Indian Navy Agniveer Mock Test - 7 - Indian Navy Agniveer MCQ

Correct option: 3.

The idiom means: To appear for the first time in some role or position.

Example sentence: The acclaimed director's daughter will be making her bow as an actor in next week's blockbuster.

The correct answer is "came forward to help"

Key Points

• The most appropriate option to substitute the underlined segment in the given sentence is 'came forward to help.'
• Here, in the given question, 'forward' should be used instead of 'forwards.'
• The word 'forwards' is a wrong usage and it does not contain meaning.
• Forward: towards the future.
  • Example: I always look forward, not back.
• Therefore, as per the points mentioned above, the correct answer is option 4. ​​

​Correct sentence: They came forward to help the children in distress.

The correct answer is "​Public influence on policy-decisions".

Key Points

• Let's consider the following statements from the above passage.
  • The role of public activisim in influencing government policy can be particularly important in promoting the positive functions of the government.
• From the above statement it is clear that the positive functions of the government can be supported by public influence on policy-decisions.

Therefore, the correct answer is Option 1.

The correct answer is "​Effective public activism".

Key Points

• Let's consider the following statements from the above passage.
  • The vigilance and involvement of the public can be quite crucial not only in ensuring an adequate expansion of these essential services but also in monitoring their functioning.
• From the above statement of the passage it is clear that the adequate monitoring of public services is possible through effective public activism.

Therefore, the correct answer is Option 4.

The correct answer is "Local community involved".

Key Points

• Let's consider the following statements from the above passage.
  • Indeed the actual reach and effective quality of the services that are meant to be, in principle available often depends a great deal on the information that the local community gathers and the extent to which it can get its voice heard.
• From the above statement it is clear that the effective quality of services depends upon making Local community involved.

Therefore, the correct answer is Option 2.

The correct answer is 'His story was, in many ways, plausible.'

Key Points

• The given sentence is a declarative sentence.
• In this case, we use commas ( , ) after the word "was" and "ways" to isolate the extra information that is not essential to the meaning of the sentence.
• The commas and everything within them could be removed, and still the sentence would make sense both scientifically and grammatically.
  • Example:
  • Mitochondria, which generate ATP, are easily seen after staining with the dye Janus green.
  • Mitochondria are easily seen after staining with the dye Janus green.
• The full stop ( . ) represents the greatest pause and separation and it is used to mark the end of a declarative or an Imperative sentence.
  • Example: Dear, patient, gentle, Nell was dead.
• ​So, we must use a full stop ( . ) at the end of the sentence.
• ​Therefore, the correct answer is Option 2.
  ​

Correct sentence: His story was, in many ways, plausible.

The correct answer is 'The Ministry of External Affairs has taken this issue solemnly.'

Key Points

• The given sentence is in Passive Voice. As per the question we have to change it into Active Voice.
• The structure of the given sentence is as follows:
  • Subject + has/have + V3 + Object. (Active Voice)
  • Subject (Objective Case) + has/have + been + V3 + Object (Subjective Case). (Passive Voice)
• Example:
  • We have looked at the plan carefully.(Active Voice)
  • The plan has been carefully looked at.(Passive Voice)
• The subject will be put in place of the object and the object will be put in place of the subject.
• 'has been taken' will be changed into 'has taken'.
• Lastly, the preposition 'by' will be removed.
• Therefore, as per the points, mentioned above, we find that the correct answer is Option 4.

Correct Sentence: The Ministry of External Affairs has taken this issue solemnly.

The correct solution is 'whose daughter'.

Key Points

• The sentence given in the question has to be filled with a determiner in order to determine the position of the teacher in relation to the classmates.
• A determiner is "a word which is used at the beginning of a noun group to indicate, for example, which thing you are referring to or whether you are referring to one thing or several".
• We use the determiner 'whose daughter' as it perfectly defines the relationship between the teacher and my classmate.
• Option 1, 'her daughter' is incorrect as it does not join the sentence, but instead separates it, i,.e "my mother met the teacher. Her daughter is our classmate".
• Option 2, 'the daughter of us' is also an incorrect option as it doesn't grammatically makes sense when used in the sentence.
• Option 3, 'who is daughter' is itself a phrase with grammatical error and cannot be used to fill in the blanks.
• Hence the correct option is option 4.

