Indian Navy MR Mock Test - 3 - Airforce X Y / Indian Navy SSR MCQ

Let (x₁,y₁) = (0,0),(x₂,y₂) = (1,√3) and (x₃,y₃) = (2,0)

Since a = b = c, the in-center will be:

Sound travels at the fastest speed in a solids medium.
Sound is a local disturbance whose propagation is facilitated by collisions between particles, this disturbance propagates in a longitudinal wave, imagine one molecule colliding with the next, and then that molecule collides with the next, and so forth. It is a mechanical wave that requires a medium to travel. The speed of sound is highest in solids, then it is slowest in liquids and slowest in gases.

Given:
Here n=3
Let the third number is x.
Mean of n observations = Sum of observations/n

Given: 
If x+y = 6 and 4x+7y = 36
According to the question,
x+y = 6------(1)
4x+7y = 36------(2)
Multiply by 4 in equation (1)
⇒ 4x+4y = 24------(3)
Subtract equation (2) from equation (3)
⇒ 4x+7y−4x−4y = 36−24
⇒ 3y = 12
⇒ y = 4
Putting y=4 in equation (1)
⇒ x = 6−4
⇒ x = 2
∴ The value of x and y is 2 and 4.

As we know,
P = S.P. – C.P.
L = C.P. – S.P.
L% = (L/C.P.) × 100
Where, P= profit, S..P.= Selling price, C.P.=cost price, L=loss.
Let the C.P. be x.
According to question, 

⇒ x(x – 500) = x(700 – x)
⇒ 2x = 1200
⇒ x = 600
So, loss = 600 – 500 = 100

∴ The required loss% is 50/3%.

First,

We have to find that 300 of what percentage of 500. Therefore,

= 60%

Let the required rate of interest be R.
Let the principal be P.
Then the simple interest =3P/4
Time = 5 years

Given: cos⁡46º cos⁡47º cos⁡48º cos⁡49º cos⁡50º … cos⁡135º
As we know that, cos⁡90º =0.
⇒ cos⁡46º cos⁡47º cos⁡48º cos⁡49º cos⁡50º … cos⁡135º
= cos⁡46º cos⁡47º cos⁡48º cos⁡49º cos⁡50º…cos90º ...cos⁡135º = 0

Given,
Mass = 100gm, radius = r
The movement is uniform circular in motion. The angle between centripetal force and displacement is 90º.
The force and displacement are perpendicular to each other = cos⁡90º =0
Work done (W) = FSCos90º = 0 J
So, no matter what is the mass, radius, or velocity, the work done would be zero.
So, the work done in one complete revolution is Zero Joule.

Heat transfer occurs in three ways:

• Conduction
• Convection
• Radiation

Radiation is the fastest method of heat transfer. Radiation is a form of energy that is emitted in the form of waves. Under this definition, the radiation includes ordinary visible light rays, infrared light rays, ultraviolet rays, X rays, etc.

Weight:
The force applied by the earth on anybody having mass is called the weight of that body.
It is denoted by W.
Mathematically it is can be written as
W = mg
Where m = mass of the body and g = acceleration due to gravity
⇒ m = W/g
⇒ m = 49/9.8
⇒ m = 5 kg

Photon: A photon is the smallest amount of electromagnetic radiation, it is called quantum.
One unit quantum is the photon.
Quanta is the plural form of quantum.
Let us see the table for electron, proton, and neutron.

The propagation of energy is done in the form of the photon; unit transfer of energy is called quanta.

• Every orbital is has a unique and characteristic shape.
• s-orbital is spherically shaped.
• p-orbital is of dumbbell shape.
• d-orbital is of double dumbbell shape.
• f-orbital is of eight lobed dumbbell shape.

Given: 
Diameter of circle, d = 112 cm
Formula used:
Circumference of semi - circle =  πr + 2r 
Calculation:
Circumference = (22/7) × 56  + 2 × r =  176 + 2 × 56 cm
∴ The circumference of half part of circle = 176 + 112 = 288 cm
∴ Option 2 is correct.

