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All questions of Notification for JEE Exam

Which of the following species has the highest ionization potential?
  • a)
    Li+
  • b)
    Mg+
  • c)
    Al+
  • d)
    Ne
Correct answer is option 'A'. Can you explain this answer?

Krishna Iyer answered
Li+ has highest ionization potential among the given species. The reason for this is after losing one electron, the Li+ ion has more stable inert gas configuration, i.e. 1s2 . Secondly, it has smallest size among all the species due to less number of electrons and high effective nuclear charge.

Which one of the following will undergo meta-substitution on monochlorination ?
  • a)
    Ethoxybenzene
  • b)
    Chlorobenzene
  • c)
    Ethyl benzoate
  • d)
    Phenol
Correct answer is option 'C'. Can you explain this answer?

Aarya Bose answered
Meta-Substitution in Monochlorination of Ethyl Benzoate

Introduction:
Monochlorination is a method of introducing a chlorine atom into an organic compound. It can occur in three positions, ortho (1,2), meta (1,3), and para (1,4), depending on the position of the hydrogen atoms on the aromatic ring. The position of substitution depends on the relative stability of the intermediate carbocations formed during the reaction. In this question, we have to identify the compound that will undergo meta-substitution on monochlorination.

Explanation:
The stability of the intermediate carbocation is directly proportional to the number of electron-donating groups present on the aromatic ring. The more the number of electron-donating groups, the more stable the carbocation becomes. Similarly, the more the number of electron-withdrawing groups, the less stable the carbocation becomes. This is because electron-donating groups stabilize the positive charge, whereas electron-withdrawing groups destabilize it.

Ethyl benzoate has an electron-withdrawing ester group (-COOEt) attached to the aromatic ring. This group destabilizes the intermediate carbocation, making it less stable than that of benzene. Hence, the reaction proceeds via the meta-substitution pathway to form meta-chloro ethyl benzoate as the major product.

On the other hand, chlorobenzene has a chlorine atom already attached to the aromatic ring. This chlorine atom is an electron-withdrawing group that destabilizes the intermediate carbocation formed during the reaction. However, it is not as destabilizing as the ester group, and hence, the reaction proceeds via the ortho-para substitution pathway to form ortho and para products.

Conclusion:
In conclusion, the compound that will undergo meta-substitution on monochlorination is ethyl benzoate. This is because the electron-withdrawing ester group attached to the aromatic ring destabilizes the intermediate carbocation, making it less stable than that of benzene. Hence, the reaction proceeds via the meta-substitution pathway to form meta-chloro ethyl benzoate as the major product.

 Symptoms of Diphtheria is –
(BHU - 86)
  • a)
    Gum bleeding
  • b)
    Fear of water
  • c)
    Suffocation
  • d)
    Stomachache
Correct answer is option 'C'. Can you explain this answer?

Shreya Singh answered
Possible obstruction that causes breathing difficulties.thus, it's suffocation and it is caused by corynebacterium diphtheria.

Can you explain the answer of this question below:
If in a square matrix A=[aij], we find that
aij = aji ∀ i,j, then A is a
  • A:
    symmetric matrix
  • B:
    diagonal matrix
  • C:
    skew symmetric matrix
  • D:
    transpose matrix
  • E:
    undefined
The answer is a.

Suman Kumar answered
If aij=aji then it is symmetric matrix but if aij=-aji then it is skew symmetric because transpose of A is equal to A for symmetric matrix .and we know that transpose of matrix is defined as aij=aji

Can you explain the answer of this question below:
If a+b+c=0, |a|=3, |b|=5, |c|=7, then the angle between a and b is
  • A:
    π/6
  • B:
    2π/3
  • C:
    5π/3
  • D:
    π/3
  • E:undefined

The answer is d.

Shanaya Shah answered
We know that the dot product of two vectors is equal to the product of their magnitudes multiplied by the cosine of the angle between them:

a · b = |a| |b| cosθ

Since a · b = 0, we have:

0 = 3 * 5 * cosθ

Simplifying, we find:

0 = 15 cosθ

Cosθ = 0

The angle θ between a and b can be any angle where cosθ = 0. This occurs when θ is equal to 90 degrees or any odd multiple of 90 degrees. Therefore, the angle between a and b is:

θ = 90 degrees or 270 degrees (or any odd multiple of 90 degrees)

In this letter series, some of the letters are missing. Choose the correct letter given below -
gfe _ ig _ eii _ fei _ gf _ ii
  • a)
    eifgi
  • b)
    figie
  • c)
    ifgie
  • d)
    ifige
Correct answer is option 'C'. Can you explain this answer?

Siddharth Roy answered
Given letter series: gfe _ ig _ eii _ fei _ gf _ ii

To solve this letter series, we need to identify the pattern followed by the letters in the series.

Pattern:

- The first letter of each group is the third letter of the previous group.
- The second letter of each group is the first letter of the previous group.
- The third and fourth letters of each group are the second and fourth letters of the previous group, respectively.
- The last two letters of the series are 'ii', which is the same as the last two letters of the previous group.

Using this pattern, we can fill in the missing letters in the series as follows:

gfe --> igf --> eii --> fei --> gfi --> ii

Therefore, the missing letters in the series are 'ifgie'.

Hence, the correct answer is option 'C'.

The element with the highest first ionization potential is
  • a)
    Boron
  • b)
    Carbon
  • c)
    Nitrogen
  • d)
    Oxygen
Correct answer is option 'C'. Can you explain this answer?

Pragati Mishra answered
Explanation:
First ionization potential (FIP) is defined as the minimum amount of energy required to remove one mole of electrons from one mole of gaseous atoms or ions in the ground state. The element with the highest first ionization potential is the hardest to ionize, which means it requires the most energy to remove an electron from its atom.

