NATA Mock Test - 3 - JEE MCQ

Given that the total number of bananas is 5 and the total number of oranges is 4, we have a total of 9 fruits.
We need to select at least one fruit out of these 9 fruits. The number of ways to select at least one fruit can be calculated as:
The total number of ways to select fruits from 9 items is the sum of combinations:
⁹C₁ + ⁹C₂ + ... + ⁹C₉.
The total number of ways to select fruits from 9 items is equal to the sum of all combinations, minus 1 (because we are excluding the case where no fruit is selected):
Therefore, the answer is: 2⁹ - 1.

Given: diameter of two circles are x and 3x.
Thus, the radii of the two circles are x/2 and 3x/2.
Also, given that both circles touch internally.
We know that, if two circles touch internally, then the distance between the centres is equal to the difference of their radii.
⇒ Distance between centres: AB = (3x/2 - x/2) = x
Hence, the distance between the centres of the circles is x.

Given: Height of the tower AB = 75 m.
Angle of depression = 30°.
⇒ ∠C = 30°.
Let the distance of the object from the base of the tower be BC.
To find BC, we have:
⇒ tan(C) = AB / BC
⇒ tan(30°) = 75 / BC
⇒ 1/√3 = 75 / BC
∴ BC = 75√3 m
Hence, the distance of the object from the base of the tower is 75√3 m.

We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
√[(x₁ - x₂)² + (y₁ - y₂)²]
Given that the distance between the points (a, 2) and (3, 4) is 8, we apply the distance formula:
√[(a - 3)² + (2 - 4)²] = 8
Squaring both sides:
(a - 3)² + (2 - 4)² = 8²
(a - 3)² + 4 = 64
(a - 3)² = 64 - 4 = 60
a - 3 = ±√60 = ± 2√15
a = 3 ± 2√15
Thus, the possible values of a are 3 + 2√15 and 3 - 2√15.

As we know that with the change in origin, the variance does not change.
Therefore, variance does not change even after giving grace marks of 10 to each of the students.
Whereas, mean, mode and median changes upon changing the origin.

To find the coordinates of the foot of the perpendicular from a point P(x, y, z) on the x-axis, the y and z coordinates will be 0, while the x-coordinate remains the same.

For point P(6, 7, 8), the foot of the perpendicular will have the coordinates (6, 0, 0).

Hence, the correct answer is A.

Given series: √8, √18, √32
This series is in AP, meaning the common difference is constant.

Let the next term be a.
So, the series becomes: √8, √18, √32, a.

We know that in an AP, the common difference is constant.
Thus,
√32 - √18 = a - √32.
⇒ √32 - √18 = a - √32
⇒ a = 2√32 - √18
⇒ a = √50

Hence, the next term is √50.
Therefore, the correct answer is C.

To find the greatest integer which divides the number 101¹⁰⁰ minus 1, we use the binomial expansion.

Using the binomial theorem:

So, x = n then

Now, let x = 100. So,

Clearly, 101¹⁰⁰ − 1 is divisible by 100²

Therefore, the correct answer is: C) 10000.

For the domain of the function

We know that a quadratic polynomial is a polynomial of degree two, i.e., the highest exponent of the variable is two.
In general, a quadratic polynomial will be of the form p(x) = ax² + bx + c, where a ≠ 0.
Thus, clearly, x² + 2x is having degree 2.
Hence, x² + 2x is a quadratic polynomial.

U is a universal set which contains all the elements in each of the subsets and is known as the intersection identity.

We know that, statements are those sentences in which we can say logically either true or false but not both.
"Two non-empty sets have always a non-empty intersection" is not a statement because two non-empty sets with no common elements can have an empty intersection.
The real number 'n' is less than 2 is not a statement because if n = 1 then this statement is true but if n = 3 then this statement is false.
Two individuals are always related is not a statement because two individuals are may or may not related.
So, answer is none of these.

H is fourth to the left of D, so H is not a neighbour of D. A is immediate right of H and immediate left of B. So A is also not a neighbour of D. F is not at the end but neighbour of E, therefore EF are not neighbours of D. And C is immediate right of B. The only neighbour of D is C.
Hence,  option(b) is correct.

 
= 183.49
= 200

From statement I, we have

'B' can be at any point around point C at the distance of 8 m.
From statement II, we have 

Therefore, the data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.

In the given options A, B and C , the regular polygons have a sum of interior angle equal to 360 or twice of 360 degree.
In the option D, it is a regular polygon called pentagon where the sum of all Interior angles is equal to 540 degrees 
Thus, the option D is correct answer.

Let the required 4 lines be as shown below:

Three or more lines in a plane are concurrent if they intersect at a single point.
Hence, the above lines are no three concurrent and no two parallel.
Now, we can extend these lines so that each of them intersects each other. Only three more lines can be joined between these 6 points as below.3

On joining the lines connecting C and E, B and D, A and F with the dotted lines. There are three such lines formed.
Hence, the correct answer is 3.

Hence, option B is correct.

The only certain outcome is that the chroma of Colour A will be lowered.

A hard strong building material made by mixing a cementing material (such as Portland cement) and a mineral aggregate (such as sand and gravel) with sufficient water to cause the cement to set and bind the entire mass.

Concrete mixers are devices capable of preparing concrete mixtures of varying strength precisely as well as quickly.

In the first angle method, the top view is drawn at the bottom of the front view. In this method, the right-hand side view is drawn on the left side of front view. First angle method is mostly used in orthographic projections.

The capability of maintaining the serviceability of a structure over a period of time.
In design, it is practiced to achieve the ability of structure , design and construction to withstand weathering actions, abrasion, chemical attack etc.

Southcentral railway has its headquarters at Secunderabad. It covers the States of Telangana, Maharashtra and Madhya Pradesh and has three divisions at Secunderabad, Hyderabad and Nanded. In 2019 Vijayawada, Guntur and Guntakal railways station were added in south coastal railway zone.

In the perspective view, we draw rays from the vanishing point. Then draw a vertical projection from a piercing point, getting intersection points of respective corner. Draw the view from the intersection point and join the intersection point.

Above is the image of truncated truss.

Above is the image of queen post truss.

Above is the image of fink truss.

Above is the image of king post truss. hence, option B is the correct answer. 

Legal possessors of land mean physical, manual control of the land or a building. This is protected by the law.