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In This Post we are  providing Chapter -4 Chemical bonding and Molecular Structure NCERT MCQ for Class 11 Chemistry which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON CHEMICAL BONDING AND MOLECULAR STRUCTURE

Question 1: Cation and anion combines in a crystal to form following type of compound

• a) ionic
• b) covalent
• c) metallic
• d) dipole-dipole

Answer: ionic

Question 2: Electrovalence of calcium and chlorine respectively is

• a) + 2, – 1
• b) 1, – 2
• c) + 1, – 1
• d) + 2, – 2

Answer: + 2, – 1

Question 3: When a metal atom combines with non-metal atom, the non-metal atom will

• a) gain electrons and increase in size
• b) gain electrons and increase in size
• c) lose electrons and increase in size
• d) lose electrons and decrease in size

Answer: gain electrons and increase in size

Question 4: In N₂ molecule, the number of electrons shared by each nitrogen atom is

• a) 3
• b) 2
• c) 5
• d) None of these

Answer: 3

Question 5: The lowest energy structure is the one with the ______ formal charges on the atoms.

• a) smallest
• b) highest
• c) zero
• d) negative

Answer: smallest

Question 6: In the cyanide ion, the formal negative charge is on

• a) N
• b) C
• c) Both C and N
• d) Resonate between C and N

Answer: N

Question 7: What are the exceptions of the octet rule ?

• a) All of these
• b) Expanded octet of the central atom
• c) An odd number of electrons on central atom
• d) The incomplete octet of central atom

Answer: All of these

Question 8: In which of the following molecules octet rule is not followed?

• a) NO
• b) CH₄
• c) NH₃
• d) CO₂

Answer: NO

Question 9: Among the following the electron deficient compound is

• a) BCl₃
• b) PCl₅
• c) CCl₄
• d) BeCl₂

Answer: BCl₃

Question 10: Which of the following is the electron deficient molecule?

• a) B₂H₆
• b) PH₃
• c) SiH₄
• d) None of these

Answer: B₂H₆

Question 11: Which of the following compounds does not follow the octet rule for electron distribution?

• a) PCl₅
• b) H₂O
• c) PH₃
• d) PCl₃

Answer: PCl₅

Question 12: Which of the following pairs will form the most stable ionic bond ?

• a) Mg and F
• b) Na and F
• c) Na and Cl
• d) Li and F

Answer: Mg and F

Question 13: Which of the following methods is used for measuring bond length ?

• a) All of these
• b) Spectroscopic techniques
• c) Electron-diffraction
• d) X-ray diffraction

Answer: All of these

Question 14: _______ is measured as the radius of an atom’s core which is in contact with the core of an adjacent atom in a bonded situation.

• a) Covalent radius
• b) Ionic radius
• c) Bond length
• d) van der Waal’s radius

Answer: Covalent radius

Question 15: All the bond lengths of sulphur – oxygen in sulphate ion, are equal because of:

• a) resonance
• b) symmetry
• c) high electronegativity of oxygen
• d) None of these

Answer: resonance

In This Post we are  providing Chapter-3 Classification of Elements and Periodicity in Properties NCERT MCQ for Class 11 Chemistry which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON CLASSIFICATION OF ELEMENTS AND PERIODICITY IN PROPERTIES

Question 1.
The set representing the correct order of first ionization potential is
(a) K > Na > Li
(b) Be > Mg > Ca
(c) B > C > N
(d) Ge > Si > C.

Answer: (b) Be > Mg > Ca

Question 2.
The increasing order of the a atomic radius for the elements Na, Rb, K and Mg is
(a) Na < K < Mg < Rb
(b) K < Na < Mg < Rb
(c) Na < Mg < K < Rb
(d) Mg < Na < K < Rb

Answer: (d) Mg < Na < K < Rb

Question 3.
The correct’ order of the first ionization potentials among the following elements: Be, B, C, N Q is
(a) B < Be < C < O < N
(b) B < Be < C < N < O
(c) Be < B < C < N < O
(d) Be < B < C < O < N

Answer: (a) B < Be < C < O < N

Question 4.
Correct order of ionization enthalpies is
(a) Zn < Cd < Hg
(b) Cd < Hg < Zn
(c) Na > Cs > Rb
(d) Cs < Rb < Na

Answer: (d) Cs < Rb < Na

Question 5.
Correct order of radii is
(a) N < Be < B
(b) F^– < O^2- < N^3-
(c) Na < Li < K
(d) Fe³⁺ < Fe²⁺ < Fe⁴⁺

Answer: (b) F^– < O^2- < N^3-

Question 6.
Set containing isoelectronic species is
(a) C2−2, NO⁺, CN^–, O2+2
(b) CO, NO, O₂ CN^–
(c) CO₂, NO₂, O₂, N₂O
(d) CO, CO₂, NO, NO₂

Answer: (a) C2−2, NO⁺, CN^–, O2+2

Question 7.
Which of the following is most electronegative?
(a) Carbon
(b) Silicon
(c) Lead
(d) Tin

Answer: (a) Carbon

Question 8.
The values of electronegativity of atoms A and B are 1.20 and 4.0 respectively. The percentage of ionic character of A-B bond is
(a) 50%
(b) 72.24%
(c) 55.3%
(d) 43%

Answer: (b) 72.24%

Question 9.
Tick the correct order of second ionization energy in the following
(a) F > O > N > C
(b) O > F > N > C
(c) O > N > F > C
(d) C > N > O > F

Answer: (b) O > F > N > C

Question 10.
Consider the isoelectronic series : K⁺, S^2-, Cl^1- and Ca²⁺, the radii of the ions decrease as
(a) Ca²⁺ < K⁺ > Cl^–, S^2-
(b) Cl^– > S^2- > K⁺ > Ca²⁺
(c) S^2- > Cl^– > K⁺ > Ca²⁺
(d) K⁺ > Ca²⁺ > S^2- > Cl.