Ionization Potential Trend:
The ionization potential of elements generally increases from left to right across a period and decreases from top to bottom within a group in the periodic table.

Comparison of First Ionization Potential:
Among the options given, Nitrogen (N) has the highest first ionization potential because of the following reasons:

- Boron (B) has an electronic configuration of 1s² 2s² 2p¹. It has a low first ionization potential because it has only three valence electrons in the 2s² 2p¹ subshells. These electrons are not strongly attracted towards the nucleus due to shielding effect and distance.
- Carbon (C) has an electronic configuration of 1s² 2s² 2p². It has a higher first ionization potential than Boron because it has four valence electrons in the 2s² 2p² subshells. The electrons are more strongly attracted to the nucleus due to a decrease in atomic radius and increased nuclear charge.
- Nitrogen (N) has an electronic configuration of 1s² 2s² 2p³. It has the highest first ionization potential among the given options because it has five valence electrons in the 2s² 2p³ subshells. The electrons are held tightly due to strong nuclear charge and lesser shielding effect.
- Oxygen (O) has an electronic configuration of 1s² 2s² 2p⁴. It has a lower first ionization potential than Nitrogen because it has six valence electrons in the 2s² 2p⁴ subshells. The electrons repel each other and are less strongly attracted to the nucleus.

Therefore, the correct answer is option 'C' Nitrogen.

Can you explain the answer of this question below:

A complex compound of Co3⁺ with molecular formula CoClxyNH₃ gives a total of three ions per molecule when dissolved in water. How many Cl⁻ ions satisfy primary as well secondary valencies in this complex?

  • A:

    3

  • B:

    4

  • C:

    1

  • D:

    0

  • E:

    undefined

The answer is c.

Maulik Nair answered
Given: Complex compound of Co3 with molecular formula CoClxyNH gives a total of three ions per molecule when dissolved in water.

To determine: How many Cl ions satisfy primary as well secondary valencies in this complex?

Solution:
- The molecular formula of the complex compound is CoClxyNH.
- The compound gives a total of three ions per molecule when dissolved in water, which means that it is a cationic complex with a charge of +3.
- The coordination number of cobalt in the complex is 6, as it is a transition metal and can form 6 coordination bonds.
- The NH ligand is neutral and does not contribute any charge to the complex.
- Therefore, the charge on the complex is +3, and the sum of the charges of the ligands must be -3 to balance the charge on the complex.
- The Cl ions have a charge of -1 each, so the number of Cl ions in the complex is equal to the absolute value of the charge on the complex, which is 3.
- The Cl ions can satisfy either primary or secondary valencies in the complex.
- Primary valencies are satisfied by the ligands directly attached to the metal ion, while secondary valencies are satisfied by the ligands that are not directly attached to the metal ion but are still part of the coordination sphere.
- Since the coordination number of cobalt in the complex is 6, all 6 coordination sites are occupied by either Cl or NH ligands.
- Therefore, all the Cl ions in the complex satisfy primary valencies and none of them satisfy secondary valencies.
- Hence, the number of Cl ions that satisfy both primary and secondary valencies in this complex is 0.
- The correct option is (c) 1.

Therefore, the answer is option 'C', 1 Cl ion satisfies either primary or secondary valency.

The area of the region bounded by the curves y = |x-2|, x = 1, x = 3 and the x-axis is
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    4
Correct answer is option 'A'. Can you explain this answer?

Partho Sen answered
Solution:

Finding the Intersection Points:

To find the area of the region bounded by the curves y = |x-2|, x = 1, x = 3 and the x-axis, we need to first find the intersection points of the given curves.

y = |x-2| is a V-shaped graph with its vertex at x = 2. Therefore, the graph of y = |x-2| intersects the x-axis at two points (1,0) and (3,0).

Area Calculation:

The region bounded by the curves y = |x-2|, x = 1, x = 3 and the x-axis is formed by two parts.

Part 1: The area of the region between the x-axis and the graph of y = |x-2| from x = 1 to x = 2.

Part 2: The area of the region between the x-axis and the graph of y = |x-2| from x = 2 to x = 3.

Part 1 Calculation:

When x varies from 1 to 2, the equation of the curve is y = 2 - x. Therefore, the area of the region between the x-axis and the graph of y = |x-2| from x = 1 to x = 2 is given by:

Area1 = ∫1^2 |x-2| dx

= ∫1^22-x dx

= [2x - x^2]1^2

= 2 - 1

= 1

Part 2 Calculation:

When x varies from 2 to 3, the equation of the curve is y = x - 2. Therefore, the area of the region between the x-axis and the graph of y = |x-2| from x = 2 to x = 3 is given by:

Area2 = ∫2^3 |x-2| dx

= ∫2^3(x-2) dx

= [(1/2)x^2 - 2x]2^3

= 3/2 - 2

= -1/2

Total Area Calculation:

The total area of the region bounded by the curves y = |x-2|, x = 1, x = 3 and the x-axis is given by:

Area = Area1 + Area2

= 1 + (-1/2)

= 1/2

Therefore, the correct option is A.

The area of the figure bounded by the curves y = cos x and y = sin x and the ordinates x = 0 and x = π/4 is
  • a)
    √2 - 1
  • b)
    √2 + 1
  • c)
    1/√2 (√2 - 1
  • d)
    1/√2
Correct answer is option 'A'. Can you explain this answer?

Nilotpal Goyal answered
The curves y = cos x and y = sin x intersect at x = π/4 and x = 5π/4. We can find the area of the bounded figure by finding the areas of the two regions separately and then adding them.

First, consider the region between the curves from x = 0 to x = π/4. We can set up an integral to find the area:

∫[0,π/4] (cos x - sin x) dx

Using integration by substitution with u = sin x, du = cos x dx, we can simplify this to:

∫[0,1] (1 - u) du = [u - u^2/2] from 0 to 1 = 1/2

So the area of this region is 1/2.

