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 CARTESIAN PRODUCT OF SETS:
 Given two non-empty sets A and B, the set of all ordered pairs (x, y), where x ∈
A and y ∈ B is called Cartesian product of A and B; symbolically, we write A ×
B = {(x, y) | x ∈ A and y ∈ B}.
 Example- A = {1, 2, 3} and B = {4, 5}, then A × B = {(1, 4), (2, 4), (3, 4), (1,
5), (2, 5), (3, 5)} and B × A = {(4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (5, 3)}.
 Two ordered pairs are equal, if and only if the corresponding first elements are
equal and the second elements are also equal.
 If there are p elements in A and q elements in B, then there will be pq elements
in A × B, i.e., if n(A) = p and n(B) = q, then n(A × B) = pq.
 If either P or Q is the null set, then P × Q will also be empty set, i.e., P × Q = φ
 If A and B are non-empty sets and either A or B is an infinite set, then so is A ×
B.
 A × A × A = {(a, b, c): a, b, c ∈ A}. Here (a, b, c) is called an ordered triplet.

Ordered Pair
An ordered pair consists of two objects or elements in a given fixed order.

Equality of Two Ordered Pairs
Two ordered pairs (a, b) and (c, d) are equal if a = c and b = d.

Cartesian Product of Two Sets
For any two non-empty sets A and B, the set of all ordered pairs (a, b) where a ∈ A and b ∈ B is called the cartesian product of sets A and B and is denoted by A × B.
Thus, A × B = {(a, b) : a ∈ A and b ∈ B}
If A = Φ or B = Φ, then we define A × B = Φ

Note:

• A × B ≠ B × A
• If n(A) = m and n(B) = n, then n(A × B) = mn and n(B × A) = mn
• If atieast one of A and B is infinite, then (A × B) is infinite and (B × A) is infinite.

Relations
A relation R from a non-empty set A to a non-empty set B is a subset of the cartesian product set A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
The set of all first elements in a relation R is called the domain of the relation B, and the set of all second elements called images is called the range of R.

Note:

• A relation may be represented either by the Roster form or by the set of builder form, or by an arrow diagram which is a visual representation of relation.
• If n(A) = m, n(B) = n, then n(A × B) = mn and the total number of possible relations from set A to set B = 2^mn

Inverse of Relation
For any two non-empty sets A and B. Let R be a relation from a set A to a set B. Then, the inverse of relation R, denoted by R^-1 is a relation from B to A and it is defined by
R^-1 ={(b, a) : (a, b) ∈ R}
Domain of R = Range of R^-1 and
Range of R = Domain of R^-1.

Functions
A relation f from a set A to set B is said to be function, if every element of set A has one and only image in set B.
In other words, a function f is a relation such that no two pairs in the relation have the first element.

Real-Valued Function
A function f : A → B is called a real-valued function if B is a subset of R (set of all real numbers). If A and B both are subsets of R, then f is called a real function.

Some Specific Types of Functions
Identity function: The function f : R → R defined by f(x) = x for each x ∈ R is called identity function.
Domain of f = R; Range of f = R

Constant function: The function f : R → R defined by f(x) = C, x ∈ R, where C is a constant ∈ R, is called a constant function.
Domain of f = R; Range of f = C

Polynomial function: A real valued function f : R → R defined by f(x) = a₀ + a₁x + a₂x²+…+ a_nxⁿ, where n ∈ N and a₀, a₁, a₂,…….. a_n ∈ R for each x ∈ R, is called polynomial function.

Rational function: These are the real function of type f(x)g(x), where f(x)and g(x)are polynomial functions of x defined in a domain, where g(x) ≠ 0.

The modulus function: The real function f : R → R defined by f(x) = |x|
or

for all values of x ∈ R is called the modulus function.
Domaim of f = R
Range of f = R⁺ U {0} i.e. [0, ∞)

Signum function: The real function f : R → R defined
by f(x) = |x|x, x ≠ 0 and 0, if x = 0
or

is called the signum function.
Domain of f = R; Range of f = {-1, 0, 1}

Greatest integer function: The real function f : R → R defined by f (x) = {x}, x ∈ R assumes that the values of the greatest integer less than or equal to x, is called the greatest integer function.
Domain of f = R; Range of f = Integer

Fractional part function: The real function f : R → R defined by f(x) = {x}, x ∈ R is called the fractional part function.
f(x) = {x} = x – [x] for all x ∈R
Domain of f = R; Range of f = [0, 1)

Algebra of Real Functions
Addition of two real functions: Let f : X → R and g : X → R be any two real functions, where X ∈ R. Then, we define (f + g) : X → R by
{f + g) (x) = f(x) + g(x), for all x ∈ X.