Concept:

• Nuclear forces are the forces between protons and neutrons and that bind them to the atomic nuclei.
  • The protons and neutrons are called nucleons.
  • The nuclear force is generally attractive in nature.
  • But at a distance less than 0.7 fm from the center of the nucleus, the nucleons are very close to each other such that after a point, they cannot come closer from attraction and starts repelling. This is where the nuclear forces are repulsive in nature and thus, the nucleus is held without nucleons colliding into itself.
  • The nuclear force is a short-range force and at distance greater than 2.5 fm from the center of the nucleus, it is non-existent.

Explanation:

• The nuclear force is short-range and can be both attractive and repulsive in nature.
• Protons are positively charged and neutrons are uncharged. The nuclear force exists between nucleons i.e. it can be between protons and protons, neutrons and protons, or neutrons and neutrons. Therefore, the nature of the force remains the same independent of their charges.
• Hence, only options A & B are correct.

The correct option is Calcium oxide.
Concept:

• Oxides are compounds formed by the reaction of metals, non-metals with oxygen. The types of oxides are:
• Basic oxide: It is a complex chemical substance oxide, which forms a salt with a chemical reaction with acids or acidic oxides and does not react with bases or basic oxides.
• E.g. Copper oxide (Cu2O), Magnesium oxide (MgO)
• Acidic oxide: It is a complex chemical substance oxide, which forms a salt with the chemical reactions with bases or basic oxides and does not react with acidic oxides.
• E.g. Carbon dioxide (CO2), Silicon dioxide (SiO2)
• Amphoteric oxide: It is a complex chemical substance, also oxides, which form a salt with the chemical reactions with acids (or acid oxides) and with bases (or basic oxides).

Key Points

• Calcium oxide does not react with sodium hydroxide (NaOH) because sodium hydroxide (NaOH) is the base and it can only react with either an acidic oxide or amphoteric oxide.
• Only the metals, whose oxides/hydroxides are amphoteric, react with strong water-soluble bases (Alkalies) to liberate Hydrogen gas. They are Be, Zn, Al, Sn, Pb, Cr, etc. & few metalloids (As, Sb, Ge) also.

Examples:

2Al + 2 NaOH + 2 H2O → 2 NaAlO2 + 3 H2

Zn + 2 NaOH → Na2ZnO2 + H2

Concept:

Blackbody: A body which absorbs all radiations incident on it is called a perfectly black body.

Wien's displacement law: The blackbody radiation curve for different temperatures peaks at a wavelength inversely proportional to the temperature.

Wien’s displacement law

CONCEPT:

Gravitational Potential Energy:

• The gravitational potential energy of a body at a point is defined as the amount of work done in bringing the body from infinity to that point against the gravitational force.
• The gravitational potential energy of a body at height h from the earth surface is given by

Where M = mass of earth, m = mass of the body, r = distance from the earth

• The unit of Gravitational potential energy is Nm.
• The dimension of gravitational potential energy is [ML2T-2].

CALCULATION:

• Initial gravitational potential energy is

 ------- (1)

• Final gravitational potential energy is

 ------- (2)

• The gain in potential energy is

⇒ ΔU = U_f - U_i

As we know,

⇒ΔU=12mgR

Explanation:

AC generator:

• An electric generator is a device that is used to convert mechanical energy into electric energy.
• It is also known as a dynamo.
• An electric generator works on the Electromagnetic Induction Principle.
• The Principle of Electromagnetic Induction states that when a conductor is connected with a changing flux, it will induce an emf across it. The value of induced emf across the conductor depends on the rate of change of flux connected with the conductor.

Galvanometer:

A moving coil galvanometer is an electromagnetic device that can measure small values of current. It consists of permanent horseshoe magnets, coil, soft iron core, pivoted spring, non-metallic frame, scale, and pointer.

Transformer:

A Transformer is used to convert low voltage (or high current) to high voltage (or low current) and high voltage to low voltage.

It works on the principle of electromagnetic induction.

The primary coil has Np turns and the other coil, called the secondary coil, has Ns turns.

Generally, the primary coil works as the input coil and the secondary coil works as the output coil of the transformer.

