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

The correct answer is "To"
Key Points

• The complete sentence is "It's five minutes to 10 o'clock.
• According to the English time system, it is not a 24-hour time system. Rather it's a 12-hour time system.
• According to this system, there are two ways of telling time- if the time is between 12 and six, the "past" is used to denote the time.
  • Example- 5:10- It's ten past five.

5:30- It's half past five.

• But when the time is between 6 and 12, we use "to".
  • Example- 5:35- It's 25 to 6.

5:45- It's quarter to 6.
Additional Information

• The usages of the other prepositions are as follows-
  • Of- They have wasted most of their time in futile conversation.
  • From- From 6 p.m. onwards, I will be there.
  • Till- I will wait for him till 6 o'clock in the evening.

The correct answer is "B"

Key Points

• The error lies in part B of the sentence because it is using the present tense verb 'create' instead of the conditional 'would create'.
• The sentence is written in the form of a hypothetical statement,
• In which case the correct verb tense to use would be the conditional 'would + base form of the verb' which indicates a future action that is dependent on a particular condition,
• In this case, the condition of becoming a successful entrepreneur.

Thus, option 3 is the correct answer.

Correct sentence: If I were a successful entrepreneur, I would create jobs to reduce unemployment rate.

The correct answer is 'no article, a'.

Key Points

• The most appropriate articles to complete the given sentence is 'no article, a'.
• In the first filler, no article should be used with the means of transportation which are preceded by the preposition 'by'.
  • Example:
    • Mohit will go to Rajasthan by the bus but will return in a cab.
    • Mohit will go to Rajasthan by bus but will return in a cab.
• ​​ In the second filler, the most appropriate article is 'a' because 'book' has a consonant sound. And we use the article 'a' before a consonant sound.
  • Example: a car, a house, a big truck, a wheel, a grey day, etc. ​
• Therefore, by reading the above explanation we find that the correct answer is Option 2.

Correct Sentence: Mr. Mukesh went to market by rickshaw to buy a book and returned by rickshaw.

Additional Information

• 'The' before a noun shows that what is referred to is already known to the speaker, listener, writer, and/or reader (it is the definite article)
• Its Comparison with the other article as follows
  

The correct answer is 'looked'.

Key Points

• The option 'looked' is the correct answer because the given statement is in the past tenses and the entire statement must be in the same tense.
• The option 'look' is incorrect because 'look' is in the present tense.
• The option 'looks' is in the present tense.
• The option 'was looked' is incorrect because the given sentence is in the active voice and 'was looked' cannot be used in an active voice sentence.
• Hence, the correct form of tenses, 'looked' should be used to make the sentence grammatically correct.
• Hence, the correct answer is 'looked'.

​Correct sentence: She came to the writing-table and looked through the letters which were waiting for her.
Additional Information

• An action verb expresses an activity that a person or thing can do.
  • Example: Rohan eats cake. (Eating is something Rohan can do.)
    The bear chased the salmon in the shallow rapids. (Chasing is something the bear can do.)
• A stative verb expresses a state rather than an action. A stative verb typically relates to a state of being, a thought, or an emotion.
  • Example: She believes in fairies.
    He feels elated.
• ​A transitive verb is one that acts on something (i.e., it has a direct object).
  • Example: The postman will give Sarah the letter. (Here, the direct object is the letter.)

Correct option: 2.

Basically, if you have a sword of Damocles hanging over you/your head, something bad seems very likely to happen to you.

Note: In Greek mythology, the courtier Damocles was forced to sit beneath the sword suspended by a single hair to emphasize the instability of a king's fortunes. Usually used in the phrase "a/the sword of Damocles hangs over (one's) (head)."

The correct answer is 'Both A and B are correct.​'.

Key Points

• The passage is a non-fiction piece on the theme of 'freedom'. The purpose of this passage is to explain, analyse, define or clarify something—to provide us with information and to show the how and why of things.

