Indian Army Agniveer Technical Mock Test - 1 - Indian Army Agniveer MCQ

The correct answer is Santhal.Key Points

• Droupadi Murmu, belonging to the Santhal tribe, recently made history becoming the first woman tribal President of India.
• She hails from Odisha’s Mayurbhanj district.
• Santhals, also spelt as Santals, are the third largest scheduled tribe community in India after the Gonds and Bhils.
• Their population is mostly distributed in Odisha, Jharkhand and West Bengal.
• The Santhals are credited for fighting against the British East India Company through the Santal Hul (revolution) of 1855-56.

The correct answer is "Kanpur".

Key Points

• Sarojini Naidu was an Indian political activist, poet, and prominent leader in India's struggle for independence.
• She was the first Indian woman president of the Indian National Congress.
• She was a prolific poet. She wrote The Golden Threshold, The Bird of Time.
• She was also known as the 'Nightingale of India'.

Additional Information

• Indian National Congress is a political party in India that was established in 1885.
• Womesh Chandra Banerjee was the first president of Congress.
• Jawaharlal Nehru dominated the congress party and won a number of elections.

The logic followed here is:

Given 9 + 7 = 58 and 3 + 11 = 124

Logic, 9 + 7 = 58

9 + 7 → 9 + 7² → 9 + 49 = 58

And 3 + 11 = 124

3 + 11 → 3 + 11² → 3 + 121 = 124

Similarly, 13 + 5

13 + 5 → 13 + 5² → 13 + 25 = 38

Therefore, 13 + 5 is equal to 38.

Hence, "Option (1)" is the correct answer.

Given:

A box includes Rs. 77 in the denominations of one rupee, 50 paise, & 25 paise coins.

Concept used:

One Rupee = 100 Paise

Calculation:

Let the number of 1 rupees coin to be x.

According to the question,

Number of 25 paise is 2x

Then, the number of 50 paise is 4x.

The box contains 77 rupees = 77 × 100 = 7700 paise

Now, equation is

⇒ 100x + (50 × 4x) + (25 × 2x) = 7700

⇒ 100x + 200x + 50x = 7700

⇒ 350x = 7700

⇒ x = 7700/350 = 22

Then,

Number of 50 paise coin is

⇒ 4x = 4 × 22 = 88.

∴ There are 88 coins in 50 paise.

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.

Given:

(x + 3) is a factor of a2 + 12x - 13

Concept used:

Factor theorem: A theorem that links factors and zeros of the polynomial.

Calculation:

Let f(x) = a2 + 12x - 13

Now, by factor theorem, if (x + 3) is a factor of f(x), then f(-3) = 0

⇒ a² + 12 × (-3) - 13 = 0

⇒ a² - 36 - 13 = 0

⇒ a² - 49 = 0

⇒ a² = 49

⇒ a = 7

∴ The required value of a is 7.

Given:

(1 + tan2θ)(1 − sinθ)(1 + sinθ)

Concept used:

(a² - b²) = (a + b)(a - b)

cosθ = 1/secθ

Calculation:

(1 + tan2θ)(1 − sinθ)(1 + sinθ)

⇒ (1 + tan2θ)(1 − sin²θ)

⇒ (sec2θ)(cos2θ)

⇒ sec2θ × 1/sec2θ

⇒ 1

∴ The required answer is 1.

Calculation:

It is given that each set A_i contains 5 elements and

∴ Number of elements is S, n(S) = 30×5 = 150

But, it is given that each element of S belong to exactly 10 of the A_i's.

∴ Number of distinct elements in S =  = 15

It is also given that each set B_j contains 3 elements and

∴ Number of elements is S, n(S) = 3×n = 3n

Also, each element of S belongs to exactly 9 of the B_j's.

∴ Number of distinct elements in S =  =

∴  = 15

⇒ n = 45

∴ The required value of n is 45.

Concept:

The null set is a subset of every set. (ϕ ⊆ A)

Every set is a subset of itself. (A ⊆ A)

The number of subsets of a set with n elements is 2ⁿ.

The number of proper subsets of a given set is 2n - 1

Calculation:

Statement I: If A = {x: x is an even natural number} and B = {y: y is a natural number}, A subset B.