Metal detector:

Ultrasound can't travel through a metal element. So it is used as a metal detector also. It works on the principle of resonance in an AC circuit

∴ (A) - (II), (B) - (I), (C) - (IV), (D) - (III)

Hence option 1) is the correct choice.

Concept used:

A matrix X is said to be involutory if

Calculations:

A =

then

Hence Matrix A is involutory.

Given:

The given limiting function is as follows,

Concept:

Use the L'hospital rule for the limit 

Where,

f'(x) and g'(x) are the derivative of f(x) and g(x).

Solution:

The given limit is as follows,

Derivating f(x) and g(x) we will get,


Hence, option 3 is correct.

Explanation:

 = sin  ----(∵ sin^-1(−12) = )

= sin [π3+π6]

= sin

= sin

= 1

The value of  is 1.

The correct answer is option (4).

For the term to be independent of n. The power of ‘x’ in the numerator and the denominator must be equal

∴ 6 – r = r

6 = 2r

⇒ r = 3

r = 3 corresponds to 4^th term,

∴ 4^th term will be independent of ‘x’

Therefore, the term independent of x in the expansion of is 160/27.

Concept:

1) The critical point of a function is the point where its first derivative is 0.

2) A function has minima if its second derivative at a critical point is greater than 0.

Calculation:

The given equation of the curve is x2 – 8x + 17.

Let f(x) = x2 – 8x + 17

∴ f'(x) = 2x - 8

For critical point, put f'(x) = 0

⇒ 2x - 8 = 0

⇒ x = 4

f''(x) = 2 > 0 hence f(x) has minima at x = 4.

∴ Minimum value of f(x) = f(4)

f(4) = 4² - 8 × 4 + 17 = 1

∴ The minimum value of x2 – 8x + 17 is 1.

The correct answer is option 3.

Calculation:

Given:

y = log(cos ex)

We know,

→  and

On Differentiating y = log(cos ex) both sides

By chain rule.

→ = - tan ex

Concept:

1) The product of the slopes of tangent and normal at a point is - 1.

2) The equation of the line passing through the point (h, k) and slope m is

y - k = m(x - h)

Calculation:

Given the equation of the curve is y = sin x

The slope of the tangent of curve y' = cos x

The slope of the tangent at point (0, 0) is cos 0 = 1

∴ Slope of normal = - 1

Hence equation of normal at (0, 0) is :

y - 0 = - 1(x - 0)

⇒ x + y = 0

∴ The equation of the normal to the curve is x + y = 0

The correct answer is option 3.

Calculation:

Given, f(x) = xx2−5x+9, x ∈ R

y =

⇒ yx² - 5xy + 9y - x = 0

⇒ yx² - (5y + 1)x + 9y = 0

Given that x is real, therefore, Discriminant ≥ 0

⇒ [- (5y + 1)]² - 4 × y × 9y ≥ 0

⇒ (5y + 1)² - 36y² ≥ 0

⇒ 25y² + 10y + 1 - 36y² ≥ 0

⇒ - 11y² + 10y + 1 ≥ 0

⇒ 11y² - 10y - 1 ≤ 0

⇒ 11y² - 11y + y - 1 ≤ 0

⇒ 11y(y - 1) + 1(y - 1) ≤ 0

⇒ (11y + 1) (y - 1) ≤ 0

∴

The values of xx2−5x+9 are .

Concept:

If the parametric equations x = x(t) and y = y(t), then the equation of the tangent line at t = a is found using the following steps:

Find the point at which the tangent is drawn, (x_o, y_o) by substituting t = "a" in the given parametric equations. i.e., (x_o, y_o) = [x(a), y(a)]

Find the derivative of the function using,

Find the slope of the tangent (m) by substituting t = "a" in the above derivative.

Find the equation of the tangent line using,

y - y_o = m(x - x_o)

Calculation:

Given the equation of the curve is x = et. cost, y = et. sin t

x = e^t⋅ cos t

 = e^t(cos t - sin t)

y = e^t⋅ sin t

dydt = e^t(sin t + cos t)

∴ Tangent of the curve at t =

⇒ dydx=12+1212−12=20

⇒ dydx is undefined.

∴ The tangent to the curve makes an angle π2 with the x-axis.

The correct answer is π2.