Answer: (c) S^2- > Cl^– > K⁺ > Ca²⁺

Question 11.
The radii of F, F^–, O, D^2- are the order of
(a) O^2- > F^– > F > O
(b) F^– > O^2- > F > O
(c) O^2- > O > F^– > F
(d) O^2- > F^– > O > F

Answer: (d) O^2- > F^– > O > F

Question 12.
Among the following groupings which represents the collection of isoelectronic species.
(a) NO⁺, C2−2, CO−2, CO
(b) N₂, C2−2, CO, NO
(c) CO, NO⁺, CN^–, C2−2
(d) NO, CN^–, N₂, O−2

Answer: (c) CO, NO⁺, CN^–, C2−2

Question 13.
According to the periodic law of elements the variation in properties of elements is related to their
(a) nuclear neutron-proton number ratio
(b) atomic masses
(c) nuclear masses
(d) atomic numbers.

Answer: (d) atomic numbers.

Question 14.
The ions O²⁺, F^–, Na⁺, Mg²⁺ and Al³⁺ are isoelectronic, their ionic radii show.
(a) a significant increase from O^2- to Al³⁺
(b) an increase from O^2- to F^– and then decrease from Na⁺ to Al³⁺
(c) a significant decrease from O^2- to Al³⁺
(d) a decrease from O^2- to F^– and then increase from Na⁺ to Al³⁺.

Answer: (c) a significant decrease from O^2- to Al³⁺

Question 15.
The ionic radii of isoelectronic species N^3-, O^2- and F^– in Å are in the order.
(a) 1.36, 1.40, 1.71
(b) 1.36, 1.71, 1.40
(c) 1.71, 1.40, 1.36
(d) 1.71, 1.36, 1.40

Answer: (c) 1.71, 1.40, 1.36

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In This Post we are  providing Chapter-2 Structure of Atom NCERT MCQ for Class 11 Chemistry which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON STRUCTURE OF ATOM

Question 1.
The increasing order (lowest first) for the values of e/m (charge/mass) for
(a) e, p, n, α
(b) n, p, e, α
(c) n, p, α, e
(d) n, α, p, e

Answer: (d) n, α, p, e
Explanation:
(i) (e/m) for (i) neutron = (01) = 0
(ii) α− particle = (24) = 0.5
(iii) Proton = (11) = 1
(iv) electron = (11837) = 1837.

Question 2.
The ionization enthalpy of hydrogen atom is 1.312 × 10⁶ J mol^-1. The energy required to excite the electron in the atom from n = 1 to n = 2 is
(a) 8.51 × 10⁵ J mol^-1
(b) 6.56 × 10⁵ J mol^-1
(c) 7.56 × 10⁵ J mol^-1
(d) 9.84 × 10⁵ J mol^-1

Answer: (d) 9.84 × 10⁵ J mol^-1
Explanation:
Energy required when an electron makes transition from n = 1 to n = 2
E₂=−(1.312 × 10⁶ × (1)²)/(2²)
= −3.28 × 10⁵ J mol^-1
E₁ = −1.312 × 10⁶ J mol^-1
ΔE = E₂ − E₁
=−3.28 × 10⁵−(−13.2 × 10⁶)
ΔE = 9.84×10⁵ J mol^-1

Question 3.
or a given principal level n = 4, the energy of its subshells is in the order
(a) s < p < d < f
(b) s > p > d > f
(c) s < p < f < d
(d) f < p < d < s

Answer: (a) s < p < d < f
Explanation:
Order of energy is:
s < p < d < f

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Question 4.
A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at:
(a) 518 nm
(b) 1035 nm
(c) 325 nm
(d) 743 nm

Answer: (d) 743 nm
Explanation:
From Law of Conservation of energy, energy of absorbed photon must be equal to combined energy of two emitted photons.
ET = E₁ + E₂ ….. (1)
Where E₁ is Energy of first emitted photon emitted and E₂is Energy of second emitted photon.
Energy E and wavelength λ of a photon are related by the equation
E= (hc)/ (λ)….. (2)
Where Plancks constant = h, c is velocity of light.
Substituting the values from (2) in (1) we get
(hc/λ_T) = (hc)/ (λ₁) + (hc)/ (λ₂)
Or (1λT) = (1λ1) + (1λ2) …… (3)
Substituting given values in (3) we get
(1355) = (1680) + (1λ2)
Or (1)(λT) = (1355) − (1680)
⇒ (1λ2) = (680 − 355)/ (355 × 680)
⇒ λ₂ = 742.77nm

Question 5.
Which of the following statements in relation to the hydrogen atom is correct?
(a) 3s orbital is lower in energy than 3p orbital
(b) 3p orbital is lower in energy than 3d orbital
(c) 3s and 3p orbitals are of lower energy than 3d orbital
(d) 3s, 3p and 3d orbitals all have the same energy

Answer: (d) 3s, 3p and 3d orbitals all have the same energy
Explanation:
A hydrogen atom has 1st configuration and these its, 3p and 3d orbitals will have same energy wrt 1s orbital.

