is 459.

Given that,
If f is an odd function 
As, 
here  f(x) = x³cos³x
We will see f(−x) = (−x)³cos³(−x)
= -x³cos³x
Therefore, f(x) is a odd function,

Given the expression (2x + 3y)¹⁷, the number of terms in the expansion of (a + b)ⁿ is n + 1.
Here, n = 17.
So, the number of terms is n + 1 = 17 + 1 = 18.
Therefore, the number of terms in the expansion of (2x + 3y)¹⁷ is 18.
Thus, the correct answer is C) 18.

Let the point B be (x, -3) and A be (0,1).
Given that AB = 5, we use the distance formula:

√[x² + (1 + 3)²] = 5
⇒ √[x² + 16] = 5

Squaring both sides:
x² + 16 = 25
⇒ x² = 25 - 16
⇒ x² = 9
⇒ x = ±3

So, the possible values of x are x = 3 or x = -3.

According to the data given in the problem,
F = −kx
The standard equation of the straight line is y = mx + c.
Comparing the given equations with the standard equation of straight line, the intercept is zero.
Hence, the graph is passing through the origin.
The slope is negative.

Let
z = 1 / (i - 1)
We know that, conjugate of a complex number z = a + ib, denoted by z̅. It is defined as
z̅ = a - ib.
⇒ z = (i + 1) / (i² - 1) (multiplying and dividing by i + 1)
⇒ z = (i + 1) / (-2)
Now, conjugate of z is
z̅ = (1 - i) / (-2)
⇒ z̅ = -2 / (2(1 + i))Finally, conjugate of z is z̅ = -1 / (i + 1)

Code for the weekdays

 Find the day on 1st March 2005.
1st March 2005 = (2004 years + Period from 1.1.2005 to 1.5.2005)
Odd days in1600 years = 0
Odd days in 400 years = 0
Jan. Feb. March
(31 + 28 + 1) Days = 60 days = 0 odd days.
Total odd days = 0 + 0 + 0 = 0
On 1st March 2005, it was Tuesday.
In March 2005 Friday falls on the 4th, 11th, 18th, and 25th.

Given,

Analysing the pattern, it can be concluded that one extra small line is added in each step in anti -clockwise.
The small line segment attached to the main figure moves 2,1, 3,1, 4,... spaces clockwise sequentially.
Following the same pattern we have the below image:

Hence, the above image is the correct answer.

Note: i). T-2020 World Cup is being organized by Australia. 
ii). Different teams are participating in the T-2020 World Cup. 

Directions are given below:
I). seven new teams which are participating for the first time are - Afghanistan, Nepal, UAE, Australia, Netherlands, Hong Kong and Ireland. 
II). Matches at different places: Melbourne, Canberra, Adelaide, Darwin, Brisbane, Perth and Hobart.

Conditions:

• Afghanistan will be playing at Canberra, but neither on Friday nor on Monday.
• The host country will be playing on Thursday at Brisbane.
• There is a gap of one day between Afghanistan and Australia match.
• Hong Kong will be playing the match before Ireland but after Netherlands at Adelaide on Wednesday.
• Ireland will be playing on the last day of the week.
• Nepal will be playing at Hobart.
• No match will be played at Melbourne on Monday.
• The match at Perth will be played on the last day of the week.
• The match at Darwin will be played on Tuesday.
• No match will be played at Hobart on Tuesday and Friday.

After observing above points we draw a table as follows:

So, correct combination is Nepal-Monday.
Hence, option IV is correct. 

According to the question
The letters given and, the codes are corresponds to each other and vice versa ,
C, W,  E,  A,  Z,  X,  J,  Y,  K,  L  
3, 9, 5, 7, 4, 8, 1, 0, 2, 6
To find the code for the letters given 
J, W, X, C, L,  Z
Using the previous codes for the letters, we get :

Hence the correct answer is 198634.

Logic: Addition of five (+5) is applied on set.