Next, consider the region between the curves from x = π/4 to x = 2π. We can set up a similar integral:

∫[π/4,2π] (cos x - sin x) dx

Using integration by substitution with u = cos x, du = -sin x dx, we can simplify this to:

-∫[1/√2,0] (1 - u) du = [u - u^2/2] from 1/√2 to 0 = 1/2 - 1/√2

So the area of this region is 1/2 - 1/√2.

Adding the areas of the two regions together, we get:

1/2 + 1/2 - 1/√2 = √2 - 1

So the area of the bounded figure is √2 - 1 square units.

The sum of the coefficients in the expansion of (1 x-3x2)3148 is
  • a) 
    8
  • b) 
    7
  • c) 
    1
  • d) 
    -1
Correct answer is option 'C'. Can you explain this answer?

Leelu Bhai answered
The trick for finding the sum of coefficients in any expansion is that just put every variable equal to 1... i.e, in this expansion put x = 1, and now see. .....

(1 + 1 - 3(1)²)³¹⁴⁸ = (-1)³¹⁴⁸ = 1.....

so the sum of coefficients of this particular expansion is 1

Find the Synonym of the word occurring in the sentence in capital letter as per the context.
The spectators looked at the batsman in AMAZEMENT when he hit sixer after sixer.
  • a)
    wonder
  • b)
    shock
  • c)
    surprise
  • d)
    suspicion
Correct answer is option 'A'. Can you explain this answer?

Meaning of AMAZEMENT - A state of extreme surprise or wonder; astonishment
In the context of situation given in sentence it can be said that people will look batsman in wonder but not in surprise after titting a sixer as batsman is there to score maximu, there is not surprise if he hits a sixer
But there can be a wonderful feeling in spectators

When ammonia is passed over heated copper oxide, the metallic copper is obtained. The reaction show that ammonia is
  • a)
    a dehydrating agent
  • b)
    an oxidising agent
  • c)
    a reducing agent
  • d)
    a nitrating agent
Correct answer is option 'C'. Can you explain this answer?

Ankita Kaur answered
Reduction of Copper Oxide by Ammonia

Ammonia is a reducing agent because it can donate electrons and reduce another substance in a chemical reaction. When ammonia is passed over heated copper oxide, the following reaction takes place:

CuO + 2NH3 → Cu + N2 + 3H2O

Explanation

The copper oxide (CuO) is a metal oxide, which contains copper in the +2 oxidation state. Ammonia (NH3) is a reducing agent because it contains a lone pair of electrons that can be donated to another substance. In this reaction, the ammonia is oxidized to nitrogen gas (N2) and water (H2O) while the copper oxide is reduced to metallic copper (Cu).

The reaction can be explained as follows:

- The ammonia molecules donate electrons to the copper ions (Cu2+) in the copper oxide.
- This causes the copper ions to gain electrons and be reduced to metallic copper (Cu).
- At the same time, the ammonia molecules lose electrons and are oxidized to nitrogen gas (N2) and water (H2O).
- The nitrogen gas and water vapor are released as gases, while the metallic copper is left behind.

Conclusion

In conclusion, ammonia is a reducing agent because it donates electrons to another substance and reduces it. In the reaction between ammonia and copper oxide, the ammonia reduces the copper oxide to metallic copper while being oxidized to nitrogen gas and water. Therefore, the correct answer to the given question is option 'C' - a reducing agent.

In the cause of auto catalysis
  • a)
    Product catalyses
  • b)
    Solvent catalyses
  • c)
    Reactant catalyses
  • d)
    Heat produced in the reaction catalyses
Correct answer is option 'A'. Can you explain this answer?

Bhavya Kumar answered
Auto catalysis involves a reaction in which the product of the reaction acts as a catalyst for its own production. The correct answer to the given question is option 'A', which states that product catalyses in the cause of auto catalysis. Let's understand this in detail.

Product catalysis in auto catalysis

Auto catalysis is a self-sustaining process that occurs when the product of a reaction catalyses its own formation. In other words, the product of the reaction acts as a catalyst for the reaction itself. This type of reaction is also called a positive feedback loop. The product catalyses the reaction by binding to the reactant and lowering the activation energy required for the reaction to occur. This leads to an increase in the rate of the reaction, which in turn produces more product, which then catalyses the reaction further. This continues until the reactant is completely consumed or the product concentration reaches a saturation point.

Examples of auto catalysis

One of the most well-known examples of auto catalysis is the Belousov-Zhabotinsky (BZ) reaction. In this reaction, a mixture of chemicals undergoes a series of oscillating reactions that produce a color change. The reaction is named after Boris Belousov and Anatol Zhabotinsky, who discovered it in 1959. The BZ reaction involves the oxidation of malonic acid by bromate ions in the presence of a catalyst, which is usually cerium ions. The product of the reaction, bromomalonic acid, acts as a catalyst for its own production, leading to a self-sustaining oscillation of the reaction.

Another example of auto catalysis is the reaction between hydrogen peroxide and iodide ions in the presence of acid. In this reaction, the product of the reaction, iodine, catalyses the reaction by reacting with hydrogen peroxide to form more iodide ions, which then react with more hydrogen peroxide to form more iodine. This leads to a rapid increase in the rate of the reaction until all the reactants are consumed.

Conclusion

In conclusion, auto catalysis is a self-sustaining process that occurs when the product of a reaction catalyses its own formation. Product catalyses the reaction by lowering the activation energy required for the reaction to occur. This leads to an increase in the rate of the reaction, which in turn produces more product, which then catalyses the reaction further. Examples of auto catalysis include the Belousov-Zhabotinsky (BZ) reaction and the reaction between hydrogen peroxide and iodide ions.