Subtraction of a real function from another: Let f : X → R and g : X → R be any two real functions, where X ⊆ R. Then, we define (f – g) : X → R by (f – g) (x) = f (x) – g(x), for all x ∈ X.

Multiplication by a scalar: Let f : X → R be a real function and K be any scalar belonging to R. Then, the product of Kf is function from X to R defined by (Kf)(x) = Kf(x) for all x ∈ X.

Multiplication of two real functions: Let f : X → R and g : X → R be any two real functions, where X ⊆ R. Then, product of these two functions i.e. f.g : X → R is defined by (fg) x = f(x) . g(x) ∀ x ∈ X.

Quotient of two real functions: Let f and g be two real functions defined from X → R. The quotient of f by g denoted by fg is a function defined from X → R as

Set
A set is a well-defined collection of objects.

Representation of Sets
There are two methods of representing a set

• Roster or Tabular form In the roster form, we list all the members of the set within braces { } and separate by commas.
• Set-builder form In the set-builder form, we list the property or properties satisfied by all the elements of the sets

Set is a collection of well defined objects which are distinct from each other. Sets are usually denoted by capital letters A, B,C,… and elements are usually denoted by small letters a, b,c,…

If ‘a’ is an element of a set A, then we write a ∈ A and say ‘a’ belongs to A or ‘a’ is in A or ‘a’ is a member of A. If ‘a’ does not belongs to A, we write a ∉ A.

Standard Notations

• N : A set of natural numbers.
• W : A set of whole numbers.
• Z : A set of integers.
• Z⁺/Z^– : A set of all positive/negative integers.
• Q : A set of all rational numbers.
• Q⁺/Q^– : A set of all positive/ negative rational numbers.
• R : A set of real numbers.
• R⁺/R^–: A set of all positive/negative real numbers.
• C : A set of all complex numbers.

Methods for Describing a Set

(i) Roster/Listing Method/Tabular Form In this method, a set is described by listing element, separated by commas, within braces.

e.g., A = {a, e, i, o, u}

(ii) Set Builder/Rule Method In this method, we write down a property or rule which gives us all the elements of the set by that rule.

e.g.,A = {x : x is a vowel of English alphabets}

Types of Sets

1. Finite Set A set containing finite number of elements or no element.

2. Cardinal Number of a Finite Set The number of elements in a given finite set is called cardinal number of finite set, denoted by n (A).

3. Infinite Set A set containing infinite number of elements.

4. Empty/Null/Void Set A set containing no element, it is denoted by (φ) or { }.

5. Singleton Set A set containing a single element.

6. Equal Sets Two sets A and B are said to be equal, if every element of A is a member of B and every element of B is a member of A and we write A = B.

7. Equivalent Sets Two sets are said to be equivalent, if they have same number of elements.

If n(A) = ⁿ (B), then A and B are equivalent sets. But converse is not true.

8. Subset and Superset Let A and B be two sets. If every element of A is an element of B, then A is called subset of B and B is called superset of A. Written as A ⊆ B or B ⊇ A

9. Proper Subset If A is a subset of B and A ≠ B, then A is called proper subset of B and we write A ⊂ B.

10. Universal Set (U) A set consisting of all possible elements which occurs under consideration is called a universal set.

11. Comparable Sets Two sets A and Bare comparable, if A ⊆ B or B ⊆ A.

12. Non-Comparable Sets For two sets A and B, if neither A ⊆ B nor B ⊆ A, then A and Bare called non-comparable sets.

13. Power Set (P) The set formed by all the subsets of a given set A, is called power set of A, denoted by P(A).

14. Disjoint Sets Two sets A and B are called disjoint, if, A ∩ B = (φ).

Venn Diagram

In a Venn diagram, the universal set is represented by a rectangular region and a set is represented by circle or a closed geometrical figure inside the universal set.

Operations on Sets

Union of Sets

The union of two sets A and B, denoted by A ∪ B is the set of all those elements, each one of which is either in A or in B or both in A and B.

Intersection of Sets

The intersection of two sets A and B, denoted by A ∩ B, is the set of all those elements which are common to both A and B.

If A₁, A₂,… , An is a finite family of sets, then their intersection is denoted by

Complement of a Set

If A is a set with U as universal set, then complement of a set, denoted by A’ or Ac is the set U – A .

Difference of Sets

For two sets A and B, the difference A – B is the set of all those elements of A which do not belong to B.