A = {2, 4, 6, 8, 10, 12, ...} and A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, ...}.

It is clear that all the elements of set A are included in set B.

So, set A is the subset of set B.

Statement I is correct.

Statement II: Number of subsets for the given set A = {5, 6, 7, 8) is 15.

Given: A = {5, 6, 7, 8}

The number of elements in the set is 4

We know that,

The formula to calculate the number of subsets of a given set is 2ⁿ

= 2⁴ = 16

Number of subsets is 16

Statement II is incorrect.

Statement III: Number of proper subsets for the given set A = {5, 6, 7, 8) is 15.

The formula to calculate the number of proper subsets of a given set is 2ⁿ - 1

= 2⁴ - 1

= 16 - 1 = 15

The number of proper subsets is 15.

Statement III is correct.

∴ Statements I and III are correct.

Given:

29 × 17 × 23 × 17 × 12 - 8

Calculation:

29 × 17 × 23 × 17 × 12 - 8

Taking unit digits

⇒ 9 × 7 × 3 × 7 × 2 - 8

⇒ 63 × 3 × 14 - 8

Again taking unit digits

⇒ 3 × 3 × 4 - 8

⇒ 36 - 8 = 28

∴ The unit digit of 29 × 17 × 23 × 17 × 12 - 8 is 8

Definitions:

Diagonal matrix: A matrix whose all elements are zero except the diagonal entries.

Scalar matrix: A type of diagonal matrix whose all diagonal entries are same.

Unit matrix(identity matrix) : A scalar matrix whose all diagonal entries are 1.

Calculation:

A square matrix [aij] such that aij = 0 for i ≠ j

⇒ All elements are zero except the diagonal entries

⇒ [aij] is a diagonal matrix.

Also, aij = k, for i = j

⇒ All diagonal entries are the same but not equal to 1

⇒ [aij] is a scalar and diagonal matrix but not a unit matrix.

∴ The correct answer is option (2).

Given:

⇒ 2log(x+3) = log81

Concept used:

a log(b) = log(b)^a

Calculation:

Here,

⇒ 2log(x+3) = log81

⇒ log(x + 3)² = log81

⇒ (x + 3)² = 81

⇒ (x + 3) =

x + 3 = 9

x = 9 - 3 = 6

∴ x = 6

Concept:

For a real polynomial, complex roots occur in conjugate pairs,

that is, if x + iy is the root of a polynomial then x - iy is also the root of that polynomial.

Calculation:

The quadratic equation with real coefficients has one root as 7 + 5i

⇒ Other root of the quadratic equation is 7 - 5i

The equation with roots 7 + 5i and 7 - 5i is

(x - ( 7 + 5i))(x - (7 - 5i)) = 0

⇒ x² - (7 + 5i + 7 - 5i)x + (7 + 5i)(7 - 5i) = 0

⇒ x2 - 14x + (7² + 5²) = 0

⇒ x2 - 14x + 74 = 0

∴ The correct answer is option (1).

The correct answer is Charle’s law.

Key Points

• Charle’s law
  • ​Charles's law states that the volume of an ideal gas is directly proportional to the absolute temperature at constant pressure.
  • When the pressure that is applied to a sample of a dry gas is maintained at the same level, the law also states that the Kelvin temperature and the volume will be directly proportional.
  • Jacques Charles, a French physicist, drafted this law in 1780. His unpublished work provided a comprehensive description of this law.
  • The ideal gas law is a special case of Charle's law.

Additional Information

• Boyle’s law
  • ​Boyle's law is a gas law that says that a gas's pressure is inversely proportional to its volume when it has a given mass and is kept at a constant temperature.
• Thomson’s law
  • ​Along the length of a material rod whose ends are at different temperatures, heat power (Qτ) is absorbed or evolved.
  • The temperature gradient along the rod and the current flow were found to be inversely correlated with this heat.
• Graham’s law
  • ​A gas's rate of diffusion or effusion is inversely proportional to the square root of its molecular weight, according to Graham's law.

The correct answer is 30°.

