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.

Given, sin⁻¹(√3/2) - sin⁻¹(1/2)
= π/3 - π/6
= π/6 = 30°

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.

We have



 
= 
= 1/2I

We know, ∫ eˣ (f(x) + f'(x)) dx = eˣ f(x) + c
∫ eˣ (x⁵ + 5x⁴ + 1) dx
= ∫ eˣ (x⁵ + 5x⁴) dx + ∫ eˣ dx
= eˣ x⁵ + eˣ + 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.

Given that, in a ΔABC, ∠A = 45°,∠B = 60°,∠C = 75°
We know that


Thus the value a:b:c is 

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.

Let, 
Let, x = a sin t
Differentiating both sides with respect to t, we get

This means dx = acostdt
At, 
At, 

Given: g(x) = f(x) ⋅ sin(x) and f′(−π) = 1.
Using the product rule of differentiation, i.e., (uv)′ = u′v + uv′, we get:
g′(x) = f′(x)sin(x) + f(x)cos(x)
Now, differentiate again with respect to x:
g′′(x) = f′′(x)sin(x) + f′(x)cos(x) + f′(x)cos(x) − f(x)sin(x)
g′′(x) = f′′(x)sin(x) + 2f′(x)cos(x) − f(x)sin(x)
Now, substitute x = −π:
g′′(−π) = f′′(−π)sin(−π) + 2f′(−π)cos(−π) − f(−π)sin(−π)
Since sin(−π) = 0 and cos(−π) = −1, we have:
g′′(−π) = f′′(−π) × 0 + 2f′(−π) × (−1) − f(−π) × 0
g′′(−π) = 0 + 2 × 1 × (−1) − 0
g′′(−π) = −2
Thus, the value of g′′(−π) is −2.

= 3

 
= 183.49
= 200

Given figure:

In the given question figure, we can see that the cut-out pieces are rotated to get the required figure. The cut pieces are numbered as shown below and placed to form the shape.

So, we can see that an oval shaped figure can be obtained.
Hence, the correct answer is 

Hence, option 'd ' is correct answer.

Given,
Govind's age =48 years
Then according to the question,
Prem's age = 48 / 2 = 24 Years
Hence, age of Prem seven years ago = 24 − 7
= 17  years

Given:
Rahul is 12th from the right in a line of boys and 4th from the left.
It can be represented as,

From the above picture, The number of boys in the line is (4 + 12) - 1 = 15.
To make a line of 28 boys, (28 - 15) i.e. 13 more boys are needed.
Thus, 13 boys must be added.

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.

• Located in Aurangabad, Maharashtra, India, it is known as Bibi Ka Maqbara or Dakkhani Taj (Taj of the Deccan).
• It was commissioned in 1660 by the Mughal emperor Aurangzeb in the memory of his wife Dilras Banu Begum.
• Designed in Mughal architecture style, marble and basaltic trap are used for construction.
• It bears a striking resemblance to the Taj Mahal, the mausoleum of Aurangzeb's mother, Mumtaz Mahal but the decline in architecture and proportions of the structure had resulted in a poor copy.
• Bibi Ka Maqbara is the second-largest structure that Aurangzeb has built, the largest being the Badshahi Mosque.

Hence, option B is correct.

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

• In the option A, if only a little of Colour A's complement is mixed in.
• In the option D, the value is higher, Only in a few special cases (eg - a bit of yellow added to Violet) might this occur. But even then, subtractive Colour issues will tend to produce a darkening.
• In the option C, Tertiary is a hue trait that won't be changed by mixing in a bit of a complement. In those cases where Colour A is a tertiary Colour, (e.g. Yellow-Green), it will stay a tertiary Colour until so much of its complement is added that it becomes a neutral.
• In option B, Chroma is the attribute that expresses the purity of a Colour. Mixing a pure hue with black, white, grey, or any other Colour reduces its purity and lowers the strength of the original hue.

The luminous value increasing from left to right. So, from this we can say that, when the luminous value of a colour is increased, it makes the colour light. 

Hence, option A is the correct answer. 

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.

The word has to Appreciate the most nearly opposite in meaning to the given word:
Exaggerate means represent something as being larger, better, or worse than it really is.
Appreciation means recognising the full worth of something or someone.
Approve means to officially agree to or accept as satisfactory.
Encourage means to give support, confidence, or hope to someone.
Only Appreciate means opposite to Depreciate.
Depreciate is the opposite of admire
Hence this is the correct answer.

These are colour combinations created by the equal mixture of two primary colours. 
Example- 
Blue +Yellow= Green,
Blue + Red = Violet (purple is a shade similar to violet.)
Red + Yellow = Orange.
On the colour wheel, secondary colours are located between primary colours.
Below colour wheel explains the relation between primary and secondary colours
Secondary color wheel, Color mixing, Mixing primary colors  

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.