Can you explain the answer of this question below:
The volume of 1.0 g of hydrogen in litres at N.T.P. is
  • A:
    2.24
  • B:
    22.4
  • C:
    1.12
  • D:
    11.2

The answer is d.

Gowri Iyer answered
Explanation:

The given conditions are N.T.P. (i.e. Normal Temperature and Pressure) and 1.0 g of hydrogen gas.

Step 1: Calculate the number of moles of hydrogen using the given mass and molar mass.

Molar mass of hydrogen (H2) = 2.016 g/mol

Number of moles of hydrogen = given mass / molar mass

Number of moles of hydrogen = 1.0 g / 2.016 g/mol

Number of moles of hydrogen = 0.496 mol

Step 2: Calculate the volume of hydrogen gas at N.T.P. using Avogadro's law.

According to Avogadro's law, equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

At N.T.P., the temperature (T) is 273 K and the pressure (P) is 1 atm.

1 mole of any gas at N.T.P. occupies a volume of 22.4 L.

Therefore, the volume of 0.496 mol of hydrogen gas at N.T.P. can be calculated as:

Volume of hydrogen gas = number of moles × molar volume at N.T.P.

Volume of hydrogen gas = 0.496 mol × 22.4 L/mol

Volume of hydrogen gas = 11.14 L

Step 3: Round off the answer to the nearest tenth.

Volume of 1.0 g of hydrogen gas at N.T.P. is approximately 11.2 L.

Therefore, the answer is (D) 11.2.

Raindrops are falling from a certain height. Assume all raindrops are spherical and have same drag coefficient. The impact speed of large raindrops compared to that of small raindrops is
  • a)
    Greater
  • b)
    Smaller
  • c)
    Same
  • d)
    Depends on height
Correct answer is option 'A'. Can you explain this answer?

Shail Saha answered
Impact speed of large raindrops compared to small raindrops

Explanation:
When raindrops fall from a certain height, they experience air resistance or drag force. The magnitude of the drag force depends on the size of the raindrop, the velocity of the raindrop, and the density of the air.

Impact speed of large raindrops:
Large raindrops have a greater mass and surface area than small raindrops. Thus, they experience a greater drag force. As a result, the large raindrops reach a terminal velocity quickly, and their impact speed is greater than small raindrops.

Impact speed of small raindrops:
Small raindrops have a smaller mass and surface area than large raindrops. Thus, they experience a smaller drag force. As a result, the small raindrops take a longer time to reach their terminal velocity, and their impact speed is smaller than large raindrops.

Dependence on height:
The impact speed of raindrops also depends on the height from which they fall. As the height increases, the impact speed of both small and large raindrops increases. However, the impact speed of large raindrops increases more rapidly than small raindrops due to their greater mass and surface area.

Thus, the impact speed of large raindrops is greater than small raindrops when they fall from a certain height.

If a liquid is heated in weightlessness, the heat is transmitted through
  • a)
    Conduction
  • b)
    Convection
  • c)
    Radiation
  • d)
    Neither, because the liquid cannot be heated in weighlessness
Correct answer is option 'A'. Can you explain this answer?

Understanding Heat Transfer in Weightlessness
When a liquid is heated in a weightless environment, the mechanism of heat transfer primarily occurs through conduction. Here's how it works:
What is Conduction?
- Conduction is the process where heat is transferred through direct contact between molecules.
- In a heated liquid, faster-moving molecules collide with slower-moving ones, transferring energy and raising the overall temperature.
Why Not Convection?
- Convection relies on the movement of fluid due to density differences caused by heating.
- In a weightless environment, the absence of gravity means that these density-driven movements are significantly reduced or do not occur.
- This makes convection ineffective for heat transfer in such conditions.
Role of Radiation
- While radiation can occur in any environment, it is not the primary mode of heat transfer in liquids.
- Radiation involves the emission of energy in the form of electromagnetic waves and is usually a slower process compared to conduction in liquids.
Conclusion
- In a weightless environment, the heat is transmitted through conduction due to the lack of convection currents.
- Understanding this principle is crucial for applications in space where liquids are often used, and effective heat management is required.
In summary, conduction is the primary method of heat transfer in liquids heated in weightlessness, as convection is hindered and radiation plays a minor role.

1 mol of CH₄ contains
  • a)
    6.02 × 10²³ atoms of H
  • b)
    4 g-atom of hydrogen
  • c)
    1.81 × 10²³ molecules of CH₄
  • d)
    3.0 g of carbon
Correct answer is option 'B'. Can you explain this answer?

Priya Bose answered
X 10^23 atoms of carbon
b)6.02 x 10^23 atoms of hydrogen
c)12.04 grams of carbon
d)2.016 grams of hydrogen

Answer: b)6.02 x 10^23 atoms of hydrogen

A solution is obtained by dissolving 12 g of urea (mol.wt. 60) in one litre of water. Another solution is obtained by dissolving 68.4 g of cane sugar (mol.wt. 342) in one litre of water at same temperature. The lowering of vapour pressure in first solution is
  • a)
    same as that of 2nd solution
  • b)
    one-fifth of the 2nd solution
  • c)
    double that of 2nd solution
  • d)
    five times that 2nd solution
Correct answer is option 'A'. Can you explain this answer?

Rajeev Mehra answered
Solution:

The lowering of vapour pressure is given by the formula

ΔP = P° - P

where,
P° = Vapour pressure of solvent in pure state
P = Vapour pressure of solvent in solution

Let us first calculate the mole fraction of urea and cane sugar in their respective solutions.