Symmetric Difference

For two sets A and B, symmetric difference is the set (A – B) ∪ (B – A) denoted by A Δ B.

Laws of Algebra of Sets

For three sets A, B and C

(i) Commutative Laws
A ∩ B = B ∩ A
A ∪ B = B ∪ A

(ii) Associative Laws
(A ∩ B) ∩ C = A ∩ (B ∩ C)
(A ∪ B) ∪ C = A ∪ (B ∪ C)

(iii) Distributive Laws
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

(iv) Idempotent Laws
A ∩ A = A
A ∪ A = A

(v) Identity Laws
A ∪ Φ = A
A ∩ U = A

(vi) De Morgan’s Laws

(a) (A ∩ B) ′ = A ′ ∪ B ′
(b) (A ∪ B) ′ = A ′ ∩ B ′
(c) A – (B ∩ C) = (A – B) ∩ (A- C)
(d) A – (B ∪ C) = (A – B) ∪ ( A – C)

(vii) (a) A – B = A ∩ B’
(b) B – A = B ∩ A’
(c) A – B = A ⇔A ∩ B= (Φ)
(d) (A – B) ∪ B= A ∪ B
(e) (A – B) ∩ B = (Φ)
(f) A ∩ B ⊆ A and A ∩ B ⊆ B
(g) A ∪ (A ∩ B)= A
(h) A ∩ (A ∪ B)= A

(viii) (a) (A – B) ∪ (B – A) = (A ∪ B) – (A ∩ B)
(b) A ∩ (B – C) = (A ∩ B) – (A ∩ C)
(c) A ∩ (B Δ C) = (A ∩ B) A (A ∩ C)
(d) (A ∩ B) ∪ (A – B) = A
(e) A ∪ (B – A) = (A ∪ B)

(ix) (a) U’ = (Φ)
(b) Φ’ = U
(c) (A’ )’ = A
(d) A ∩ A’ = (Φ)
(e) A ∪ A’ = U
(f) A ⊆ B ⇔ B’ ⊆ A’

Important Points to be Remembered

• Every set is a subset of itself i.e., A ⊆ A, for any set A.
• Empty set Φ is a subset of every set i.e., Φ ⊂ A, for any set A.
• For any set A and its universal set U, A ⊆ U
• If A = Φ, then power set has only one element i.e., ⁿ (P(A)) = 1
• Power set of any set is always a non-empty set. Suppose A = {1, 2}, thenP(A) = {{1}, {2},{1,2}, Φ}.(a) A ∉ P(A) (b) {A} ∈ P(A)
• (vii) If a set A has n elements, then P(A) or subset of A has 2_n elements.
• (viii) Equal sets are always equivalent but equivalent sets may not be equal. The set {Φ} is not a null set. It is a set containing one element Φ.

Results on Number of Elements in Sets

• n (A ∪ B) = n(A) + (B)- n(A ∩ B)
• n(A ∪ B) = n(A)+ n(B), if A and B are disjoint.
• n(A – B) = n(A) – n(A ∩ B)
• n(A Δ B) = n(A) + n(B)- 2n(A ∩ B)
• n(A ∪ B ∪ C)= n(A)+ n(B)+ n(C)- n(A ∩ B) – n(B ∩ C)- n(A ∩ C)+ n(A ∩ B ∩ C)
• n (number of elements in exactly two of the sets A, B, C) = n(A ∩ B) + n(B ∩ C) + n (C ∩ A)- 3n(A ∩ B ∩ C)
• n (number of elements in exactly one of the sets A, B, C) = n(A) + n(B) + n(C) – 2n(A ∩ B) – 2n(B ∩ C) – 2n(A ∩ C) + 3n(A ∩ B ∩ C)
• n(A’ ∪ B’)= n(A ∩ B)’ = n(U) – n(A ∩ B)
• n(A’ ∩ B’ ) = n(A ∪ B)’ = n(U) – n(A ∪ B)
• n(B – A) = n(B)- n(A ∩ B)

Ordered Pair

An ordered pair consists of two objects or elements in a given fixed order.

Equality of Ordered Pairs Two ordered pairs (a1, b1) and (a2, b2) are equal iff a1 = a2 and b1 = b2.