Question 6.
The magnetic quantum number specifies
(a) Size of orbitals
(b) Shape of orbitals
(c) Orientation of orbitals
(d) Nuclear Stability

Answer: (c) Orientation of orbitals
Explanation:
The magnetic quantum number specifies orientation of orbitals.

Question 7.
The electronic configuration of silver atom in ground state is
(a) [Kr]3d¹⁰4s¹
(b) [Xe]4f¹⁴5d¹⁰6s¹
(c) [Kr]4d¹⁰5s¹
(d) [Kr]4d⁹5s²

Answer: (c) [Kr]4d¹⁰5s¹
Explanation:
The electronic configuration of Ag in ground state is [Kr]4d¹⁰5s¹

Question 8.
Which of the following element has least number of electrons in its M-shell?
(a) K
(b) Mn
(c) Ni
(d) Sc

Answer: (a) K
Explanation:
K = 19 = 1s²2s²2p⁶3s²3p⁶s¹
3s²3p⁶ = m-shell
= k has only 8 electrons in M shell

Question 9.
Which one of the following sets of ions represents a collection of isoelectronic species? (Atomic nos.: F = 9, Cl = 17, Na = 11, Mg = 12, Al = 13, K = 19, Ca = 20, Sc = 21)
(a) K⁺, Ca²⁺, Sc³⁺, Cl^–
(b) Na⁺, Ca²⁺ , Sc³⁺, F^–
(c) K⁺, Cl^–, Mg²⁺, Sc³⁺
(d) Na⁺, Mg²⁺, Al³⁺, Cl^–

Answer: (a) K⁺, Ca²⁺, Sc³⁺, Cl^–
Explanation:
Isoelectronic species are those which have same number of electrons.
K⁺ = 19 – 1 = 18; Ca²⁺ = 20 – 2 = 18; Sc³⁺ = 21 – 3 = 18; Cl^– = 17 + 1 = 18
Thus all these ions have 18 electrons in them.

Question 10.
In the ground state, an element has 13 electrons in its M-shell. The element is_____.
(a) Copper
(b) Chromium
(c) Nickel
(d) Iron

Answer: (b) Chromium
Explanation:
M shell means it is third shell ⇒ n = 3
Number of electrons in M shell = 13
⇒ 3s²3p⁶3d⁵
The electronic configuration is: (1s²) (2s² 2p⁶) (3s² 3p⁶ 3d⁵) (4s¹)
The element is chromium is Cr.

Question 11.
The electrons of the same orbitals can be distinguished by
(a) Principal quantum number
(b) Azimuthal quantum number
(c) Spin quantum number
(d) Magnetic quantum number

Answer: (c) Spin quantum number
Explanation:
Electrons occupying the same orbital are distinguished by Spin quantum number.
For spin Quantum number it has two values +1/2 or -1/2,
Hence the value of n, l , m are same for the two electrons occupying in the same orbitals, but only the is different, which is
Therefore, Spin quantum number explains the direction through which the electron spins in an orbital. so obviously there are only 2 possible directions. Which is either clockwise or anticlockwise.
So the electron which are available in the same orbitals, must have opposite spins. Hence spin quantum number distinguished b/w the two electrons.

Question 12.
Consider the ground state of Cr atom (Z = 24). The numbers of electrons with the azimuthal quantum numbers, l = 1 and 2 are, respectively:
(a) 12 and 4
(b) 12 and 5
(c) 16 and 4
(d) 16 and 5Answer

Answer: (b) 12 and 5
Explanation:
₂₄Cr → 1s² 2s²2p⁶ 3s² 3p⁶ 3d⁵ 4s¹
As we know for p, l = 1 and d, l = 2
For l = 1, total number of electrons = 12 [2p⁶ and 3p⁶]
For l = 2, total number of electrons = 5 [3d⁵]

Question 13.
A body of mass 10 mg is moving with a velocity of 100 ms^-1. The wavelength of de-Broglie wave associated with it would be (Note: h = 6.63 × 10^-34 Js)
(a) 6.63 × 10^-37 m
(b) 6.63 × 10^-31 m
(c) 6.63 × 10^-34 m
(d) 6.63 × 10^-35 m

Answer: (b) 6.63 × 10^-31 m
Explanation:
m = 10 mg
= 10 × 10^-6 kg
v = 100 ms^-1
λ = (h)(mv)
= (6.63×10^-34)/ (10 × 10^-6 × 100)
= 6.63 × 10^-31 m

Question 14.
The ionization enthalpy of hydrogen atom is 1.312 × 10⁶ J mol^-1. The energy required to excite the electron in the atom from n = 1 to n = 2 is
(a) 8.51 × 10⁵ J mol^-1
(b) 6.56 × 10⁵ J mol^-1
(c) 7.56 × 10⁵ J mol^-1
(d) 9.84 × 10⁵ J mol^-1

Answer: (d) 9.84 × 10⁵ J mol^-1
Explanation:
Energy required when an electron makes transition from n = 1 to n = 2
E₂ = −(1.312 × 10⁶ × (1)²)/(2²)
= −3.28 × 10⁵ J mol^-1
E₁ = −1.312 × 10⁶ J mol^-1
ΔE = E₂ − E₁
= −3.28 × 10⁵−(−13.2 × 10⁶)
ΔE = 9.84 × 10⁵ J mol^-1

Question 15.
In Hydrogen atom, energy of first excited state is – 3.4 eV. Then find out KE of same orbit of Hydrogen atom
(a) 3.4 eV
(b) 6.8 eV
(c) -13.6 eV
(d) +13.6 eV

Answer: (a) 3.4 eV
Explanation:
For hydrogen atom,
The kinetic energy is equal to the negative of the total energy.
And the potential energy is equal to the twice of the total energy.
The first excited state energy of orbital = -3.4 eV
and The kinetic energy of same orbital = -(-3.4 eV) = 3.4 eV
Therefore, the kinetic energy of same orbit of hydrogen atom is 3.4 eV.

