NATA Mock Test - 7 - JEE MCQ

Given, 

∴ m₃ < m₁ < m₄ < m₂

According to the question, we need to solve the following trigonometric expression:
(sin²30° + cos²30°) − (sin²60° + cos²60°) + (sin²45° + cos²45°)
We know that for any angle A,
sin²A + cos²A = 1
Applying this identity:
⇒ 1 − 1 + 1 = 1
Hence, the correct answer is: A. 1.0

Given that, x + 1/x = 2
⇒ x² + 1 = 2x
⇒ x² - 2x + 1 = 0
⇒ x² = (2 ± √4) / 2
⇒ x = 2/2
⇒ x = 1
Therefore, tan⁻¹(x) = tan⁻¹(1)
= tan⁻¹(tan(π/4))
= π/4.

Given integral is 

Put, x = sin(t) ⇒dx = cos(t)dt

New limits are 0, π/2

Apply integration by parts,

To get the sum of coefficients, substitute x = 1 in the binomial expression.
∴ (1 + 2)ⁿ = 6561
∴ 3ⁿ = 6561 = 3⁸
∴ n = 8
Now, the general term is given by:
T_{r + 1} = ⁸C_r  2^8-rx^-8+2x

Since the term is independent of x, we have:
-8 + 2r = 0
⇒ r = 4
∴ The coefficient of the independent term, T₅ = ⁸C₄ x 2⁴ = 16 ⁸C₄.

We know that for a system of two linear equations to have no solution, their slopes must be equal.
Given the equation:
kx + 2y = 5
Rewriting in slope-intercept form (y = mx + c):
2y = -kx + 5
y = (-k/2)x + 5/2 → (1)
The standard form of a line is y = mx + c, where m is the slope.
Now, given the second equation:
3x + y = 1
Rewriting in slope-intercept form:
y = -3x + 1 → (2)
From equations (1) and (2), equating the slopes:
k/2 = -3
k = 6
Hence, the correct option is C.

= 
= 
= 

Given,
sin 120° - i cos 120°
= sin(90° + 30°) - i cos(90° + 30°)
= cos 30° - i[sin 30°]
[:: sin(90° + θ) = cos θ & cos(90° + θ) = -sin θ]
= cos 30° + i sin 30°
So, the given expression is expressed as cos 30° + i sin 30° in polar form.

As we know, If set A contains m elements and set B contains n elements, then A×B contains m×n elements.
So, 3 × n(B) = 1
⇒ n(B) = 5

Given, G = √xy ⇒ G² = xy

Start with the given equation:

logₚ(log₄|x| − 2 + px) = x

First, simplify the expression inside the logarithm:

logₚ(log₄|x| − 2 + px) = x
⇒ log₄|x| − 2 + px = px (Since logₚ(a) = a for any p > 1)

Now, simplify further:

log₄|x| − 2 = 0 (Canceling out px from both sides) ⇒ log₄|x| = 2

Next, solve for |x|:

log₄|x| = 2
⇒ |x| = 4² = 16

Therefore, x = ±16.

Finally, the sum of all real values of x is:

16 + (-16) = 0.

Conclusion:
The sum of all real values of x is 0.

Thus, the correct answer is D) 0.

Total number of students: Eight
Follow the instructions and draw the answer figure satisfying all the conditions.
T belongs to Bihar and sits second to the left of V who belongs to Rajasthan. R does not belong to UP.
The immediate neighbour of T faces R who sits third to the left of the one who belongs to Haryana.

There are two persons between those who belong to UP and Bihar and neither of them sits opposite P.
R and V are immediate neighbours and neither of them belongs to Punjab or Bihar. P who belongs to Haryana sits second to the right of the one who belongs to Punjab.
Q and T neither belongs to Punjab nor sit adjacent to P. U does not belong to Punjab. Both S and W do not belong to UP or MP. Q belongs to Delhi while S belongs to Kerala. Q is not an immediate neighbour of P.
The final arrangement is:

From the above given circular seating arrangement, we can conclude that 'T' sits third to the right of U.
Hence, 'T' is the correct answer.

Given:
x * y = 3x + 2y
Now,
2 * 3 = (3 × 2) + (2 × 3)
= 6 + 6
= 12          ......(i)
3 * 4 = (3 × 3) + (2 × 4)
= 9 + 8
= 17          ......(ii)
Adding equation (i) and (ii):
2 * 3 + 3 * 4 = 12 + 17 = 29
Hence, the required value is 29.

