NATA Mock Test - 7 - JEE MCQ

On solving

Let AB be the tower and let AC be its shadow.

Let the height of the tower = x meters.
Then, the length of its shadow = √3 * x meters.

If θ is the angle of elevation of the sun, then:

tan(θ) = x / √3 * x = 1 / √3 = tan(30°)

∴ θ = 30°

Hence, the angle of elevation of the sun is 30°.

Let the points A(0, 1, 2), B(2, −1, 3), and C(1, −3, 1) be the vertices of the triangle.
Let the sides of the triangle be a, b, and c.
For side c = AB: c = √((2 - 0)² + (-1 - 1)² + (3 - 2)²) = √(4 + 4 + 1) = √9 = 3
For side a = BC: a = √((1 - 2)² + (-3 - (-1))² + (1 - 3)²) = √(1 + 4 + 4) = √9 = 3
For side b = CA: b = √((1 - 0)² + (-3 - 1)² + (1 - 2)²) = √(1 + 16 + 1) = √18
Now, check if the triangle is a right-angled triangle using the Pythagorean theorem: a² + c² = b²
3² + 3² = √18²
9 + 9 = 18
So, it is a right-angled and isosceles triangle.
Therefore, the correct answer is B) Isosceles right-angled.

Here, A and B are independent events.
So,
P(A ∩ B) = P(A) × P(B) = 0.2 × 0.3 = 0.06
Now, use the formula for the probability of either A or B failing:
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Thus,
P(A ∪ B) = 0.2 + 0.3 − 0.06 = 0.44

2x² - 7x + 1 = 0

∵ First equation has irrational roots.
∵ Both the roots will be common.

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.

Standard deviation =  

= |a| = 2 (given)

Given integral is 

Put, x = sin(t) ⇒dx = cos(t)dt

New limits are 0, π/2

Apply integration by parts,

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.

= 
= 
= 

y² = x, y = 4

Required Area = 

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.

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.

• 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.

According to the given data:
The required pass percentage in the examination is 40%.
The marks scored by Ram in the examination are 185.
He failed in the examination by 15 marks.
Assume the total marks in the exam = x
Required pass marks = 40% of x
Given:
Marks scored by Ram + Marks he fell short by = Pass marks
So,
40% of x = 185 + 15
⇒ 0.4x = 200
⇒ x = 200 / 0.4 = 500
Hence, the maximum marks are 500.

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.

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.

This track is of sparrows, because the larger the group of birds, the more likely you are to find predators and other potential threats than a single bird.
Bird groups can also confuse or overwhelm predators by "bullying" (when birds attack or hunt and drive away potential predators) or agile flight.
Hence, Option A is correct.

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

Acropolis, central, defensively oriented district in ancient Greek cities, located on the highest ground and containing the chief municipal and religious buildings.

• Pig iron is when hot metal is cast into an ingot before being charged to the steel plant.
• They are used as raw materials for iron steel making.
• The white forge pig iron is used to make wrought iron.

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.

Term used to describe false balcony with or without railing at the outer plane of the window opening to the floor and when the window is open, the appearance of a balcony. .
They are common in France, Portugal, Spain, and Italy.

As per rule of projection when horizontal plane is rotated 90 degree in clockwise direction, top and front view will overlap. Overlapping projection views create confusion in the drawing.Therefore 2nd angle projection system is not used.

(As shown below)

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.

Contrast refers to the arrangement of opposite elements and effects. Contrast can be used to create variety, visual interest, and drama in an artwork.
For example, light and dark colors, smooth and rough textures, large and small shapes.

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.