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In This Post we are  providing Chapter-1 Some Basic Concepts of Chemistry NCERT MCQ for Class 11 Chemistry which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON SOME BASIC CONCEPTS OF CHEMISTRY

Question 1.
What will be the volume of mixture after the reaction

(a) 1.5 L
(b) 0.5 L
(c) 1 L
(d) 0.0 L

Answer: (b) 0.5 L

Question 2.
A compound has hemoglobin like structure, it has only one Fe. It contains 4.6% of Fe. The approximate molecular mass is
(a) 100 g mol^-1
(b) 1200 g mol^-1
(c) 1400 g mol^-1
(d) 1600 g mol^-1

Answer: (b) 1200 g mol^-1

Question 3.
How much of NaOH is required to neutralize 1500 cm³ of 0.1 NHCl?
(a) 40 g
(b) 4 g
(c) 6 g
(d) 60 g

Answer: (c) 6 g

Question 4.
10 dm³ of N₂ gas and 10 dm³ of gas X at the same temperature contains the same number of molecules. The gas X is
(a) CO
(b) CO₂
(c) H₂
(d) NO

Answer: (a) CO

Question 5.
The percentage of nitrogen in urea is about
(a) 46
(b) 85
(c) 18
(d) 28

Answer: (a) 46

Question 6.
The modem atomic weight scale is based upon
(a) ¹²C
(b) ¹²O₈
(c) ¹H
(d) ¹³C

Answer: (a) ¹²C

Question 7.
The prefix 10¹⁸ is
(a) giga
(b) exa
(c) kilo
(d) nano
(e) mega

Answer: (b) exa

Question 8.
Number of atoms in 558.6 g Fe (Molar mass Fe = 55.86 g mol^-1) is
(a) twice that in 60 g carbon
(b) 6.023 × 10²²
(c) half that of 8g He
(d) 558.6 × 6.023 × 10²³

Answer: (a) twice that in 60 g carbon

Question 9.
Number of grams of oxygen in 32.2 g Na₂SO₄.10 H₂O is
(a) 20.8
(b) 22.4
(c) 2.24
(d) 2.08

Answer: (b) 22.4

Question 10.
250 ml of a sodium carbonate solution contains 2.65 grams of Na₂CO₃. If 10 ml of this solution is diluted to one litre, what is the concentration of the resultant solution (mol. wt. of Na₂CO₃ = 106)
(a) 0.1 M
(b) 0.001 M
(c) 0.01 M
(d) 10^-4 M

Answer: (b) 0.001 M

Question 11.
An aqueous solution of 6.3 g of oxalic acid dihydrate is made upto 250 ml. The volume of 0.1 N NaOH required to completely neutralize 10 ml of this solution is
(a) 40 ml
(b) 20 ml
(c) 10 m
(d) 4 ml

Answer: (a) 40 ml

Question 12.
How many moles of electrons weight one kilogram?
(a) 6.023 × 10²³
(b) 19.108 × 10³¹
(c) 6023×10549.108
(d) 9.108 × 10⁸

Answer: (d) 9.108 × 10⁸

Question 13.
One mole of calcium phosphide on reaction with excess of water gives
(a) One mole of phosphine
(b) Two moles of phosphoric acid
(c) Two moles of phosphine
(d) One mole of phosphorous pentoxide

Answer: (c) Two moles of phosphine

Question 14.
Which has maximum number of atoms?
(a) 24 g of C (12)
(b) 56 g of Fe (56)
(c) 27 g of Al (27)
(d) 108 g of Ag (108)

Answer: (a) 24 g of C (12)

Question 15.
Mixture X = 0.02 mol of [CO(NH₃)₅ SO₄] Br and 0.02 mol of [CO(NH₃)₅ Br] SO₄ was prepared in 2 liters of a solution.
1 liter of mixture X + excess of AgNO₃ → Y
1 liter of mixture X + excess of BaCl₂ → Z
Number of moles of Y and Z are
(a) 0.01, 0.01
(b) 0.02, 0.01
(c) 0.01, 0.02
(d) 0.02, 0.02

Answer: (a) 0.01, 0.01

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In This Post we are  providing Chapter-15 Waves NCERT MCQ for Class 11 Physics which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON WAVES

Question 1: The property of a medium necessary for wave propagation is

• a) All of the above
• b) Elasticity
• c) Inertia
• d) Low resistance

Answer: All of the above

Question 2: The ratio of the speed of a body to the speed of sound is called

• a) Mach number
• b) Sonic index
• c) Doppler ratio
• d) Refractive index

Answer: Mach number

Question 3: Sound waves transfer

• a) both energy and momentum
• b) only energy not momentum
• c) momentum
• d) energy

Answer: both energy and momentum

Question 4: The reason for introducing Laplace correction in the expression for the velocity of sound in a gaseous medium is

• a) no change in the heat of the medium during the propagation of the sound through it
• b) no change in the temperature of the medium during the propagation of the sound through it
• c) change in the pressure of the gas due to the compression and rarefaction
• d) change in the volume of the gas

Answer: no change in the heat of the medium during the propagation of the sound through it

Question 5: Which of the following changes at an antinode in a stationary wave?