• Statement A refers to the passage's mention of how Nature demands certain things from individuals, such as for at least twelve hours of the day, and that failing to do these things could lead to death. This implies that if one does not obey Nature's "call" or demands, there could be fatal consequences, which supports Statement A.

• Statement B aligns with the part of the passage that discusses the power held by employers. The passage states that an employer can dictate the terms of your employment, and can dismiss you, leaving you to join the "unemployed." This supports the statement that they could dismiss you if you do not heed your employer.

• Thus, Statements A and B are consistent with the ideas presented in the passage.

Therefore, the correct answer is Option 3.

The correct answer is 'Both Landlords and Police'.

Key Points

• The passage is a non-fiction piece on the theme of 'freedom'. The purpose of this passage is to explain, analyse, define or clarify something—to provide us with information and to show the how and why of things.
• Read the lines of the passage- "Your landlord may refuse to let you live on his estate if you go to chapel instead of to church, or if you vote for anyone but his nominee, or if you practise osteopathy or if you open a shop."
• After reading the above lines from the passage we can conclude that people who exert pressure on man’s freedom is a landlords.
• The passage mentions that people who exert pressure on man's freedom are landlords and employers, who have the power to dictate various aspects of their tenants' and employees' lives. Additionally, the passage notes that laws enforced by the police also restrict freedom, but reasonable laws can actually increase freedom by protecting individuals from harm. Therefore, both landlords and police are correct answers.

Therefore, the correct answer is Option 4.

The correct answer is 'strike'.

Key Points

• The passage is a non-fiction piece on the theme of 'freedom'. The purpose of this passage is to explain, analyse, define or clarify something—to provide us with information and to show the how and why of things.
• Read the lines of the passage- "Your only remedy at present is the Trade Union Weapon of the strike which is only the old Oriental device of starving on your enemy’s doorstep until he does you justice. "
• After reading the above lines from the passage we can conclude that the only remedy available to the workers to get their demands fulfilled is strike.

Therefore, the correct answer is Option 2.

The correct answer is 'might'.

Key Points

• In this context, 'might' is used to express a possibility or uncertainty.
• 'Will' would suggest certainty, which contradicts the fact that he has not worked hard.
• 'Can' refers to ability, not to possibility in this context.
• 'Do' is not a modal verb and is not used to express possibility.

Therefore, the correct answer is Option 2.

Concept:

Spherical mirror:

• ​A spherical mirror is a mirror that has the shape of a piece cut out of a spherical surface.
• There are two types of spherical mirrors: Concave mirrors and convex mirror

​Concave mirror:

• If the reflective surface is on the side curved inwards, it is a concave mirror.

• Concave mirrors are commonly used as shaving mirrors or by dentists and even in telescopes.

​

• The reflected image is magnified but the field of view is limited. Concave mirrors are also called converging mirrors.

Convex mirror:

• ​If the reflective surface is curved outwards, it is a convex mirror.
• Convex mirrors are used extensively as part of car mirrors

​

• Depending on the focal length, the reflected image is reduced in size but the field of view is more. This is very useful for drivers as blind spots are drastically reduced. Convex mirrors are also called fish eye or diverging mirrors.
• ​The relation between the radius R and the focal length f in the spherical mirror, R = 2f

Calculation:

Given,

The radius of the spherical ball, R = 20 cm

For a concave mirror, the radius is, R = - 20cm

For the convex mirror, the radius is, R = 20 cm

The relation between the radius R and the focal length f in the spherical mirror, R = 2f

Concept:

Simple Harmonic Motion or SHM is a specific type of oscillation in which the restoring force is directly proportional to the displacement of the particle from the mean position.