Cartesian Product of Sets

For two sets A and B (non-empty sets), the set of all ordered pairs (a, b) such that a ∈ A and b ∈ B is called Cartesian product of the sets A and’ B, denoted by A x B. A x B={(a,b):a ∈ A and b ∈ B}

If there are three sets A, B, C and a ∈ A, be B and c ∈ C, then we form, an ordered triplet (a, b, c). The set of all ordered triplets (a, b, c) is called the cartesian product of these sets A, B and C.

i.e., A x B x C = {(a,b,c):a ∈ A,b ∈ B,c ∈ C}

Properties of Cartesian Product

For three sets A, B and C

• n (A x B)= n(A) n(B)
• A x B = Φ, if either A or B is an empty set.
• A x (B ∪ C)= (A x B) ∪ (A x C)
• A x (B ∩ C) = (A x B) ∩ (A x C)
• A x (B — C)= (A x B) — (A x C)
• (A x B) ∩ (C x D)= (A ∩ C) x (B ∩ D)
• If A ⊆ B and C ⊆ D, then (A x C) ⊂ (B x D)
• If A ⊆ B, then A x A ⊆ (A x B) ∩ (B x A)
• A x B = B x A ⇔ A = B
• If either A or B is an infinite set, then A x B is an infinite set.
• A x (B’ ∪ C’ )’ = (A x B) ∩ (A x C)
• A x (B’ ∩ C’ )’ = (A x B) ∪ (A x C)
²elements in common.
• If ≠ B, then A x B ≠ B x A
• If A = B, then A x B= B x A
• If A ⊆ B, then A x C = B x C for any set C.

In This Post we are  providing Chapter-12 Thermodynamics 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 THERMODYNAMICS

Question 1.
One gram of sample of NH₄NO₃ is decomposed in a bomb calorimeter. The temperature of the calorimeter increases by 6.12 K. The heat capacity of the system is 1.23 kj/deg. What is the molar heat of decomposition of NH₄NO₃?
(a) -7.53 kj/mol
(b) -398.1 kj mol^-1
(c) -16.1 kj/mol
(d) -602 kj/mol.

Answer: (d) -602 kj/mol.

Question 2.
AHr of graphite is 0.23 kj/mol and ∆H_f for diamond is 1.896 kj mol^-1, ∆H_transition from graphite to diamond is
(a) 1.66 kj/mol
(b) 2.1 kj/mol
(c) 2.33 kj/mol
(d) 1.5 kj/mol

Answer: (a) 1.66 kj/mol

Question 3.
The bond energies of C-C, C=C; H-H and C-H linkages are 350, 600, 400 and 410 kj per mole respectively. The heat of hydrogenation of ethylene is
(a) -170 kj mol^-1
(b) -260 kj mol^-1
(c) 400 kj mol^-1
(d) -450 kj mol^-1

Answer: (a) -170 kj mol^-1

Question 4.
Which of the following reaction defines ∆H0f?
(a) C(Diamond) + O₂(g) → CO₂(g)
(b) 12 H₂(g) + 12 F₂(g) → HF(g)
(c) N₂(g) + 3H₂(g) → 2NH₃(g)
(d) CO(g) + 12 O₂(g) → CO₂(g)

Answer: (b) 12 H₂(g) + 12 F₂(g) → HF(g)

Question 5.
One mole of a hon-ideal gas undergoes a change of state (2.0 atm, 3.0 L, 95 K) → (4.0 atm, 5.0 L, 245 K) with a change in internal energy, ∆U = 30.0 L atm. The change in enthalpy (∆H) of the process in L atm is
(a) 44.0
(b) 42.3
(c) 44.0
(d) not defined because pressure is not constant.

Answer: (c) 44.0

Question 6.
Which one of the following statement is false?
(a) Work is a state function
(b) Temperature is a state function
(c) Change in the state is completely defined when the initial final states are specified
(d) Work appears at the boundary of the system

Answer: (a) Work is a state function

Question 7.
Molar heat capacity of water in equilibrium with ice at constant pressure is
(a) zero
(b) infinity
(c) 40.45 kj K^-1 mol^-1
(d) 75.48 JK^-1 mol^-1

Answer: (b) infinity

Question 8.
For the reaction C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(I) at constant temperature ∆H – ∆E is
(a) + RT
(b) – 3RT
(c) + 3RT
(d) -RT

Answer: (b) – 3RT

Question 9.
For which one of the following equations AH_reaction equals ∆H0f for the product?
(a) N₂(g) + O₃(g) → N₂O₃(g)
(b) CH₄(g) + 2Cl₂(g) → CH₂Cl₂(l) + 2HCl(g)
(c) Xe(g) + 2F₂(g) → XeF₄(g)
(d) 2C(g) + O₂(g) → 2CO₂(g)

Answer: (c) Xe(g) + 2F₂(g) → XeF₄(g)