• a) Neither pressure nor density
• b) Both pressure and density
• c) Pressure only
• d) Density only

Answer: Neither pressure nor density

Question 6: What is the effect of humidity on sound waves when humidity increases?

• a) Speed of sound waves is more
• b) Speed of sound waves is less
• c) Speed of sound waves remains same
• d) Speed of sound waves becomes zero

Answer: Speed of sound waves is more 

Question 7: Which of the following statements is/are correct about the standing wave?

I. In a standing wave the disturbance produce is confined to the region where it is produced.
II. In a standing wave, all the particles cross their mean position together.
III. In a standing wave, energy is transmitted from one region of space to other

• a) I and II
• b) Only II
• c) Only III
• d) I, II and III

Answer: I and II

Question 8: The rate of transfer of energy in a wave depends

• a) directly on the square of the wave amplitude and square of the wave frequency
• b) directly on the square of the wave amplitude and root of the wave frequency
• c) directly on the wave amplitude and square of the wave frequency
• d) None of these

Answer: directly on the square of the wave amplitude and square of the wave frequency

Question 9: If vibrations of a string are to be increased by a factor of two, then tension in the string must be made

• a) twice
• b) eight times
• c) half
• d) four times

Answer: twice

Question 10: The fundamental frequency of a closed end organ pipe is n. Its length is doubled and radius is halved. Its frequency will become nearly

• a) n/2
• b) n/3
• c) n
• d) 2 n

Answer: n/2

Question 11: The fundamental frequency of an organ pipe is 512 Hz. If its length is increased, then frequency will

• a) decrease
• b) increase
• c) remains same
• d) cannot be predicted

Answer: decrease

Question 12: What is the effect of increase in temperature on the frequency of sound produced by an organ pipe?

• a) increases
• b) no effect
• c) decreases
• d) erratic change

Answer: increases

Question 13: Frequencies of sound produced from an organ pipe open at both ends are

• a) even and odd harmonics
• b) only odd harmonics
• c) only even harmonics
• d) only fundamental note

Answer: even and odd harmonics

Question 14: closed organ pipe (closed at one end) is excited to support the third overtone. It is found that air in the pipe has

• a) four nodes and four antinodes
• b) four nodes and three antinodes
• c) three nodes and four antinodes
• d) three nodes and three antinodes

Answer: four nodes and four antinodes

Question 15: If there are six loops for 1 m length in transverse mode of Melde’s experiment., the no. of loops in longitudinal mode under otherwise identical conditions would be

• a) 3
• b) 6
• c) 12
• d) 8

Answer: 3

In This Post we are  providing Chapter-14 Oscillations NCERT MCQ for Class 11 Physics which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON OSCILLATIONS

Question 1: Select the incorrect statement(s) from the following.

I. A simple harmonic motion is necessarily periodic.
II. A simple harmonic motion may be oscillatory
III. An oscillatory motion is necessarily periodic

• a) II and III
• b) I and II
• c) I only
• d) I and III

Answer: II and III

Question 2: Suppose a tunnel is dug along a diameter of the earth. A particle is dropped from a point, a distance h directly above the tunnel, the motion of the particle is

• a) oscillatory
• b) simple harmonic
• c) parabolic
• d) non-periodic

Answer: oscillatory

Question 3: The graph plotted between the velocity and displacement from mean position of a particle executing SHM is

• a) ellipse
• b) straight line
• c) circle
• d) parabola

Answer: ellipse

Question 4: A body executing linear simple harmonic motion has a velocity of 3 m/s when its displacement is 4 cm and a velocity of 4 m/s when its displacement is 3 cm. What is the amplitude of oscillation ?

• a) 5 cm
• b) 7.5 cm
• c) 10 cm
• d) 12.5 cm

Answer: 5 cm

Question 5: 

Assertion : A particle executing simple harmonic motion comes to rest at the extreme positions .

Reason : The resultant force on the particle is zero at these positions

• a) Assertion is correct, reason is incorrect
• b) Assertion is incorrect, reason is correct
• c) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
• d) Assertion is correct, reason is correct; reason is a correct explanation for assertion

Answer: Assertion is correct, reason is incorrect

Question 6: The total energy of a particle executing S.H.M. is proportional to

• a) square of amplitude of motion
• b) velocity in equilibrium position
• c) frequency of oscillation
• d) displacement from equilibrium position

Answer: square of amplitude of motion

Question 7: Which of the following is true about total mechanical energy of SHM ?

• a) It is never zero
• b) It is always zero
• c) It is zero at extreme position
• d) It is zero at mean position.

Answer: It is never zero

Question 8: 

Assertion : The graph of total energy of a particle in SHM w.r.t. position is a straight line with zero slope.

Reason : Total energy of particle in SHM remains constant throughout its motion.

• a) Assertion is correct, reason is correct; reason is a correct explanation for assertion
• b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
• c) Assertion is correct, reason is incorrect
• d) Assertion is incorrect, reason is correct.

Answer: Assertion is correct, reason is correct; reason is a correct explanation for assertion

Question 9: A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as a function of displacement x. Which of the following statement is true?

• a) K.E. is maximum when x = 0.
• b) T.E. is zero when x = 0.
• c) K.E. is maximum when x is maximum
• d) P.E. is maximum when x = 0.

Answer: K.E. is maximum when x = 0.