Concept:

• sin3x = 3sinx - 4sin³x
• cos3x = 4cos³x - 3cosx

Calculation:

f(x) = 3(sin x − cos x) + 4(cos3 x − sin3 x)

f(x) = 3sinx - 3cosx + 4cos³x - 4sin³x

f(x) = (3sinx - 4sin³x) + (4cos³x - 3cosx)

f(x) = sin3x + cos3x

f'(x) = 3cos3x - 3sin3x

Now, f'(x) = 0

⇒ 3cos3x - 3sin3x = 0

⇒ cos3x - sin3x = 0

⇒ sin3x = cos3x

⇒ tan3x = 1

Hence, the maximum value of given function is =

= 12+12=2

∴ The correct option is (2)

Concept:

Explanation:

Concept:

• Coefficient of (r + 1)^th term in the expansion of (1 + x)^r is ⁿC_rx^r.
• We know that .

Calculation:

The coefficient of rth term in the expansion of (1 + x)14 is 14Cr-1

Coefficient of (r + 1)^th term in the expansion of (1 + x)¹⁴ is ¹⁴C_r

Coefficient of (r + 2)^th term in the expansion of (1 + x)14 is 14Cr+1

Given the coefficient of rth, (r + 1)th and (r + 2)th terms in the expansion of (1 + x)14 are in A.P.

⇒ 2(14Cr ) = 14Cr-1 + 14Cr+1

Rewriting the equation.

⇒  = 2.

We know that

⇒

⇒

⇒ 2r² - 28r + 210 - 2(15 - r)(r + 1) = 0

⇒ 4r² - 56r + 180 = 0

⇒ r² - 14r + 45 = 0

⇒ (r - 5)(r - 9) = 0

⇒ r = 5 or r = 9

The required value of r is 5 or 9.

Concept:

A function f(x) is continuous at x = a, if  
Calculation:

Given that f(x) is continuous at x = 0.

⇒ Left hand limit (LHL) at x = 0 = Right hand limit (RHL) at x = 0 = f(0)

(LHL)x=0(LHL)x=0 = f(0) (∵ f(x) is continuous at x = 0)

⇒  8 = a

∴ a = 8

The required value of a is 8.

Concept:

Trigonometry:

• tan  = 1.

Algebra:

• (a ± b)² = a² ± 2ab + b².

Calculation:

1 + tan2 x - 2 tan x = 0

⇒ 1² - 2 (1) (tan x) + (tan x)² = 0

⇒ (1 - tan x)² = 0

⇒ 1 - tan x = 0

⇒ tan x = 1

⇒ x = .

Given statement : [{(32 × 20) - (2 ÷ 3)} + (2 - 4)] ÷ 3

According to the question, after interchanging the signs :

​⇒[{(32 - 20) + (2 × 3)} ÷ (2 + 4)] × 3

⇒[{12 + 6} ÷ 6] × 3

⇒[18 ÷ 6] × 3

⇒3 × 3

⇒9

The leader who opposed the Champaran satyagraha of Mahatma Gandhi was N.G Ranga.

Key Points

• Gandhiji successfully led this Satyagraha in March-April, 1917.
• Gandhiji went to jail during Satyagraha which was his first jail/arrest in India.
• It was Gandhiji's first Satyagraha in India.
• European planters forced the cultivators to cultivate indigo on 3/20th of their holdings (known as the tinkathia system).
• The Government appointed a Commission and nominated Gandhiji as one of its members.

• Planters refunded only twenty-five per cent of the money they had taken illegally from the peasants.

• During this satyagraha N.G Ranga opposed Gandhiji.

• N.G Ranga was the founding member of All India Kisan Sabha (AIKS) at the Lucknow session of the Congress in April 1936.

• Sahajanda Saraswati was elected as its first president and Ranga as a general secretary.

Hence we can conclude that the leader who opposed the Champaran satyagraha of Mahatma Gandhi was N.G Ranga.

Additional Information

• Ferozeshah Mehta was one of the founding members of the Indian National Congress.
• Madan Mohan Malviya was a moderate leader and opposed separate electorates for Muslims under the Lucknow Pact of 1916. The Mahamana title was conferred on him by Gandhiji.
• Bal Gangadhar Tilak was an extremist leader of the Indian National Movement.