Question 10.
Enthalpy of CH₄ + 12 O₂ → CH₃OH is negative.
If enthalpy of combustion of CH₄ and CH₃OH are x and y respectively then which reaction is correct?
(a) x > y
(b) x < y
(c) x = y
(d) x ≥ y

Answer: (b) x < y

Question 11.
The heat required to raise the temperature of a body by 1 K is called
(a) Specific heat
(b) Thermal capacity
(c) Water equivalent
(d) Molar heat capacity

Answer: (b) Thermal capacity

Question 12.
In a reaction involving only solids and liquids, which of the following is true?
(a) ∆H < ∆E (b) ∆H = ∆E (c) ∆H > ∆E
(d) ∆H = ∆E + RT∆₁₁

Answer: (b) ∆H = ∆E

Question 13.
In which of the following process, the process is always non-feasible?
(a) ∆H > 0, ∆S > 0
(b) ∆H < 0, ∆S > 0
(c) ∆H > 0, ∆S < 0
(d) ∆H < 0, ∆S < 0

Answer: (c) ∆H > 0, ∆S < 0

Question 14.
Internal energy does not include
(a) Nuclear energy
(b) Vibrational energy
(c) Rotational energy
(d) Energy of gravitational pull

Answer: (d) Energy of gravitational pull

Question 15.
Which of the following reactions is endothermic?
(a) N₂ + O₂ → 2NO
(b) H₂ + Cl₂ → 2HCl
(c) H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₁₁O
(d) None of these

Answer: (a) N₂ + O₂ → 2NO

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In This Post we are  providing Chapter-11 Thermal Properties of Matter 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 THERMAL PROPERTIES OF MATTER

Question 1: 

Assertion: The triple point of water is a standard fixed point in modern thermometry.
Reason: The triple point of a substance is unique i.e. it occurs at one particular set of values of pressure and temperature

• a) Assertion is correct, reason is correct; reason is a correct explanation for assertion
• b) Assertion is incorrect, reason is correct
• c) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
• d) None of these

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

Question 2: A metal sheet with a circular hole is heated. The hole

• a) gets larger
• b) gets deformed
• c) gets smaller
• d) None of these

Answer: gets larger

Question 3: A solid ball of metal has a spherical cavity inside it. The balln is heated. The volume of cavity will

• a) increase
• b) decrease
• c) remain unchanged
• d) have its shape changed

Answer: increase

Question 4:

Assertion : Water kept in an open vessel will quickly evaporate on the surface of the moon.
Reason : The temperature at the surface of the moon is much higher than boiling point of the water.

• a) Assertion is correct, reason is incorrect
• b) None of these
• 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 5: Consider the following statements and select the correct statement(s).

I. Water can never be boiled without heating.
II. Water can be boiled below room temperature by lowering the pressure.
III. On releasing the excess pressure water refreezes into ice.

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

Answer: II and III

Question 6: Two marks on a glass rod 10 cm apart are found to increase their distance by 0.08 mm when the rod is heated from 0°C to 100°C. A flask made of the same glass as that of rod measures a volume of 1000 cc at 0°C. The volume it measures at 100°C in cc is

• a) 1002.4
• b) 1008.2
• c) 1004.2
• d) 1006.4

Answer: 1002.4

Question 7: Mass of water which absorbs or emits the same amount of heat as is done by the body for the same rise or fall in temperature is known as

• a) water equivalent of the body
• b) latent heat capacity of the body
• c) specific heat capacity of the body
• d) thermal capacity of the body

Answer: water equivalent of the body

Question 8: Heat is transmitted from higher to lower temperature through actual mass motion of the molecules in

• a) convection
• b) radiation
• c) conduction
• d) None of these

Answer: convection

Question 9: Good absorbers of heat are

• a) good emitters
• b) non-emitters
• c) poor emitters
• d) highly polished

Answer: good emitters

Question 10: Three bodies A, B and C have equal area which are painted red, yellow and black respectively. If they are at same temperature, then

• a) emissive power of C is maximum
• b) emissive power of A is maximum
• c) emissive power of B is maximum
• d) emissive power of A, B and C are equal.