Key Points

• Reflection: The phenomenon in which a light ray is sent back into the same medium from which it is coming, on interaction with a boundary, is called reflection.
• Laws of reflection: it states that, if a light ray is reflected from a plane flat polished surface its angle of the incident will always be equal to the angle of reflection
  • i.e., The angle of incidence (θ i ) = Angle of reflection (θ r )
• ​Hence the angle of reflection will be 30°.

The correct answer is 2 minutes.

Explanation:

• The Earth rotates around the Sun, resulting in day and night and changes in years.
• The day begins with the sunrise, and the night begins with the sunset.
• When the Sun crosses the horizon, it is said to be sunset.
• The line where the Earth's surface and the sky appear to meet is known as the horizon.
• And, as we know, if we look at the Sun from Earth, the Earth's atmosphere is denser than the Sun's. As a result, we are seeing it from denser atmospheric air.
• As a result, the Sun appears to be raised above the horizon, and we can see it 2 minutes before sunrise.
• The same thing happens at sunset, where we can see the Sun 2 minutes after sunset.
• As a result, the time difference between the actual sunset and the apparent sunset is approximately 2 minutes.

Concept:

Work: It's the energy transferred to or from an object via the application of force.

Explanation:

Work done by a constant force:

• It's equal to the product of the force and displacement.
• Work done (W) = force (F) × displacement (s)​

The necessary conditions for the work done are:

• There should be a force (F) acting on the body
• There should be some displacement (s)

Hence, when either of these is zero, the work done would be zero.
Key Points

• Work done is negative when the force acts opposite to the direction of displacement.
• Work done is positive when the force is in the direction of displacement.​

The correct answer is A negative force implies attractive nature.

Key Points

• Think of it like this Positive(P) x Negative(N) always gives you a Negative(N), whereas when you times PxP or NxN It always equals to P. you can apply this to Charged Particles Two postives give a Repulsive force ( P) and two non-alike charges give a Negative, therefore you can say that attraction is negative.
• Similarly, in the case of magnetic forces, a positive force can be attractive between the north and south poles of a magnet, while it can be repulsive between north and north poles, or south and south poles.
• Therefore, the sign of the force alone cannot determine whether the nature of the force is attractive or repulsive.
• The nature of the force depends on the properties of the specific physical system and the objects involved.

Property of a liquid is it always occupies minimum surface area, this phenomenon of liquid is known as Surface Tension.

A force which is known as “Van der Waals” forces, draw the liquid particles together.

Mathematically surface tension is defined as the ratio of Forces and the ratio of the surface force F to the length d along which the force acts.

● Example of Surface Tension –

• In a dropper, the water does not flow in a continuous stream, but rather in a series of drops.
• Several insects are able to walk on water.
• Bubbles are round.
• Needle floating on water.

CONCEPT:

• When an electric current is passed through a conductor, the conductor becomes hot after some time and produces heat.
• This happens due to the conversion of some electric energy passing through the conductor into heat energy. This effect of electric current is called the heating effect of the current or the Joule heating effect.
• The appliances based on the heating effect of electric current work on both AC and DC supply.
• The amount of heat liberated can be given as

H = I²RT

where, H = Heat Generated in Joules, I = Current in Amperes, R = Resistance of coil in Ohms, T = time in seconds

Calculation:
Given:
H = 60,000 J , R = 10 Ω, T = 1 minute = 60 second

The correct answer is Coherent beam.

Key Points

LASER - Light Amplification by Stimulated Emission of Radiation:

• A laser is an unusual light source as it is quite different from a light bulb or a flashlight.
• A laser is a device that is used to produce a highly monochromatic, coherent, a unidirectional beam of light
• A laser device makes use of atoms or molecules to emit light at particular wavelengths and amplifies that light to produce a narrow beam of radiation.​

• Wavelength has measured the distance between the adjacent crest or trough

The correct answer is Option 2.

Key Points

• An object can be called a stationary object when it is not moving or its position is not changing with respect to its surroundings.
• In other words, a stationary object is at rest or in a state of equilibrium.
• This is in contrast to a moving object, which is in motion and has a changing position with respect to its surroundings.
• It's important to note that whether an object is stationary or not depends on the frame of reference.
• For example, an object may be stationary with respect to the ground but may be moving with respect to a moving vehicle.