Given:
The cost price of 91 books is equal to the selling price of 65 books.
Concept used:
Profit = SP - CP
Profit% = Profit/CP × 100 
Calculation:
Let the cost price of each book be Rs. 1
CP of 65 books = Rs. 65
SP of 65 books = CP of 91 books = Rs. 91
Profit = Rs. (91 - 65) = Rs. 26
Profit% = ((26/65)× 100) = 40%
∴ The required profit% is 40%.

Given:
In the first case:
10 men can do a piece of work in 50 days,
In the second case:
x men are additionally added to do the task in 20 days.
Concept used:
M₁ × D₁ = M₂ × D₂
Where, 
M₁ and M₂ are the numbers of men in the first case and second case respectively.
D₁ and D₂ are the numbers of days required in the first case and second case respectively.
Calculation:
According to the question,
⇒ 10 × 50 = (10 + x) × 20
⇒ 500 = (10 + x) × 20
⇒ 50 = (10 + x) × 2
⇒ 10 + x = 25
⇒ x = 15
The additional number of persons added to complete the task in 20 days = 15
Therefore, '15' is the required answer.

Formula:
180° = π
Calculation:
180° = π
⇒ 1° = π/180
∴ 150° = (150°/180°) × π = (5/6)π 

Given:
Length of the train = 225 m
Speed of the train = 145 km/h
Speed of the man = 17 km/h
Concept used:
Time = Distance/speed
Relative speed = When two objects move opposite to each other then their relative speed is equal to the sum of their individual speeds.
When a train of x m crosses a man or a pole then it will cross its own length.
km/h × 5/18 = m /sec
Calculation:
Relative speed of the train in km/h = 145 + 17
⇒ 162 km/h
Relative speed of the train in m/sec = 162 × 5/18
⇒ 45 m/sec
According to the concept, the train will cover its own length
So, time = 225/45
⇒ 5 sec
Time taken by the train to cover the man = 5 sec
∴ In 5 sec it will pass the man.

Given:
f(x) = ax³  + 4x² - 2x -­ 6
Product of zeros = 2
Concept used: 
Product of zeros = -(d/a)
Calculation:
In the given polynomial,
d = - 6 & a = a
⇒ - (d/a) = 2
⇒ -(-6)/a = 2
⇒ a = 6/2
⇒ a = 3
∴ If the product of zeros of the polynomial f(x) = ax³  + 4x² - 2x -­ 6 is 2, then the value of 'a' = 3.

Given:
615 coins consist of one rupee, 50 paise and 25 paise coins.
Their values are in the ratio of 3 : 5 : 7.
Calculation:
Let number of coins of 1 rupee, 50 Paise and 25 Paise be M, N and P respectively
⇒ M + N + P = 615
Also,
⇒ 100M ∶ 50N ∶ 25P = 3 ∶ 5 ∶ 7
Let
⇒ M ∶ N ∶ P = K
Then,
⇒ M = 3K/100, N = 5K/50, P = 7K/25
According to question,
⇒ (3K/100) + (5K/50) + (7K/25) = 615
⇒ 3K + 10K + 28K = 61500
⇒ 41K = 61500
⇒ K = 1500
∴ Number of 50 Paise coins = 5K/50 = (1500 × 5)/50 = 150
Therefore the number of 50 paise coins is 150.

Pendulum clocks become slow in summer because the length of the pendulum increases due to which the time period increases and the pendulum takes more time to complete one oscillation. Thus it becomes slow in summer.
In summer due to an increase in the temperature of the atmosphere, the length of the pendulum (l) will increase.

• The time period of the pendulum, T= 2π √l/g i.e T ∝ √l. So it will make less number of oscillations per day. So the clock will run slowly in summer.

In winter temperature of the atmosphere decreases. So the length of the pendulum decreases.