Answer: emissive power of C is maximum

Question 11: Sweet makers do not clean the bottom of cauldron because

• a) black and rough surface absorbs more heat
• b) absorption power of black and bright surface is more.
• c) transmission power of black and rough surface is more.
• d) emission power of black and bright surface is more

Answer: black and rough surface absorbs more heat

Question 12: 4200 J of work is required for

• a) increasing the temperature of 100 g of water through 10°C
• b) increasing the temperature of 1 kg of water through 10°C
• c) increasing the temperature of 500 g of water through 10°C
• d) increasing the temperature of 10 g of water through 10°C

Answer: increasing the temperature of 100 g of water through 10°C

Question 13: The latent heat of vaporization of a substance is always

• a) greater than its latent heat of fusion
• b) less than its latent heat of fusion
• c) greater than its latent heat of sublimation
• d) equal to its latent heat of sublimation

Answer: greater than its latent heat of fusion

Question 14: Which of the following statements regarding specific heat capacity of a substance are correct ? It depends on

I. mass of substance.
II. nature of substance.
III. temperature of substance.
IV. volume of substance.

• a) II and III
• b) None of these
• c) I and II
• d) III and IV

Answer: II and III

Question 15: A quantity of heat required to change the unit mass of a solid substance, from solid state to liquid state, while the temperature remains constant, is known as

• a) latent heat of fusion
• b) sublimation
• c) latent heat
• d) hoar frost

Answer: latent heat of fusion

In This Post we are  providing Chapter-10 Mechanical Properties of Fluids 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 MECHANICAL PROPERTIES OF FLUIDS

Question 1.
A number of small drops of mercury coalesce adiabatically to form a single drop. The temperature of drop
(a) Increases
(b) Is infinite
(c) Remains unchanged
(d) May decrease or increase depending upon size

Answer: (d) May decrease or increase depending upon size

Question 2.
Surface tension of a soap solution is 1.9 × 10^-2N/m. work done in blowing a bubble of 2.0 cm diameter will be
(a) 7.6 × 10^-6 p J
(b) 15.2 × 10^-6 p J
(c) 1.9 × 10^-6 p J
(d) 1 × 10^-4 p J

Answer: (b) 15.2 × 10^-6 p J

Question 3.
Plants get water through the roots because of
(a) Capillarity
(b) Viscosity
(c) Gravity
(d) Elasticity

Answer: (a) Capillarity

Question 4.
Choose the wrong statement from the following.
(a) Small droplets of a liquid are spherical due to surface tension
(b) Oil rises through the wick due to capillarity
(c) In drinking the cold drinks through a straw, we use the phenomenon of capillarity
(d) Gum is used to stick two surfaces. In this process we use the property of Adhesion

Answer: (c) In drinking the cold drinks through a straw, we use the phenomenon of capillarity

Question 5.
The height of a liquid in a fine capillary tube
(a) Increases with an increase in the density of a liquid
(b) Decreases with a decrease in the diameter of the tube
(c) Decreases with an increase in the surface tension
(d) Increases as the effective value of acceleration due to gravity is decreased

Answer: (d) Increases as the effective value of acceleration due to gravity is decreased

Question 6.
At critical temperature, the surface tension of a liquid
(a) Is zero
(b) Is infinity
(c) Is the same as that at any other temperature
(d) Can not be determined

Answer: (a) Is zero

Question 7.
A capillary tube when immersed vertically in a liquid records a rise of 3 cm. if the tube is immersed in the liquid at an angle of 60° with the vertical, then length of the liquid column along the tube will be
(a) 2 cm
(b) 3 cm
(c) 6 cm
(d) 9 cm

Answer: (c) 6 cm

Question 8.
When the angle of contact between a solid and a liquid is 90°, then
(a) Cohesive force > Adhesive force
(b) Cohesive force < Adhesive force
(c) Cohesive force = Adhesive force
(d) Cohesive force >> Adhesive force

Answer: (c) Cohesive force = Adhesive force

Question 9.
Water rises up to a height of 5 cm in a capillary tube of radius 2 mm. what is the radius of the radius of the capillary tube if the water rises up to a height of 10 cm in another capillary?
(a) 4 mm
(b) 1 mm
(c) 3 mm
(d) 1 cm

Answer: (b) 1 mm

Question 10.
If the surface of a liquid is plane, then the angle of contact of the liquid with the walls of container is
(a) Acute angle
(b) Obtuse angle
(c) 90°
(d) 0°

Answer: (d) 0°

Question 11.
Two soap bubbles have radii in the ratio of 4 : 3. What is the ratio of work done to below these bubbles?
(a) 4 : 3
(b) 16 : 9
(c) 09 : 16
(d) 3 : 4

Answer: (b) 16 : 9

Question 12.
The height of water in a capillary tube of radius 2 cm is 4 cm. what should be the radius of capillary, if the water rises to 8 cm in tube?
(a) 1 cm
(b) 0.1 cm
(c) 2 cm
(d) 4 cm