The Correct answer is Phosphorus doesn’t react with water

Explanation:

• Phosphorus was discovered by Hennig Brand in 1669.
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  • Phosphorus has the smell of garlic.
  • Elemental phosphorus exists in two different forms namely white phosphorus and red phosphorus.
  • Phosphorus is never found as a free element on earth due to its high reactivity.
  • < />Phosphorus is stored in water to prevent its contact with atmospheric oxygen.
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    • The element kept in water is white phosphorus.
    • White phosphorus emits green light on exposure to the atmosphere.
    • White phosphorus burns in the atmosphere at 30º C.
    • Red phosphorus is used for making safety matches.
    • Phosphorus is used in the fertilizer industry.
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      • Sodium (Na) and potassium (K) are kept in Kerosene to avoid moisture and oxidation.
      • White phosphorous is kept underwater to avoid oxidation, also it is insoluble in water.
      • "Phosphorus oxide is formed" is incorrect. While phosphorus oxides can be formed in other reactions involving phosphorus, in this specific reaction with water, phosphorous acid (phosphorus hydroxide) is formed, not a phosphorus oxide.
      • "Hydrogen gas is released" is also incorrect. Although hydrogen is present in the reactants (water), it is not released as a gas in this specific reaction.

The correct answer is Evaporation

Key Points

• Evaporation is used to separate salt from seawater.
  • Evaporation is the process by which a liquid turns into a gas at any temperature.
  • Evaporation is an essential part of the water cycle.
  • Evaporation of water occurs when the surface of the liquid is exposed, allowing molecules to escape and form water vapour; this vapour can then rise up and form clouds. With sufficient energy, the liquid will turn into vapour.
  • The salt can be separated from the seawater by a simple process of evaporation.
• Separation of salt from water:
  • Pour the salt water into a shallow pan.
  • As the water evaporates, the salt will remain behind.​

​

Additional Information

• Centrifugation is a process that involves using a centrifuge, a machine with a rapidly rotating container, to separate substances based on their density or sedimentation rate.
• Crystallization is a process in which solute particles come together in a systematic and ordered manner to form a solid crystal structure. This phenomenon occurs when a substance transitions from a dissolved or liquid state to a solid state, creating a regular arrangement of atoms, ions, or molecules in a repeating pattern known as a crystal lattice.

Option 4 is correct, i.e. 2n2.Key Points

• Each shell can contain only a fixed number of electrons.
• The general formula is that the nth shell can in principle holds up to 2n2 electrons.

The correct answer is 1 : 8.

Key Points Concept:

• Molecular mass is the sum of the atomic masses of the elements present in a molecule.
• The mass of one mole of a substance in grams is called its molar mass.

Explanation:

It is obtained by multiplying the atomic mass of each element by the number of its atoms and adding them together

1 mole of hydrogen = 1gm

1 mole of oxygen = 16gm

Water (H2O) = 2 Hydrogen atoms + 1 Oxygen atom

2 mole of hydrogen = 2gm

1 mole of oxygen = 16 gm

The ratio of the mass of Hydrogen: Ratio of mass of Oxygen = 2/16 = 1/8

The ratio of the mass of Hydrogen to the mass of Oxygen is always 1:8.

The correct answer is Hydration.

Key PointsRedox Reaction:

• Redox reactions are oxidation-reduction chemical reactions in which the reactants undergo a change in their oxidation states.
• The term ‘redox’ is a short form of reduction-oxidation.
• All the redox reactions can be broken down into two different processes: a reduction process and an oxidation process.
• The oxidation and reduction reactions always occur simultaneously in redox or oxidation-reduction reactions.
• The substance getting reduced in a chemical reaction is known as the oxidizing agent, while a substance that is getting oxidized is known as the reducing agent.
• The different types of redox reactions are
  • Decomposition Reaction
  • Combination Reaction
  • Displacement Reaction
  • Disproportionation Reactions
• ​Examples of Redox Reaction-
  • The rusting of iron: In this reaction, the metal iron is oxidised by the oxygen in the air to form the oxide known as rust.
  • The burning of fossil fuels: When coal, oil, or natural gas are burned, they are oxidised by the oxygen in the air to form carbon dioxide and water vapour.
  • The production of electricity in a power plant
  • Lightening- The formation of oxides of nitrogen from nitrogen and oxygen by lightning is a redox reaction.