Statement I does not mention the day of the week on which either Arun or Salim celebrated their birthday. Therefore, we can not find the day of born of Salim. Hence, this statement is not sufficient to answer the given question.
According to statement II, Salim's sister was born on the third day of week, i.e. Wednesday, and Salim was born two days before Wednesday, i.e. Monday.
Hence, the data in statement II alone are sufficient to answer the question, while the data in statement l alone are not sufficient to answer the question.

• Lifters are usually utilised to measure the volume of liquid.
• Gram (measure): A unit of measurement of weight and mass.
• Kilogram :A unit of measurement of weight and mass.
• Tonne a metric unit of mass equal to 1,000 kilograms.

Thus, Litres is used to measure volumes, others measure weight ​and that's the reason 
Hence, option A is correct answer.

The given series: 3, 5, 7, 9, 11, 13, ?
Rule followed – Given number + 2 = Next number
We find that:
3 + 2 = 5
5 + 2 = 7
7 + 2 = 9
9 + 2 = 11
11 + 2 = 13
13 + 2 = 15
So, the next number is 15.
Hence, option A is the correct answer.

In the given question, 
C scored more than only A and E. Hence, either A or E scored the minimum marks.
Also, it is given that E did not score the least. So, A got the minimum marks.
Thus, C > E > A ----(1)
D scored less than only BB. Therefore, B got the maximum marks and D got the second highest marks.
Thus, B > D ----(2)
So from the above two inequalities, we can conclude that:
B > D > F > C > E > A ----(3)
Given that the 3rd highest marks = F's marks = 81 E's mark = 62
Therefore, 81 > C > 62----(4)
The option C i.e 70 comes between the given marks.
The option C is the correct answer.

According to the given information in the question, Vijayan face was in the direction towards south direction, then he walked total 45 m, the following figure can be drawn, 

It is clear from the above figure, Vijayan is 15 m far in the east direction.

Therefore, option B is correct.

In order to locate and record sites in the landscape, archaeologists rely on survey or reconnaissance methods. 
These may be conveniently divided into three categories: aerial surveys, surface surveys, and subsurface testing.
An aerial photograph, in broad terms, is any photograph taken from the air. Normally, air photos are taken vertically from an aircraft using a highly-accurate camera.

Milan cathedral, Abbay aux homes and West minister abbey, all of them are churches/ public places of worship.
Doges palace is a residential building.
Hence, option A is the odd one out.

Ranthambore National Park is a vast wildlife reserve near the town of Sawai Madhopur in Rajasthan, northern India and is a former royal hunting ground and home to tigers, leopards and marsh crocodiles.
Periyar National Park, also known as Periyar Tiger Reserve, is in the mountainous Western Ghats of Kerala, southern India and Manas National Park or Manas Wildlife Sanctuary is a national park, UNESCO Natural World Heritage site, a Project Tiger reserve, an elephant reserve.
Hence, only pair A and B are correct.

The flat slab forming the uppermost member of the capital of a column.
An ornamented abacus adds a lot to the decor.

The Red Data Book is a state document made for documenting local subspecies and also for those species of animals and plants which are rare and endangered, which exist within a country.

The indefinite article 'a' is used here. There are two indefinite articles 'a' and 'an'. 'a' is used before a noun to define it as something non-specific. We use 'a' before words such 'graphic designer', 'photographer' which defines a relationship between a noun and an object.
Here the article 'a' defines a relationship between the 'Photographer' and his 'Neighbour'.
Here, 'Photographer' acts as a noun, and 'neighbour' acts as an object.

A horizontal orthographic projection of a building onto a vertical plane, or 2D representation of a 3D space.
There are different types of elevation Front, Side, Rear and Section.

Primary colour are Red, Blue, Green. They are a set of colours from which all other colours are derived.
When they are combined and mixed they give different colours.
When white or black is combined with these colours creates tints (lighter tones) and shades (darker hues) to them. 

Ecology is the branch of biology that deals with the study of the relationship between organisms and their physical environment.
Entomology deals with the study of the relationship between insects with humans. Biology deals with the study of life science. Ornithology deals with the study of birds.

A colour wheel is defined as a circular arrangement of colours organized by their chromatic relationship to one another. 
It is a tool that helps artists to visualize colour and relationships between primary, secondary and tertiary colours.
The first colour wheel was presented by Sir Isaac Newton in the 17th century when he first discovered the visible spectrum of light.

When the prism is placed vertically on one of its end faces, the end face on which the prism rest is called the base and the vertical sides faces are the lateral faces.