Answer: (a) 1 cm

Question 13.
Water rises up to a height of 4 cm, in a capillary tube immersed vertically in water. What will be the length of water column in the capillary tube, if the tube is immersed in water, at an angle of 60° with the vertical?
(a) 4 cm
(b) 6 cm
(c) 8 cm
(d) 2 cm

Answer: (c) 8 cm

Question 14.
The surface of water in contact with glass wall is
(a) Plane
(b) concave
(c) convex
(d) Both b and c

Answer: (b) concave

Question 15.
Pressure inside two soap bubbles is 1.01 and 1.02 atmospheres. ratio between their volume is
(a) 102 : 101
(b) (102)3 : (101)3
(c) 8 : 1
(d) 2 : 1

Answer: (c) 8 : 1

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In This Post we are  providing Chapter-9 Mechanical Properties of Solids 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 MECHANICAL PROPERTIES OF SOLIDS

Question 1: Shearing strain is expressed by

• a) angle of shear
• b) decrease in volume
• c) angle of twist
• d) increase in volume

Answer: angle of shear

Question 2: A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is

• a) 0.03
• b) 0.02
• c) 0.06
• d) 0.01

Answer: 0.03

Question 3:

Assertion : Identical springs of steel and copper are equally stretched. More work will be done on the steel spring
Reason : Steel is more elastic than copper.

• 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 4: The Poisson’s ratio of a material is 0.5. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by 4%. The percentage increase in the length is

• a) 4%
• b) 2.5%
• c) 2%
• d) 1%

Answer: 4%

Question 5: Modulus of rigidity of ideal liquids is

• a) zero
• b) infinity
• c) unity
• d) some finite small non-zero constant value

Answer: zero

Question 6: Beyond the critical speed, the flow of fluids becomes

• a) turbulent
• b) streamline
• c) steady
• d) very slow

Answer: turbulent

Question 7: Streamline flow is more likely for liquids with

• a) low density and high viscosity
• b) low density and high viscosity
• c) high density and high viscosity
• d) high density and high viscosity

Answer: low density and high viscosity

Question 8: For flow of a fluid to be turbulent

• a) both
• b) fluid should have high density
• c) velocity should be large
• d) None of these

Answer: both

Question 9: In Bernoulli’s theorem which of the following is conserved?

• a) Energy
• b) Mass
• c) Linear momentum
• d) Angular momentum

Answer: Energy

Question 10: A liquid is allowed to flow into a tube of truncated cone shape. Identify the correct statement from the following

• a) the speed is low at the wider end and high at the narrow end.
• b) the speed is high at the wider end and high at the narrow end
• c) the speed is same at both ends in a stream line flow.
• d) the liquid flows with uniform velocity in the tube.

Answer: the speed is low at the wider end and high at the narrow end.

Question 11: As the temperature of a liquid is raised, the coefficient of viscosity

• a) decreases
• b) increases
• c) remains the same
• d) may increase or decrease depending on the nature of liquid

Answer: decreases

Question 12: After terminal velocity is reached, the acceleration of a body falling through a fluid is

• a) zero
• b) equal to g
• c) less than g
• d) greater than g

Answer: zero

Question 13: Terminal velocity of ball depends on

• a) density difference of liquid and ball
• b) density of ball only
• c) density of liquid only
• d) area of the ball

Answer: density difference of liquid and ball

Question 14: Surface tension of a liquid is due to

• a) cohesive force between molecules
• b) adhesive force between molecules
• c) electrical force between molecules
• d) gravitational force between molecules

Answer: cohesive force between molecules

Question 15: If a soap bubble formed at the end of the tube is blown very slowly, then the graph between excess pressure inside the bubble with time will be a

• a) parabolic curve sloping down
• b) parabolic curve sloping up
• c) straight line sloping down
• d) straight line sloping up

Answer: parabolic curve sloping down

In This Post we are  providing Chapter-8 Gravitation 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 GRAVITATION

Question 1: Newton’s universal law of gravitation applies to

• a) both small and big bodies
• b) only valid for solar system
• c) planets only
• d) small bodies only

Answer: both small and big bodies

Question 2: The value of G varies with

• a) None of these
• b) radius of the planet
• c) depth below the ground
• d) height above the earth’s surface

Answer: None of these

Question 3: Force of gravitational attraction is least

• a) at the equator
• b) at the poles
• c) at a point in between equator and any pole
• d) None of these

Answer: at the equator

Question 4:

Assertion : If earth suddenly stops rotating about its axis, then the value of acceleration due to gravity will become same at all the places.
Reason : The value of acceleration due to gravity depends upon the rotation of the earth.