Question 10: The total energy of the particle executing simple harmonic motion of amplitude A is 100 J. At a distance of 0.707 A from the mean position, its kinetic energy is

• a) 50 J
• b) 100 J
• c) 12.5 J
• d) 25 J

Answer: 50 J

Question 11: When the displacement of a particle executing simple harmonic motion is half of its amplitude, the ratio of its kinetic energy to potential energy is

• a) 3 : 1
• b) 1 : 2
• c) 2 : 1
• d) 1 : 3

Answer: 3 : 1

Question 12: If the maximum velocity and acceleration of a particle executing SHM are equal in magnitude, the time period will be

• a) 6.28 sec
• b) 12.56 sec
• c) 3.14 sec
• d) 1.57 sec

Answer: 6.28 sec

Question 13: A simple pendulum oscillates in air with time period T and amplitude A. As the time passes

• a) T remains same and A decreases
• b) T decreases and A is constant
• c) T increases and A is constant
• d) T and A both decrease

Answer: T remains same and A decreases

Question 14: Which of the following will change the time period as they are taken to moon?

• a) A simple pendulum
• b) A torsional pendulum
• c) A physical pendulum
• d) A spring-mass system

Answer: A simple pendulum

Question 15: For an oscillating simple pendulum, the tension in the string is

• a) maximum at mean position
• b) constant throughout the motion
• c) cannot be predicted
• d) maximum at extreme position

Answer: maximum at mean position

In This Post we are  providing Chapter-13 Kinetic Energy NCERT MCQ for Class 11 Physics which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON KINETIC ENERGY

Question 1: In kinetic theory of gases, it is assumed that molecules

• a) have same mass but negligible volume
• b) have different mass as well as volume
• c) have same volume but mass can be different
• d) have same mass but can have different volume

Answer: have same mass but negligible volume

Question 2: The internal energy of a gram-molecule of an ideal gas depends on

• a) pressure alone
• b) volume alone
• c) temperature alone
• d) both on pressure as well as temperature

Answer: pressure alone

Question 3: The phenomenon of Browninan movement may be taken as evidence of

• a) kinetic theory of matter
• b) electromagnetic theory of radiation
• c) corpuscular theory of light
• d) photoelectric phenomenon

Answer: kinetic theory of matter

Question 4: According to kinetic theory of gases, at absolute zero temperature

• a) molecular motion stops
• b) liquid hydrogen freezes
• c) liquid helium freezes
• d) water freezes

Answer: molecular motion stops

Question 5: At a given temperature the force between molecules of a gas as a function of intermolecular distance is

• a) first decreases and then increases
• b) always increases
• c) always decreases
• d) always constant

Answer: first decreases and then increases 

Question 6: For Boyle’s law to hold, the gas should be

• a) perfect and of constant mass and temperature
• b) real and of constant mass and temperature
• c) perfect and constant temperature but variable mass
• d) real and constant temperature but variable mass

Answer: perfect and of constant mass and temperature

Question 7: Boyle’ law is applicable for an

• a) isothermal process
• b) isochoric process
• c) adiabatic process
• d) isobaric process

Answer: isothermal process

Question 8: The deviation of gases from the behavior of ideal gas is due to

• a) attraction of molecules
• b) absolute scale of temp
• c) covalent bonding of molecules
• d) colourless molecules

Answer: attraction of molecules

Question 9: In a mixture of gases at a fixed temperature

• a) heavier molecule has lower average speed
• b) lighter molecule has lower average speed
• c) heavier molecule has higher average speed
• d) None of these

Answer: heavier molecule has lower average speed

Question 10: The average kinetic energy of gas molecules depends upon which of the following factor?

• a) Temperature of the gas
• b) Nature of the gas
• c) Volume of the gas
• d) None of these

Answer: Temperature of the gas

Question 11: The temperature of a gas is a measure of

• a) the average kinetic energy of the gaseous molecules
• b) the average potential energy of the gaseous molecules
• c) the average distance between the molecules of the gas
• d) the size of the molecules of the gas

Answer: the average kinetic energy of the gaseous molecules

Question 12: In the isothermal expansion of 10g of gas from volume V to 2V the work done by the gas is 575J. What is the root mean square speed of the molecules of the gas at that temperature?

• a) 499m/s
• b) 532m/s
• c) 520m/s
• d) 398m/s

Answer: 499m/s

Question 13: In a diatomic molecules, the rotational energy at a given temperature

• a) obeys Maxwell’s distribution
• b) have the same volue for all molecules
• c) equals the translational kinetic energy for each molecule
• d) None of these

Answer: obeys Maxwell’s distribution

Question 14: Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will.

• a) remains the same
• b) decrease for some and increase for others
• c) decrease
• d) increase

Answer: remains the same

Question 15: Pressure exerted by a gas is

• a) directly proportional to the density of the gas
• b) directly proportional to the square of the density of the gas
• c) inversely proportional to the density of the gas
• d) independent of density of the gas

Answer: directly proportional to the density of the gas

Complex Number

Complex number is of the form a +ib where a is real part and b is imaginary part. Here i = √ -1

 E.g.: 2+ i3 ;  7+ i9 etc

Complex Numbers are used in many scientific fields.

 Two complex numbers are equal if:

• Real parts are equal
• Imaginary parts are equal

E.g. Two complex numbers z1 = a + ib and z2 = c + id are equal if a = c and b = d.

Algebra of a Complex number

Addition of two complex numbers

Let z1 = a + ib and z2 = c + id be any two complex numbers.   Then, z1 + z2 = (a + c) + i (b + d)

 For example, (2 + i3) + (4 +i5) = 6 + i8

The addition of complex numbers satisfies the following properties:

• Closure law : z1 + z2  = complex Number
• Commutative law: z1 + z2 = z2 + z1
• Associative law: (z1 + z2) + z3 = z1 + (z2 + z3).
• Additive identity : z + 0 = z.
• Additive inverse : z + (–z) = 0.