Mole fraction of urea = (Number of moles of urea) / (Total number of moles)

Number of moles of urea = (Given mass of urea) / (Molar mass of urea)
= 12 g / 60 g/mol
= 0.2 mol

Total number of moles = (Mass of solute) / (Molar mass of solute) + (Mass of solvent) / (Molar mass of solvent)
= 12 g / 60 g/mol + 1000 g / 18 g/mol
= 0.2 mol + 55.56 mol
= 55.76 mol

Mole fraction of urea = 0.2 / 55.76
= 0.0036

Similarly, we can calculate the mole fraction of cane sugar in its solution.

Mole fraction of cane sugar = (Number of moles of cane sugar) / (Total number of moles)

Number of moles of cane sugar = (Given mass of cane sugar) / (Molar mass of cane sugar)
= 68.4 g / 342 g/mol
= 0.2 mol

Total number of moles = (Mass of solute) / (Molar mass of solute) + (Mass of solvent) / (Molar mass of solvent)
= 68.4 g / 342 g/mol + 1000 g / 18 g/mol
= 0.2 mol + 55.56 mol
= 55.76 mol

Mole fraction of cane sugar = 0.2 / 55.76
= 0.0036

As we can see, the mole fraction of both solutes is the same in their respective solutions.

Now, let us calculate the lowering of vapour pressure in each solution using the formula mentioned above.

For urea solution,

P° = Vapour pressure of water in pure state at the given temperature
= 23.8 mmHg (at 25°C)

P = Vapour pressure of water in urea solution
= Xwater x P°
= (1 - Xurea) x P°
= (1 - 0.0036) x 23.8 mmHg
= 23.72 mmHg

ΔP = P° - P
= 23.8 mmHg - 23.72 mmHg
= 0.08 mmHg

For cane sugar solution,

P° = Vapour pressure of water in pure state at the given temperature
= 23.8 mmHg (at 25°C)

P = Vapour pressure of water in cane sugar solution
= Xwater x P°
= (1 - Xcane sugar) x P°
= (1 - 0.0036) x 23.8 mmHg
= 23.72 mmHg

ΔP = P° - P
= 23.8 mmHg -

Can you explain the answer of this question below:

Find the Missing Number.

  • A:

    19

  • B:

    23

  • C:

    24

  • D:

    31

The answer is d.

Akshay Shah answered
The numbers outside the circle, they all are perfect squares and when the square root of those numbers are added they result in the number inside the triangle. Look at the first circle25=sqrt(5) and so on. 3+4+5+6=18
So similarly now for the last circle 64=sq(8)25=sq(5)144=sq(12)36=sq(6)
Add them 8+5+12+6=31.

The ratio of intensities of two waves is 9:1. When they superimpose, the ratio of maximum to minimum intensities will become
  • a)
    4 : 1
  • b)
    3 : 1
  • c)
    2 : 1
  • d)
    9 : 1
Correct answer is option 'A'. Can you explain this answer?

Milan Datta answered
Given information:
- The ratio of intensities of two waves is 9:1.

To find:
- The ratio of maximum to minimum intensities when the waves superimpose.

Solution:

When two waves superimpose, the resulting intensity is the sum of the individual intensities. Let's assume the intensities of the two waves are I1 and I2, with I1 being 9 times larger than I2.

So, I1 = 9x and I2 = x, where x is a constant.

The maximum intensity occurs when the two waves are in phase and add constructively, resulting in the sum of the intensities. The minimum intensity occurs when the two waves are completely out of phase and cancel each other, resulting in the difference of the intensities.

Maximum Intensity:
When the two waves are in phase, the maximum intensity is the sum of the intensities:

Imax = I1 + I2 = 9x + x = 10x

Minimum Intensity:
When the two waves are completely out of phase, the minimum intensity is the difference of the intensities:

Imin = I1 - I2 = 9x - x = 8x

Ratio of Maximum to Minimum Intensities:
The ratio of maximum to minimum intensities is given by:

Ratio = Imax / Imin = (10x) / (8x) = 10/8 = 5/4

Now, we need to simplify this ratio to the form given in the answer options.

Simplifying the Ratio:
Ratio = 5/4 = (5/4) * (4/4) = 20/16 = 5/4

Comparing this simplified ratio with the answer options, we can see that the correct answer is option A, 4:1.

Answer:
The ratio of maximum to minimum intensities when the waves superimpose is 4:1.

If a is any vector then |axi|2+|axj|2+|axk|2=
  • a)
    a2
  • b)
    2a2
  • c)
    3a2
  • d)
    0
Correct answer is option 'B'. Can you explain this answer?

Kajal Datta answered
Explanation:

- Given: If 'a' is any vector, then the expression to be evaluated is |axi|2+|axj|2+|axk|2.
- Let's expand the given expression using the properties of the modulus of a vector.
Expansion:

- |axi|2 = (a2xi2) = a2
- |axj|2 = (a2xj2) = a2
- |axk|2 = (a2xk2) = a2
- Adding these expressions together, we get:
|axi|2+|axj|2+|axk|2 = a2 + a2 + a2 = 3a2
- Therefore, the correct answer is option 'C', which is 3a2.

Nitrogen atom has an atomic number of 7 and oxygen has an atomic number 8. The total number of electrons in a nitrate ion will be
  • a)
    8
  • b)
    16
  • c)
    32
  • d)
    64
Correct answer is option 'C'. Can you explain this answer?

Manasa Bajaj answered
Understanding the problem:
In a nitrate ion (NO3-), there are 1 nitrogen atom and 3 oxygen atoms combined. We need to calculate the total number of electrons in the nitrate ion.