• Velocity of SHM,  --- (1)
• Acceleration, a = ω²x ---- (2)
• Where, x = displacement of the particle from the mean position,
• A = maximum displacement of the particle from the mean position (amplitude)
• ω = Angular frequency

Calculation:

Given, acceleration a = 3 cm/s² at x = 1 cm

Then from equation 2,

3 = ω² × 1

⇒ ω² = 3 ----- (3)

Now, velocity v = 6 cm/s at x = 2 cm

Then from equation 1

Squaring both side,

Putting the value of ω² from equation 3, we get

⇒ A = 4 cm

Additional Information

• Velocity is maximum at mean position
• Velocity is minimum or zero at extreme position.
• Acceleration is maximum at the extreme position, x = ± A
• Acceleration is minimum or zero at the mean position, a = 0

Concept:

The efficiency of Carnot or any reversible engine is given by:|

where, η = Efficiency of Carnot Engine, T1 = Source temperature in K, and T2 = Sink Temperature in K.

Calculation:

Given:


Putting values from eq(i) in eq(ii),

CONCEPT:

• Bernoulli's Principle: It states the total mechanical energy of the moving fluid comprising the energy associated with the fluid pressure (P), the gravitational potential energy of elevation ρgh, and the kinetic energy of the fluid motion  always remains constant. i.e. 
  

  Where p and v are the pressure exerted by the fluid and the velocity of the fluid repectively, ρ is the density of the fluid, h is the height of the container.

• Bernoulli's Principle basically states energy conservation for fluids.

EXPLANATION:

• Bernoulli's Principle basically states energy conservation for fluids
  

  Using Bernoulli's Principle at hole opening and at the free surface of the container

  At both places, pressure is atmospheric pressure P₀

  At the free surface, velocity will be zero because when liquid comes out of the hole, the free surface will not move or move very little.

  
  

CONCEPT:

Moment of inertia:

• The moment of inertia of a rigid body about a fixed axis is defined as the sum of the product of the masses of the particles constituting the body and the square of their respective distances from the axis of the rotation.
• The moment of inertia of a particle is

⇒ I = mr2

Where r = the perpendicular distance of the particle from the rotational axis.

• Moment of inertia of a body made up of a number of particles (discrete distribution)

⇒ I = m1r12 + m2r22 + m3r32 + m4r42 + -------

Rotational kinetic energy:

• The energy, which a body has by virtue of its rotational motion, is called rotational kinetic energy.
• A body rotating about a fixed axis possesses kinetic energy because its constituent particles are in motion, even though the body as a whole remains in place.
• Mathematically rotational kinetic energy can be written as -

⇒ KE

Where I = moment of inertia and ω = angular velocity.

EXPLANATION:

• The moment of inertia of the ring about an axis passing through the center and perpendicular to its plane is given by

⇒ I_ring = MR²

• Moment of inertia of the disc about an axis passing through center and perpendicular to its plane is given by -

• As we know that mathematically rotational kinetic energy can be written as

• According to the question, the angular velocity of a thin disc and a thin ring is the same. Therefore, the kinetic energy depends on the moment of inertia.
• Therefore, a body having more moments of inertia will have more kinetic energy and vice - versa.
• So, from the equation, it is clear that,

⇒ Iring > Idisc

∴ Kring > Kdisc

• The ring has higher kinetic energy.

 Important Point

Concept:

• A comb moving through dry hair gets electrically charged through induction.
• Induction charging is a charging method that charges an object without actually touching the object to any other charged object.
• The charging by induction process is where the charged particle is held near an uncharged conductive material that is grounded on a neutrally charged material.
• 
• 
• 

Explanation:

• When a comb is moved through dry air, charge transfer takes place between the comb and hair and so the comb becomes electrically charged.
• Electric field lines of force always originate at the positive charge and terminate at the negative charge.
• So, they do not form a closed loop.
• Whereas the magnetic field lines of force always form a closed loop.

Hence, both statements are correct.

Explanation:

Given, I=∫02{x}dx

where, {x} denotes the fractional part of a real number x.

We know that {x} = x - [x]; where [x] denotes the floor of x, greatest integer less than or equal to x.

Now,

Between 0 and 1, [x]=0 and between 1 and 2, [x]=1

⇒ I = 1

Concept:

• For any base b which is a transcendental number the logarithm log_bn of every integer n ≥ 2 is an irrational number.
• A rational number is a number, which can be written as p/q where p & q are integers and q ≠ 0.