Difference of two complex numbers

Let z1 = a + ib and z2 = c + id be any two complex numbers.   Then, z1 – z2 = (a – c) + i (b – d)

 For example, (6 + i3) – (2 + i) = 4 + i2

Multiplication of two complex numbers

Let z1 = a + ib and z2 = c + id be any two complex numbers.   Then, z1 * z2 = (ac – bd) + i(ad + bc)

 For example, (3 + i5) (2 + i6)  = (3*2 – 5*6 ) + i(3*6 +5*2)  = -24 + i28

The multiplication of complex numbers satisfies the following properties:

• Closure law : z1 * z2  = complex Number
• Commutative law: z1 * z2 = z2 * z1
• Associative law: (z1 * z2) *z3 = z1 * (z2 * z3).
• Multiplicative identity : z * 1 = z.
• Multiplicative inverse : z * (1/z) = 1.    (where z ≠ 0)
• Distributive law  :  z1 (z2 + z3) = z1 z2 + z1 z3

Division of two complex numbers

Given any two complex numbers z1 and z2, where z2 ≠ 0 ,   z1/z2  = z1 * (1/z2)

 For example, let z1 = 2+ 3i and z2 = 2 +2i,

z1* z2 =  (2+ 3i)/ (2+ 2i)

To solve this, we will rationalize the denominator

z1* z2 =  (2+ 3i)/ (2+ 2i)   *  (2- 2i)/ (2- 2i)     =  (-2 + i10) / 8   = -1/4 + i5/4

Power of I

• i² = -1
• i³ = -i
• i⁴ = 1
• i⁵ = i
• i⁶ = -1   etc
• i^-1 = -i
• i^-2 = -1
• i^-3 = i
• i^-4 = 1

Identities

• (z₁ + z₂)² = z₁² + z₂² + 2z₁z₂
• (z₁ – z₂)² = z₁² + z₂² – 2z₁z₂
• (z₁ + z₂)³ = z₁³ + z₂³ + 3z₁z₂² + 3z₁²z₂
• (z₁ – z₂)³ = z₁³ – z₂³ + 3z₁z₂² _– 3z₁²z₂
• z₁² – z₂²  = (z₁ + z₂) (z₁ – z₂)

Refer ExamFear video lessons for Proofs for these identities.

Example: Express (5 – 3i)³ in the form a + ib.

Solution:  (5 – 3i)³ = 5³ – 3 × 52 × (3i) + 3 × 5 (3i)² – (3i)³ = 125 – 225i – 135 + 27i = – 10 – 198i.

Modulus & Conjugate  of a complex Number

Let z = a + ib be a complex number.   Modulus of z, denoted by | z |, is defined to be real number (a² + b² )^1/2 ,  | z | = (a² + b²)^1/2

Numerical: Find the Modulus of (3 – 4i )

Solution:  | z | = (a² + b² )^1/2 = (3² + 4²)^1/2  = 5

Let z = a + ib be a complex number.  The conjugate of z, denoted as �, is the complex number a – ib, i.e., �  = a – ib.

Also Z* � = | Z |²

Or   Z^–1 =   � / | Z |²    ( Useful to find inverse of a complex number)

Numerical: Find the conjugate  of  (3 + 4i )

Solution:  Conjugate � = 3-4i

Numerical: Find inverse of  (3 + 4i )

  Z^–1 =   � / | Z |²    = (3 – 4i)/5     = 3/5 – 4/5i

Argand Plane & Polar representation

Complex numbers can represented in 2 forms

• Argand Plane
• Polar Representation

Argand Plane

The complex number x + iy  can be represented  geometrically as the unique point  P(x, y) in the XY-plane and vice-versa. Plane with complex number assigned to each of its point is called complex or Argand plane.

Let’s plot some points on the graph.

Note: Modulus of the complex number is distance between point P(x, y) to the origin O (0, 0)

Polar representation

Let point P represent z = x + iy.  

Let   x = r cos θ , y = r sin θ and therefore, z = r (cos θ + i sin θ).

 Here – π < θ ≤ π

Point P is uniquely determined by the ordered pair of real numbers (r, θ), called the polar coordinates of the point P.

Numerical: Represent the complex number z =1+ i √3 in the polar form.

Solution:  let z =1+ i √3  = r(cos θ + i sin θ)

 r=| z | = (a² + b² )^1/2      = ((1)² + (√3)²)^1/2     = 2

Comparing real parts of  z =1+ i √3  = r(cos θ + i sin θ)   = 2(cos θ + i sin θ) 

1 = 2 cos θ  

or  cos θ   = ½  

or cos θ    = π/3

Therefore,  polar representation will be  z = r(cos θ + i sin θ) = 2(cos π/3 + i sin π/3)

Quadratic Equation

We have seen of real numbers in the cases where discriminant is non-negative, i.e., ≥ 0,

Let us consider the following quadratic equation: ax² + bx + c = 0 with real coefficients a, b, c and a ≠ 0.

Also, let us assume that the b² – 4ac < 0.