Calculating the number of electrons:
- Nitrogen atom (N) has an atomic number of 7, which means it has 7 electrons.
- Oxygen atom (O) has an atomic number of 8, which means it has 8 electrons.
- In a nitrate ion (NO3-), there is 1 nitrogen atom and 3 oxygen atoms.
- Total number of electrons in the nitrate ion = Number of electrons in nitrogen atom + Number of electrons in oxygen atoms
- Number of electrons in nitrogen atom = 7
- Number of electrons in 1 oxygen atom = 8
- Total number of electrons in 3 oxygen atoms = 3 x 8 = 24
- Total number of electrons in the nitrate ion = 7 (from nitrogen) + 24 (from oxygen) = 31

Conclusion:
The total number of electrons in a nitrate ion (NO3-) is 31.

A train is moving with a constant velocity.If a pendulum is hanging from its roof, then its time period will
  • a)
    increase
  • b)
    decrease
  • c)
    remain the same
  • d)
    become zero
Correct answer is option 'C'. Can you explain this answer?

Parth Majumdar answered
Explanation:
When a train is moving with a constant velocity, there is no acceleration acting on the pendulum. Hence, the time period of the pendulum will remain the same.

To understand this concept better, let's consider the following points:

1. Time period of a pendulum:
The time period of a pendulum is the time taken by it to complete one oscillation. It depends on the length of the pendulum and the acceleration due to gravity.

2. Acceleration due to gravity:
Acceleration due to gravity is a constant value of 9.8 m/s^2. It is the acceleration experienced by an object due to the gravitational force of the Earth.

3. Effect of acceleration on the pendulum:
When the train is accelerating, the pendulum experiences an additional acceleration apart from the acceleration due to gravity. This changes the effective acceleration acting on the pendulum, which in turn affects its time period.

4. Constant velocity:
When the train is moving with a constant velocity, there is no acceleration acting on the pendulum. Hence, the effective acceleration acting on the pendulum remains the same as the acceleration due to gravity. This does not affect the time period of the pendulum.

Conclusion:
Therefore, the time period of the pendulum hanging from the roof of a train moving with a constant velocity will remain the same.

The bromination of benzene in presence of FeBr₃ is an example of
  • a)
    electrophilic addition
  • b)
    free radical addition
  • c)
    electrophilic substitution
  • d)
    nucleophilic addition
Correct answer is option 'C'. Can you explain this answer?

Alok Choudhury answered
Electrophilic Substitution: Bromination of Benzene

Electrophilic substitution is a type of organic reaction in which an electrophile replaces a functional group or atom in a molecule. The bromination of benzene in the presence of FeBr is an example of electrophilic substitution.

Mechanism of Electrophilic Substitution

1. Generation of Electrophile

In the bromination of benzene, an electrophile is generated by the reaction between bromine and iron (III) bromide. The electrophile generated is Br+.

Br2 + FeBr3 → Br+ + FeBr4-

2. Formation of Sigma Complex

The electrophile Br+ then forms a sigma complex with the benzene ring. The pi electrons of the benzene ring are attracted towards the electrophile and form a bond with the Br+ ion.

3. Rearrangement of Sigma Complex

The sigma complex then undergoes a rearrangement in which the carbon-carbon single bonds are broken, and the pi electrons are rearranged. This rearrangement leads to the formation of a new intermediate called arenium ion.

4. Loss of Proton

The arenium ion then loses a proton to form the final product, which is bromobenzene.

Overall Reaction

The overall reaction for the bromination of benzene is as follows:

C6H6 + Br2 → FeBr3/Br2 C6H5Br + HBr

Conclusion

The bromination of benzene is an example of electrophilic substitution, in which an electrophile replaces a hydrogen atom on the benzene ring. This reaction is important in organic chemistry as it is a key step in the synthesis of many important organic compounds.

Which of the following law directly explains the law of conservative of mass?
  • a)
    Hund's rule
  • b)
    Dalton's law
  • c)
    Avogadro's law
  • d)
    Berzelius hypothesis
Correct answer is option 'B'. Can you explain this answer?

Rounak Unni answered
Explanation:

Dalton's law directly explains the law of conservation of mass. The law of conservation of mass states that in a chemical reaction, the total mass of the reactants is equal to the total mass of the products. This law was first proposed by Antoine Lavoisier in 1789. Dalton's law is a fundamental law of chemistry that states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases in the mixture. This law is based on the assumption that the total number of particles in the system is conserved.

Dalton's law is closely related to the law of conservation of mass because it implies that the total number of particles in a closed system is conserved. This means that the total mass of the system is conserved as well. Thus, if a chemical reaction involves the formation or consumption of gases, the total mass of the system will remain constant. This is because the total number of particles in the system is conserved.

In summary, Dalton's law directly explains the law of conservation of mass because it is based on the assumption that the total number of particles in a closed system is conserved. This means that the total mass of the system is conserved as well, and the law of conservation of mass is a direct consequence of this fact.

Can you explain the answer of this question below:
Find out the term in the number series which is wrong.
3, 2, 8, 9, 13, 22, 18, 32, 23, 42
  • A:
    8
  • B:
    9
  • C:
    13
  • D:
    22

The answer is b.

Sparsh Roy answered
Wrong term in the number series

Explanation:
The given series is:
3, 2, 8, 9, 13, 22, 18, 32, 23, 42

We can see that the series is alternating between two different sequences. Let's break down the series into two sequences:

Sequence 1: 3, 8, 13, 18, 23, ...

We can observe that this sequence is increasing by 5 each time.

Sequence 2: 2, 9, 22, 32, 42, ...

We can observe that this sequence is increasing by 7, 13, 10, and 10 respectively.

The term that is wrong in the series should belong to sequence 2 as sequence 1 is correct.

Now, let's calculate the expected values of sequence 2 and compare them with the given values:

- Expected value after 2: 2 + 7 = 9
- Given value after 2: 2
- Expected value after 9: 9 + 13 = 22
- Given value after 9: 22
- Expected value after 22: 22 + 10 = 32
- Given value after 22: 18
- Expected value after 32: 32 + 10 = 42
- Given value after 32: 23

We can see that the given value after 9 is 22 while the expected value is 9. Hence, the wrong term in the series is 22.