Formula used:

• log mn = log m + log n
• log_aa = 1
• log_aⁿb = (1/n) log_ab

Calculation:

Statement:1 log₁₀50 is a rational number.

log1050 = log1050 = log10(5 × 10)

log1050 = log105 + log1010

log1050 = log105 + 1

As discussed, log105 is an irrational number, log1050 will be also irrational.

Statement:2 log100 10 is an irrational number.

log₁₀₀10 = log_10²10 = (1/2)log₁₀10 = 1/2

Which is a rational number.

∴ Both statements are incorrect.

Concept:

• cos 2x = 2cos2x - 1 = 1 - 2 sin²x
• 

Calculation:

Given,

⇒

⇒

⇒

⇒

⇒

∴ The correct answer is option (3).

Calculation:

Given: z =

=

=

=

=

=

= -1 + i

So Real part = -1

∴ The correct option is (1)

Concept:

If a1, a2, a3,...are in GP with common ratio r, then 1/a1, 1/a2, 1/a3,.......are also in GP with common ratio 1/r.

If a, ar, ar2, ar3,.....,arn-1 are in GP then nth term of GP is given by Tn = arn-1

If a1, a2, a3, a4 are in GP, then common ratio of GP is given by,

If a be the first term, r be the common ratio of a GP then,

Let S∞ denote the sum of infinite term of GP, then , where -1 < r < 1.

Calculation:

Given GP is 2, 4, 8, 16.....

⇒ a = 2, r = 2 > 1

Let, n terms needed to get the sum 254.

We know that

⇒ 2ⁿ - 1 = 127

⇒ 2ⁿ = 2⁷

⇒ n = 7

Concept:

1) For three vectors to be coplanar, their scalar triple product should be zero.

2) Scalar triple product of vectors  and  is denoted by .

Calculation:

Given vectors are λî + ĵ + 2k̂, î + λĵ − k̂ and 2î − ĵ + λk̂

For the three vectors to be coplanar, their scalar triple product is zero.

⇒  = 0

⇒ λ(λ² - 1) - (λ + 2) + 2(- 1 - 2λ) = 0

⇒ λ³ - 6λ - 4 = 0

⇒ (λ + 2)(λ² - 2λ - 2) = 0

Therefore, the vectors are coplanar for λ = - 2.

The correct answer is option 1.

Concept:

Order of the differential equation: The order of the highest derivative present in the differential equation is the order of the differential equation.

Degree of the differential equation: The power of the highest derivative present in the differential equation is the degree of the differential equation.

Degree, n = 1

m + n = 2 + 1 = 3

The value of m + n is 3.

Therefore, the correct answer is 3.

Concept:

The value of the determinant  can be obtained by expanding along any row or column.

Expanding along the third column, the value of the determinant is

c(dh - eg) - f(ah - bg) + i(ae - bd)

Calculation:

Given,

Expanding LHS along column 3,

⇒ 0(x2 + 2x + 2- 2) - 0(1 - 2) + 1(1 - (x2 + 2x + 2)) = 0

⇒ 0 + 0 - x² - 2x - 1 = 0

⇒ x2 + 2x + 1 = 0

⇒ (x + 1)² = 0

∴ x = -1

Concept:

I. The equation of a hyperbola with the centre at origin and foci on the x-axis is given by:

II. The equation of a hyperbola with the centre at origin and foci on the y-axis is given by:

Calculation:

Given

z2 + z-2 = 2

⇒

Possible only when,

z² = 1 ⇒ (x + iy)² = 1

x² - y² + 2 ixy = 1 + i0

Comparing real and imaginary part form both the side

So, x² - y² = 1 and xy = 0

xy = 0 (not possible)

So, x² - y² = 1 is represent equation of hyperbola

Given :

To find mode from grouped frequency distribution.

Formula used :

Mode = l+(f1−f02f1−f0−f2)×h

Where, I = the lower limit of the modal class.

h = the size of the class interval.

f1 = the frequency of the modal class.

f₀ denotes the frequency of the class preceding the modal class.

f2 denotes the frequency of the class succeeding the modal class.