Numerical: Solve x² + x + 1= 0

Solution:  Determinant,  b² – 4ac = 12 – 4 × 1 × 1 = 1 – 4 = – 3

X = (-1 ± I √3)/2

• One key basis for mathematical thinking is deductive reasoning. In contrast to deduction, inductive reasoning depends on working with different cases and developing a conjecture by observing incidences till we have observed each and every case. Thus, in simple language we can say the word ‘induction’ means the generalisation from particular cases or facts.
• Statement: A sentence is called a statement, if it is either true ot false.
• Motivation: Motivation is tending to initiate an action. Here Basis step motivate us for mathematical induciton.
• Principle of Mathematical Induction: The principle of mathematical induction is one such tool which can be used to prove a wide variety of mathematical statements. Each such statement is assumed as P(n) associated with positive integer n, for which the correctness for the case n = 1 is examined. Then assuming the truth of P(k) for some positive integer k, the truth of P (k+1) is established.
• Working Rule:
  Step 1: Show that the given statement is true for n = 1.
  Step 2: Assume that the statement  is true for n = k.
  Step 3: Using the assumption made in step 2, show that the statement is true for n = k  + 1. We have proved the statement is true for n = k. According to step 3, it is also true for k + 1 (i.e., 1 + 1 = 2). By repeating the above logic, it is true for every natural number

Principle of Mathematical Induction
Mathematical induction is one of the techniques, which can be used to prove a variety of mathematical statements which are formulated in terms of n, where n is a positive integer.

Let P(n) be given statement involving the natural number n such that
(i) The statement is true for n = 1, i.e. P(1) is true.
(ii) If the statement is true for n = k (where k is a particular but arbitrary natural number), then the statement is also true for n = k + 1 i.e. truth of P(k) implies that the truth of P(k + 1). Then, P(n) is true for all natural numbers n.

Angle

Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final position of ray after rotation is called terminal side of the angle. The point of rotation is called vertex. If the direction of rotation is anti-clockwise, the angle is said to be positive and if the direction of rotation is clockwise, then the angle is negative.

When a ray OA starting from its initial position OA rotates about its end point 0 and takes the final position OB, we say that angle

AOB (written as ∠ AOB) has been formed. The amount of rotation from the initial side to the terminal side is Called the measure of the angle.

Positive and Negative Angles

An angle formed by a rotating ray is said to be positive or negative depending on whether it moves in an anti-clockwise or a clockwise direction, respectively.

Measurement of Angles

There are three system for measuring angles,

1. Sexagesimal System/Degree Measure (English System)

In this system, a right angle is divided into 90 equal parts, called degrees. The symbol 1° is used to denote one degree. Each degree is divided into 60 equal parts, called minutes and one minute is divided into 60 equal parts, called seconds. Symbols 1′ and 1″ are used to denote one minute and one second, respectively.

i.e., 1 right angle = 90°
1° = 60′
1′ = 60″

2. Centesimal System (French System)

In this system, a right angle is divided into 100 equal parts, called ‘grades’. Each grade is subdivided into 100 min and each minute is divided into 100 s.

i.e., 1 right angle = 100 grades = 100g
1g = 100′
1′ = 100″

3. Circular System (Radian System) In this system, angle is measured in radian.

A radian is the angle subtended at the centre of a circle by an arc, whose length is equal to the radius of the circle.

The number of radians in an angle subtended by an arc of circle at the centre is equal to arc/radius.

Relationships

(i) π radian = 180° or 1 radian (180°/π)= 57°16’22” where, π = 22/7 = 3.14159
(ii) 1° = (π/180) rad = 0.01746 rad
(iii) If D is the number of degrees, R is the number of radians and G is the number of grades in an angle θ, then

(iv) θ = l/r where θ = angle subtended by arc of length / at the centre of the circle, r = radius of the circle.

Trigonometric Ratios

Relation between different sides and angles of a right angled triangle are called trigonometric ratios or T-ratios

Trigonometric (or Circular) Functions

Let X’OX and YOY’ be the coordinate axes. Taking 0 as the centre and a unit radius, draw a circle, cutting the coordinate axes at A,B, A’ and B’, as shown in the figure.

Now, the six circular functions may be defined as under
(i) cos θ = x
(ii) sin θ = y
(iii) sec θ = 1/x, x ≠ 0
(iv) cosec θ = 1/y, y ≠ 0
(v) tan θ = y/x, x ≠ 0
(vi) cot θ = x/y, y ≠ 0

Domain and Range

Range of Modulus Functions

sin θ|≤ 1, |cos θ| ≤ 1, |sec θ| ≥ 1, |Cosec θ| ≥ 1 for all values of 0, for which the functions are defined.

Trigonometric Identities

An equation involving trigonometric functions which is true for all those angles for which the functions are defined is called trigonometrical identity. Some identities are

Sign of Trigonometric Ratios

Trigonometric Ratios of Some Standard Angles

Trigonometric Ratios of Some Special Angles

Trigonometric Ratios of Allied Angles

Two angles are said to be allied when their sum or difference is either zero or a multiple of 90°.

The angles — θ, 90° ± θ, 180° ± θ, 270° + θ, 360° —θ etc., are angles allied to the angle θ, if θ is measured in degrees.

Trigonometric Periodic Functions

A function f(x) is said to be periodic, if there exists a real number T> 0 such that f(x + T)= f(x) for all x. T is called the period of the function, all trigonometric functions are periodic.

Maximum and Minimum Values of Trigonometric Expressions

Trigonometric Ratios of Compound Angles

The algebraic sum of two or more angles are generally called compound angles and the angles are known as the constituent angle. Some standard formulas of compound angles have been given below.

Transformation Formulae

Trigonometric Ratios of Multiple Angles

Trigonometric Ratios of Some Useful Angles