Therefore, the correct answer is option B) 9.

If the sum of n terms of the series 23 + 43 + 63 + ... ∞ is 3528, then n equals
  • a)
    6
  • b)
    7
  • c)
    8
  • d)
    9
Correct answer is option 'A'. Can you explain this answer?

Athul Kapoor answered
Given Information:
The series is 23 + 43 + 63 + ... ∞ and the sum of n terms is 3528.

Solution:

Finding the common difference (d):
The series is an arithmetic progression where each term differs by a common difference.
Let the first term of the series be a = 23 and the common difference be d.
The second term = 23 + d = 43
The third term = 23 + 2d = 63
And so on...
Since the sum of n terms is given by Sn = n/2 * [2a + (n-1)d], we can substitute the given values:
3528 = n/2 * [2*23 + (n-1)d]

Solving for n:
3528 = n/2 * [46 + (n-1)d]
3528 = n/2 * [46 + (n-1)d]
704 = n * (46 + (n-1)d)
704 = 46n + n^2 - n
Rearranging the equation:
n^2 + 45n - 704 = 0
(n + 64)(n - 11) = 0
Therefore, n = -64 or n = 11. Since n cannot be negative, n = 11.
Hence, the sum of the first 11 terms of the series is 3528. So, the correct option is (A) 6.

Can you explain the answer of this question below:
If the parametric equation of a curve is given by x=et cos t, y=et sin t, then tangent to the curve at the point t=(π/4) makes the angle with the axis of x
  • A:
    0
  • B:
    π/4
  • C:
    π/3
  • D:
    π/2
  • E:undefined

The answer is d.

Nandita Chopra answered
Understanding the Parametric Equations
The curve is defined by the parametric equations:
- x = e^t * cos(t)
- y = e^t * sin(t)
To find the angle the tangent makes with the x-axis at t = π/4, we need to calculate the derivatives.
Finding the Derivatives
1. Calculate dx/dt:
- dx/dt = e^t * cos(t) - e^t * sin(t)
- Simplified: dx/dt = e^t (cos(t) - sin(t))
2. Calculate dy/dt:
- dy/dt = e^t * sin(t) + e^t * cos(t)
- Simplified: dy/dt = e^t (sin(t) + cos(t))
Finding the Slope of the Tangent
The slope of the tangent line at any point is given by dy/dx:
- dy/dx = (dy/dt) / (dx/dt)
- Substituting the expressions:
dy/dx = (e^t (sin(t) + cos(t))) / (e^t (cos(t) - sin(t)))
- The e^t terms cancel out:
dy/dx = (sin(t) + cos(t)) / (cos(t) - sin(t))
Evaluate at t = π/4
- At t = π/4, we know:
sin(π/4) = cos(π/4) = 1/√2.
- Substitute into dy/dx:
dy/dx = [(1/√2) + (1/√2)] / [(1/√2) - (1/√2)]
dy/dx = (2/√2) / 0
Conclusion: Tangent is Vertical
Since the slope is undefined (division by zero), the tangent line is vertical. A vertical line makes an angle of π/2 (90 degrees) with the x-axis.
Thus, the correct answer is option 'D': the tangent makes an angle of π/2 with the x-axis.

A problem in mathematics is given to 3 students whose chances of solving individually are 1/2, 1/3, and 1/4. The probability that the problem will be solved atleast by one is
  • a)
    1/4
  • b)
    1/24
  • c)
    23/24
  • d)
    3/4
Correct answer is option 'D'. Can you explain this answer?

Probability of Solving the Problem

To find the probability that the problem will be solved by at least one student, we can use the following formula:

P(at least one student solves the problem) = 1 - P(no student solves the problem)

So, we need to find the probability that no student solves the problem and subtract it from 1 to get the probability that at least one student solves the problem.

Probability that No Student Solves the Problem

The probability that no student solves the problem is the product of the probabilities that each student does not solve the problem. So, we can use the following formula:

P(no student solves the problem) = P(student 1 does not solve the problem) x P(student 2 does not solve the problem) x P(student 3 does not solve the problem)

We are given the individual probabilities of solving the problem for each student as follows:

- P(student 1 solves the problem) = 1/2
- P(student 2 solves the problem) = 1/3
- P(student 3 solves the problem) = 1/4

So, the probabilities that each student does not solve the problem are:

- P(student 1 does not solve the problem) = 1 - P(student 1 solves the problem) = 1 - 1/2 = 1/2
- P(student 2 does not solve the problem) = 1 - P(student 2 solves the problem) = 1 - 1/3 = 2/3
- P(student 3 does not solve the problem) = 1 - P(student 3 solves the problem) = 1 - 1/4 = 3/4

Therefore, the probability that no student solves the problem is:

P(no student solves the problem) = (1/2) x (2/3) x (3/4) = 1/4

Probability that At Least One Student Solves the Problem

Now, we can use the formula we derived earlier to find the probability that at least one student solves the problem:

P(at least one student solves the problem) = 1 - P(no student solves the problem) = 1 - 1/4 = 3/4

Therefore, the correct answer is option D (3/4).

Choose the one which can be substituted for the given words/sentences :
Food which agrees with one's taste
  • a)
    Pungent
  • b)
    Palatable
  • c)
    Sensuous
  • d)
    Edible
Correct answer is option 'B'. Can you explain this answer?

Nitya Sarkar answered
Substitution of Words: Palatable

Definition:
Palatable refers to something that is pleasant to taste or agreeable to one's taste buds.

Explanation:
The given options are pungent, palatable, sensuous, and edible. Out of these options, the word that can be substituted for "food which agrees with one's taste" is palatable. This is because palatable food is something that is pleasing to the taste buds and is agreeable to the person who is consuming it.