Calculation :

l = 20, f₁ = 30, f₀ = 15, f₂ = 6, h = 30 - 20 = 10

Mode =  = 23.85

∴ The answer is 23.85.

Total Mango trees = 40%

Remaining trees = (100 – 40 – 50)% = 10%

Hence, Option B is correct.

The figure that will replace the question mark (?) in the following figure series is shown below:

1) Dot rotates clockwise direction and one by one dot is increasing.

2) Hexagon sides one by one removed.

3) 1st to 2nd figure increases one line with a dot.

2nd to 3rd figure one arrow is increased.

3rd to 4th figure increases one line with a dot.

Hence, ‘option 4’ is the correct answer.

The correct answer is 4.

Key Points

• The National Emblem of India was adopted on 26 January 1950.
• It is inspired by the Lion Capital of Ashoka which is a statue from 250 BCE situated at Sarnath.
• The animals demonstrated on the pillar are horse, bull, elephant, and lion.
• The elephant denotes Buddha’s outset (the dream of a white elephant entering her womb dreamt by Buddha’s mother at the time of Buddha’s conception).
• The bull symbolizes the Zodiac sign of Buddha- Taurus.
• The horse signifies Buddha’s horse which he rode at the time of departing from the citadel.
• The lion indicates enlightenment.
• The Emblem is the part of the official letterhead of all the papers of the Government of India and also appears in the Indian currency.
• It can be seen in many Indian places and on Indian passports as well.
• Ashok Chakra on its base has been used as the center of the National Flag of India.

The correct answer is Gandhi Nagar.

Key PointsGandhinagar

• It is the capital city of Gujarat.
• This city lies on the west bank of the Sabarmati River.
• The famous Akshardham temple is also located in Gandhinagar.
• According to the 2011 census of India, Gandhinagar district has an 84.16% literacy rate and the female literacy rate is 75.76%.

 Additional Information

• Godhra
  • The word "Godhra" means land of cows.
  • It is a municipality in the Panchmahal district of Gujarat.
  • Godhra is famous for being the starting point of the 2002 Gujarat riots.
• Baroda
  • Baroda also known as Vadodara is the second-largest city in Gujarat.
  • It is situated on the bank of the Vishwamitri River.
  • This city is famous for Laxmi Vilas Palace, the residence of the Maratha royal Gaekwad dynasty.
• Ahemdabad
  • Ahmedabad is India's first world heritage city listed in UNESCO's World Heritage City list of 2017.
  • This city is located on the bank of the Sabarmati River.
  • Ahemdabad city is also known as 'Manchester of India'.
  • The world's largest cricket stadium, Narendra Modi Stadium is also located in Ahmedabad city.

The correct answer is the United Kingdom.

In News

• PIB News: The 7th edition of the joint military exercise “AJEYA WARRIOR-23” between India and the United Kingdom is being conducted at Salisbury Plains, United Kingdom.

Key Points AJEYA WARRIOR - 2023:

• The 7th edition of the joint military exercise “AJEYA WARRIOR-23” between India and the United Kingdom is being conducted in the United Kingdom from 27 April to 11 May 2023.
• Exercise AJEYA WARRIOR is a biennial training event with the United Kingdom which is conducted alternatively in the United Kingdom and India.
• The aim of the exercise is to build positive military relations, imbibe each other’s best practices, and promote the ability to operate together while undertaking company-level sub-conventional operations in urban and semi-urban environments under UN mandate.
• The scope of this exercise involves a Command Post Exercise (CPX) at the Battalion level and Company level Field Training Exercise (FTX).
• During the exercise, participants will engage in a variety of missions testing their operational acumen in various simulated situations; showcasing and refining their tactical drills, and learning from each other’s operational experience.
• This exercise made another significant milestone in defense cooperation between the Indian Army and British Army which will further foster the bilateral relations between the two nations.