NATA Sample Papers & Mock Test - 10 Free Online Test 2026

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

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

We know, 

Let the radius of the circle C₂ be r cm.
Given, the radius of the circle C₁ is 3 cm.
Distance between their centres = 10 cm
The length of the transverse common tangent = 5√3 cm
Length of the transverse common tangent = √(d² - (r₁)² - (r₂)²), where r₁ and r₂ are the radii of the circles and d is the distance between the centres.
So, 5√3 = √(10² - (3² + r²))
5√3 = √(100 - (9 + r²))
⇒ 5√3 = √(91 - r²)
(5√3)² = (91 - r²)
⇒ 75 = 91 - r²
⇒ r² = 16
⇒ r = 4
Therefore, the radius of the circle C₂ is 4 cm.

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

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.

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.

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.

In the given question, we have to find the relation K and E.
From the given statements:

Since the gender of K is not defined thus we cannot determine whether K is daughter or son of E.
Hence, 'cannot be determined' is the 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.

The given information is represented in the following table:

From the above table, it is clear that the correct combination of Exam – Day – Time Duration is:Maths – Thursday – 50 mins
Conclusion: Option B is the correct answer.

The first, second, third, fourth, fifth and sixth letters of the word are moved by two, three, four, five, six and seven Units forward to obtain the corresponding letters of the code.(C + 2 = E), ( A + 3 = D), (N + 4 = R) ... and so on . 
Similarly, the Corresponding letters in FRIENDS will also shift respectively.

HUMJTK is our Answer.

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.

Since apples and oranges are two separate kinds of fruits, they both will be represeneted as separate circles within the larger circle of fruits. 

In the given options

• The options A,B and C has 5 sides to make different shapes
• This option has only 4 side to arrive at the option

Hence, option D is odd figure with four sides.

• These two return lines are the antennas. Radio waves (signals) escape through these plastic pipes. Earlier models also consisted of these lines.
• But the back walls were made of glass, so they were hidden inside. The signal can easily escape through the glass.
• But they can't escape through aluminium. Generally, the back of many phones is made of ceramic, fibreglass, glass, etc.
• The back of the iPhone 6 and 6S is aluminium, so we need to provide a way to let the signal escape. This was also Apple's move after receiving customer complaints about the low signal strength of previous models.

Hence, Option B is correct.

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.

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 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"

Absorption is the process that actually turns sunlight into red light. 
If wavelengths of light from a certain region of the spectrum are absorbed by a material, then the materials will appear to be the complementary colour
The pigments in stained glass window selectively absorb some Colours of incoming light, while allow other Colours to transmit through the glass.

• Chroma refers to the degree of vividness of a Colour, or how pure it is compared to its representative on the Colour wheel. It can also be called saturation, or Colour intensity.
• The value of each of the 7 samples is very close. The hues are all orange, though simultaneous contrast "encourages" the leftmost samples to take on a blueish quality... but they are still orange.
• So, the only thing changing dramatically is Chroma.
• On the left are very low chroma samples -- almost gray.
• On the right is a rich chroma sample.

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

Floor covering is a term to generically describe any finish material applied over a floor structure to provide a walking surface. 

• Flooring options include wood, engineered flooring materials, vinyl, tile and carpet. 
• Floor joists are horizontal structural members that span an open space, often between beams, which subsequently transfer the load to vertical structural members.
• These joists, part of the floor system, carry the weight of everything inside a room, including walls, furniture, appliances, and even people.

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.