Let us understand the meanings of other options:
- Pungent: It refers to something that has a strong, sharp smell or taste, usually unpleasant.
- Sensuous: It refers to something that is related to the senses and can be used to describe something that is pleasing to the senses, including taste.
- Edible: It refers to something that is fit for consumption or can be eaten.

Hence, palatable is the most appropriate word that can be used to describe food that agrees with one's taste.

Example:
The restaurant served a variety of dishes, but only a few were palatable to me.

α-particles can be detected using
  • a)
    thin aluminium sheet
  • b)
    barium sulphate
  • c)
    zinc sulphide screen
  • d)
    gold foil
Correct answer is option 'C'. Can you explain this answer?

Shrish Pandey answered
Brother Rutherford use zinc sulphide screen during his alpha scattering experiment because zinc sulphide is photo senstive when an alpha particle hit this screen a flash shines at that place so it was useful for Rutherford to predict atoms structure

Which of the following element belongs to the third row transition series?
  • a)
    V
  • b)
    Sc
  • c)
    Au
  • d)
    Mn
Correct answer is option 'C'. Can you explain this answer?

Belongs to Third Row Transition Series

The transition elements are the elements in the periodic table that have incomplete d subshells in their atomic structure. The third row transition series includes the transition elements Scandium (Sc) through Zinc (Zn), which are located in rows 4 through 7 of the periodic table.

Identifying the Element

Out of the given options, only one element belongs to the third row transition series. We can use the periodic table to identify this element.

- V (Vanadium) belongs to the fourth row transition series, as it is located in row 4 of the periodic table.
- Sc (Scandium) belongs to the third row transition series, as it is located in row 4 of the periodic table.
- Au (Gold) belongs to the fifth row transition series, as it is located in row 6 of the periodic table.
- Mn (Manganese) belongs to the third row transition series, as it is located in row 4 of the periodic table.

Therefore, the only element that belongs to the third row transition series from the given options is Mn (Manganese).

Conclusion

In conclusion, the correct answer to the question is option 'D' (Mn), as it is the only element from the given options that belongs to the third row transition series.

The compound that decolourises alkaline KMnO₄ is
  • a)
    C₃H₈
  • b)
    C₂H₄
  • c)
    CH₄
  • d)
    CCl₄
Correct answer is option 'B'. Can you explain this answer?

Explanation:
The decolorisation of KMnO4 is a redox reaction. The process involves the transfer of electrons from one substance to another. The compound that decolorises alkaline KMnO4 is an organic compound that is capable of reducing KMnO4 from its purple colour to a brownish colour.

Alkaline KMnO4 is a strong oxidising agent. It can oxidise a wide range of organic compounds, including alcohols, aldehydes, ketones, and carboxylic acids. However, certain organic compounds can reduce KMnO4 to its brownish colour.

The correct answer to this question is option B, which is CH3COOH. Acetic acid is a weak organic acid that can reduce KMnO4 in the presence of a strong base. The reaction of acetic acid with alkaline KMnO4 produces MnO2, which is a brown precipitate.

The balanced chemical equation for the reaction is:

2KMnO4 + 3CH3COOH + 4KOH → 2MnO2 + 3CH3COOK + 2K2CO3 + 2H2O

In this reaction, the acetic acid acts as a reducing agent, while the KMnO4 acts as an oxidising agent. The reaction produces MnO2, which is a brown precipitate.

Conclusion:
In conclusion, the compound that decolorises alkaline KMnO4 is an organic compound that is capable of reducing KMnO4 from its purple colour to a brownish colour. The correct answer to this question is option B, which is CH3COOH. Acetic acid is a weak organic acid that can reduce KMnO4 in the presence of a strong base to produce MnO2, which is a brown precipitate.

Can you explain the answer of this question below:
Spot the error.
  • A:
    This is an instance
  • B:
    of the blind
  • C:
    leading the blinds
  • D:
    No error

The answer is c.

Maheshwar Unni answered
Identifying the Error:
There is an error in option 'c' of the given sentence.

Explanation:

Understanding the Phrase:
- The phrase "the blind leading the blind" is a well-known saying that means ignorant or inexperienced people are following others who are just as ignorant or inexperienced.

Corrected Sentence:
- The correct phrase should be "the blind leading the blind" instead of "the blinds leading the blinds."

Conclusion:
- The error lies in the incorrect usage of the phrase in option 'c'. The correct phrase should be used to convey the intended meaning effectively.

Complete the analogous pair.
Lira : Italy : : Bhat :?
  • a)
    Malaysia
  • b)
    Dubai
  • c)
    Thailand
  • d)
    Burma
Correct answer is 'C'. Can you explain this answer?

Tanvi Iyer answered
Analogous Pair:

An analogous pair is a pair of words that have a certain relationship between them and can be matched with another pair of words that has the same type of relationship. In this question, we are given a pair of words, 'Lira: Italy' and we have to find the analogous pair for 'Bhat'.

Lira: Italy:

Lira is the currency of Italy. Italy is the country where Lira is used as a currency. Therefore, the relationship between Lira and Italy is that Lira is the currency of Italy.

Bhat: Thailand:

Bhat is the currency of Thailand. Thailand is the country where Bhat is used as a currency. Therefore, the relationship between Bhat and Thailand is that Bhat is the currency of Thailand.

Therefore, the correct answer is option c) Thailand.

Can you explain the answer of this question below:
The no. of essential amino acids in human body is
  • A:
    8
  • B:
    10
  • C:
    18
  • D:
    20

The answer is b.

Rahul Bansal answered
There are 20 different amino acids – nine of which are called “essential” and 11 of which are labeled as “non-essential". These amino acids are lysine, leucine, isoleucine, histidine, methionine, phenylalanine, methionine, tryptophan, valine.

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