The Pattern is as follows:
23 + 5 = 28, 28 + 5 = 33
26 + 5 = 31, 31 + 5 = 36
17 + 5 = 22, 22 + 5 = 27

But,
14 + 5 = 19, 19 + 5 = 24 ≠ 25
So, the logic of this set is different from others.

Hence, (14, 19, 25) is the correct answer.

The given question, the following relation can be obtained as:
The options A and B are ruled out, as the circle in the both options is coming before the rectangle at the start.
The option C is also ruled out as the circle in the option is placed in the wrong position after the rectangle at the start.
The option D is correct as the circle is placed in the right position after the rectangle at the start.
Hence, the correct option is D

Inclined letters are single stroke letters which lean to the right making a slope of 75 degree with the horizontal as per the guidance of Indian standards. These are not recommended for beginners until they have mastered in vertical lettering. Inclined and vertical lettering should never appear on the same drawing .

Sigle stroke lettering resembles uniformly in the lines thickness which can be obtained in one stroke. One stroke resembles the uniform lead diameter.

The total length of the railway line in Andhra Pradesh was about 5046 km, but it becomes 3703.25 km after the formation of Telangana from Andhra Pradesh. The total rail density of the state is 16.59 per 1000 km.

Chiaroscuro, from Italian chiaro, “light,” and scuro, “dark”, technique employed in the visual arts to represent light and shadow as they define three-dimensional objects.
It refers to the use of light and shadow to create the illusion of light from a specific source shining on the figures and objects in the painting.

The colour circle is defined as a diagram with a continuous sequence of hues arranged in the order of the spectrum.
The circular arrangement of colours organised with relationship to each other is also known as colour circles.
The first colour wheel has been attributed to Sir Isaac Newton, who in 1706 arranged red, orange, yellow, green, blue, indigo, and violet into a natural progression on a rotating disk. As the disk spins, the colours blur together so rapidly that the human eye sees white.

Climate is the long-term weather pattern in an area, typically averaged over 3030 years. 
Climate is divide into

• Tropical.
• Dry.
• Temperate.
• Continental.
• Polar.

Topography is the relief of an area. If an area is close to a body of water it tends to make milder climates. Mountainous areas tend to have more extreme weather because it acts as a barrier to air movements and moisture.

Change in the temperature, rainfall, and climate pattern, result in change in vegetation of various plant. The nutrient cycles, microbial activities, as well as physiological activities of plants will vary due to the change in climate.

Catastrophic - involving or causing sudden great damage or suffering
Mysterious - that you do not understand or cannot explain; strange Tough - difficult; having or causing problems
Disastrous - terrible, harmful or failing completely
Delicate - easy to damage or break
Here in the given question, the term catastrophic is closely related to the meaning of the term disastrous and hence disastrous is the correct answer.

Pantone matching system colours are the specific colour formula to reproduce accurately in print or standardized colour matching. They are also known as a spot colour.
Spot colour is useful for documents that require only a few colours, such as newsletters, brochures and stationery.
Spot colour is also used to match specific colours very closely.

Fluorescent lamps are a lamp type that is commonly used to provide illumination for settings such as commercial lighting, industrial lighting, classroom lighting, and retail lighting.

• The sizes, light colours, and wattage of fluorescent tubes vary significantly.
• Like sunlight, fluorescent light is also white light, and it is also made up of many wavelengths.

As we know, the English Alphabet consists of 26 letters.
Assume – 228 = LS
Thus,
228 = L(12) × S(19) (as per alphabet placement in numbers)
Assume ‘?’ as x
Similarly,
378 = R × X
378 = 18 × X
X = 378 / 18
X = 21
Number 21 is U, when alphabets are placed numerically.
Thus, correct answer is option B.

• 32 storey high structure with climatic sensitivity as per the requirement of a growing city.
• The building is 28 storeys (85 metres) high and square in plan: 21 meters x 21 meters.
• The basic interlock is that of a three and four-bedroom apartment with the larger flats formed by the addition of another half level.
• The orientation of the building is based on the climatic effect of the sunlight and cool breeze from the sea.