• Hence time period of oscillation will also decrease. As a result, the pendulum makes more oscillations in a given time i.e. the clock will run fast in winter.

Given that:
⇒ R₁ = 3 Ω , R₂ = 6 Ω, R₃ = 12 Ω
⇒ Let R be the total resistance of the parallel combination.
We know that,

Therefore, the total resistance of the circuit is 12/7 Ω.

Given,
Power = 2 kW
time = 1 hr × 30 days = 30 hours
Energy = Power ×​ Time
⇒ Energy = 2 × 30 = 60 kWh = 60 unit
The cost of using a 2kW motor pump for 1 hour each day for 30 days = 60 × 1.5 = Rs. 90.

Given:
Number of observation (weights) = 13
Calculation:

⇒ Frequency of 25 is maximum so, the mode is 25
∴ The mode weight is 25 kg.
∴ The correct option is 2 i.e. 25 kg.

• A mixture is made up of more than one type of pure form of matter, known as a substance.
• No physical process can separate a substance from other types of matter.
• Alloys are mixtures of two or more metals or a metal and non-metal that cannot be physically separated into their constituents. However, an alloy is still considered a mixture because it demonstrates the properties of its constituents and can have a variable composition.
• Brass is an alloy composed of copper and zinc, and the proportions of copper (approximately 70%) and zinc (30%) can be varied to produce a variety of brasses with varying properties. As a result, it is a mixture.

• Kesari was the newspaper started by Lokmanya Balgangadhar Tilak to serve the cause of India's freedom struggle.
• Bal Gangadhar Tilak was an Indian social reformer and freedom activist. He was one of the prime architects of modern India and probably the strongest advocates of Swaraj or Self Rule for India.
• Towards his nationalistic goals, Bal Gangadhar Tilak published two newspapers viz. 'Mahratta' in English and 'Kesari' in Marathi. Both the newspapers stressed on making the Indians aware of the glorious past and encouraged the masses to be self reliant. In other words, the newspaper actively propagated the cause of national freedom.

Forint is the currency of Hungary.
It was formerly divided into 100 fillér, but fillér coins are no longer in circulation. The introduction of the forint on 1 August 1946 was a crucial step in the post-World War II stabilization of the Hungarian economy, and the currency remained relatively stable until the 1980s.

Gandak, Mahananda and Kosi are the south-flowing rivers of Bihar. Son is the north-flowing river of Bihar. Son river originates from the Amarkantak plateau in the Anuppur district of Madhya Pradesh.

• Son River flows through Shahdol district in Madhya Pradesh state before turning sharply eastward where it encounters the southwest-northeast Kaimur Range.
• It flows through Madhya Pradesh, Chhatisgarh, Uttar Pradesh, Jharkhand, and finally joins Ganga in Bihar near Patna.
• Ghaghra, Johilla, Chhoti Mahanadi, Gopad, Rihand, Kanhar, and North Koel are the tributaries of the Son river.
• The Bansagar Dam in Madhya Pradesh is also on the Son river.
• The Mahananda River is a transboundary river that flows through the Indian states of Bihar and West Bengal, and Bangladesh. It is an important tributary of the Ganges.

Eminent musician Pandit Budhaditya Mukherjee is associated with sitar.
Pandit Budhadityaji was born in 1955 in Durg, Chattisgarh. He is considered as the leading sitarist of his generation, Budhadityaji received his entire training in Sitar from his father, Pandit Bimalendu Mukherjee. He has, since 1979, performed in 26 countries including the UK., USA., Canada, Australia, New Zealand, the UAE, Armenia, and in almost all European countries. On June 30, 1990, Budhaditya Mukherjee created history by becoming the first-ever musician to perform at the House of Commons, London.

Doddabetta is a mountain in the Western Ghats ranges of India. It is the highest peak of the Nilgiri Mountains in the Nilgiri District of the state of Tamil Nadu and the highest of all the mountains to the south of the Himalayas. This peak is 2637 meters above sea level.