The correct answer is option 1

Key Points

• Chemical equilibrium is a state in a reversible chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction.
• The concentrations of the reactants and products remain constant when a system is at equilibrium, even though reactions are still happening.
• Equilibrium is a dynamic state, not a static one. It's a balance of continuous action with reactants forming products and vice versa.
• Changing the concentration of either reactants or products will shift the equilibrium. Increasing the concentration of reactants pushes the equilibrium to the right (favouring products), while increasing the concentration of products pushes it to the left (favoring reactants).
• The equilibrium constant (K) quantitatively represents the ratio of the concentrations of products to reactants at equilibrium, with each concentration raised to the power of its stoichiometric coefficient. The value of K at a particular temperature demonstrates whether the reactants or products are favoured in the equilibrium.
• An equilibrium expression is a mathematical representation of a chemical reaction at equilibrium. It is derived from the balanced chemical equation for the reaction and the equilibrium constant.
• 

Additional Information

• A reaction is said to be at equilibrium when the rate of the forward reaction (reactants transforming into products) equals the rate of the backward reaction (products transforming back into reactants). At this point, there are still reactions happening, but there's no net change in the concentrations of reactants and products.
• The statement "50% of the reactants are converted to products" doesn't necessarily describe equilibrium. Equilibrium doesn't require a specific ratio of reactants to products; rather, it requires the rates of the forward and backward reactions to be equal.
• The volume of reactants being equal to the volume of products is not a condition for chemical equilibrium. Equilibrium is about the rates of the forward and backward reactions, not the volumes or quantities of reactants and products.
• If all reactants are converted to products, the reaction is considered complete, not at equilibrium. A system at equilibrium still has both reactants and products present because the forward and reverse reactions continue to occur at the same pace.

Conclusion:-

So, the Reaction is said to be in equillibrium when the rate of transformation of reactants to products is equal to the rate of transformation of products to the reactants.

The correct answer is Alkyne.

Key Points

• A hydrocarbon in which two carbon atoms are joined by a triple bond is called an Alkyne.
• A hydrocarbon is an organic compound consisting entirely of hydrogen and carbon.

Important Points

• Alkane
  • These are organic compounds that consist entirely of single-bonded carbon and hydrogen atoms and lack any other functional groups.
  • General Formula- C_nH_2n+2
  • They are the principal constituent of gasoline and lubricating oils and are extensively employed in organic chemistry.
• Alkene
  • These are a class of hydrocarbons unsaturated compounds with at least one carbon-to-carbon double bond.
  • General Formula-C_nH_2n
  • Alkenes are more reactive than alkanes due to the presence of the double bond.
  • They are used in the synthesis of alcohols, plastics, lacquers, detergents, and fuels as starting materials.
• Alkyne
  • These are organic molecules made of the functional group carbon-carbon triple bonds.
  • Chemical Formula-C_nH_2n−2
  • Alkynes are commonly used to artificially ripe fruits.

Correct answer: 1)

Concept:

• An electrochemical cell is a device capable of either generating electrical energy from chemical reactions or facilitating chemical reactions through the introduction of electrical energy.
• Galvanic cells play a crucial role in our day-to-day lives by providing electric current of a small power scale.

Explanation:

• An electrochemical cell has a zinc electrode dipped in a solution of zinc sulfate and forms the anode (negative electrode).
• It has a copper electrode dipped in a solution of copper sulfate and forms the anode (positive electrode) of the cell.
• The anode is connected to the cathode externally with the help of a wire and internally with the help of the salt bridge.
• Electrons flow from anode to cathode through the external supply in an electrochemical cell.

• The transfer of electrons in the external circuit from the anode to the cathode generates an electric current from the cathode to the anode (opposite to the flow of electrons).

Conclusion:

Thus, In an electrochemical cell, electrons travel from the anode to the cathode through the external Circuit.