• 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 5: The height of the point vertically above the earth’s surface, at which acceleration due to gravity becomes 1% of its value at the earth’s surface is (Radius of the earth = R)

• a) 9 R
• b) 10 R
• c) 20 R
• d) 8 R

Answer: 9 R

Question 6: The speed of earth’s rotation about its axis is w. Its speed is increases to x times to make the effective acceleration due to gravity equal to zero at the equator. Then x is

• a) 17
• b) 34
• c) 8.5
• d) 1

Answer: 17

Question 7: Where will it be profitable to purchase one kilogram sugar?

• a) At equator
• b) At 40° latitude
• c) At poles
• d) At 45° latitude

Answer: At equator

Question 8: Earth is flattened at poles, bulged at the equator. This is due to

• a) the centrifugal force is more at the equator than at the poles
• b) the angular velocity of spinning about its axis is more at equator
• c) the angular velocity of spinning about its axis is less at equator
• d) earth revolves round the sun in an elliptical orbit

Answer: the centrifugal force is more at the equator than at the poles

Question 9: A particle is suspended from a spring and it stretches the spring by 1 cm on the surface of earth. By how much amount the same particle will stretch the same spring at a place 800 km above the surface of earth.

• a) 0.79 cm
• b) 1.38 cm
• c) 2.38 cm
• d) 1.59 cm

Answer: 0.79 cm

Question 10: Average density of the earth

• a) is directly proportional to g
• b) is inversely proportional to g
• c) does not depend on g
• d) is a complex function of g

Answer: is directly proportional to g

Question 11: If the earth were to rotates faster than its present speed, the weight of an object will

• a) decrease at the equator but remain unchanged at the poles
• b) remain unchanged at the equator but decrease at the poles
• c) remain unchanged at the equator but increase at the poles
• d) increase at the equator but remain unchanged at the poles

Answer: decrease at the equator but remain unchanged at the poles

Question 12: At what height from the ground will the value of g be the same as that in 10 km deep mine below the surface of earth?

• a) 5 km
• b) 15 km
• c) 10 km
• d) 20 km

Answer: 5 km

Question 13: The ratio of radii of earth to another planet is 2/3 and the ratio of their mean densities is 4/5. If an astronaut can jump to a maximum height of 1.5 m on the earth, with the same effort, the maximum height he can jump on the planet is

• a) 0.8 m
• b) 0.5 m
• c) 1.25 m
• d) 1 m

Answer: 0.8 m

Question 14: Consider Earth to be a homogeneous sphere. Scientist A goes deep down in a mine and scientist B goes high up in a balloon. The gravitational field measured by

• a) each decreases at different rates
• b) each decreases at the same rate
• c) B goes on decreasing and that by A goes on increasing
• d) A goes on decreasing and that by B goes on increasing

Answer: each decreases at different rates

Question 15: In some region, the gravitational field is zero. The gravitational potential in this region.

• a) must be constant
• b) must be zero
• c) must be variable
• d) cannot be zero

Answer: must be constant

In This Post we are  providing Chapter-7 System of Particles and Rotational Motion 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 SYSTEM OF PARTICLES AND ROTATIONAL MOTION

Question 1.
A body of M.I. 3 kg m² rotating with an angular velocity 2 rad/s has the same K.E. as a mass of 12 kg moving with a velocity of
(a) 1 m/s
(b) 2 m/s
(c) 4 m/s
(d) 8 m/s

Answer: (a) 1 m/s

Question 2.
A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is
(a) L/2
(b) L/4
(c) 2 L
(d) 4 L

Answer: (b) L/4

Question 3.
A thin uniform, circular ring is rolling down an inclined plane of inclination 300 without slipping. Its linear acceleration along the inclined plane will be
(a) g/2
(b) g/3
(c) g/4
(d) 2g/3

Answer: (a) g/2

Question 4.
Moment of inertia depends on
(a) Distribution of particles
(b) Mass
(c) Position of axis of rotation
(d) All of these

Answer: (d) All of these

Question 5.
Calculate the M.I. of a thin uniform ring about an axis tangent to the ring and in a plane of the ring, if its M.I. about an axis passing through the center and perpendicular to plane is 4 kg m².
(a) 12 kg m²
(b) 3 kg m²
(c) 6 kg m²
(d) 9 kg m²

Answer: (c) 6 kg m²

Question 6.
If a body is rotating about an axis, passing through its center of mass then its angular momentum is directed along its
(a) Radius
(b) Tangent
(c) Circumference
(d) Axis of rotation

Answer: (d) Axis of rotation

Question 7.
A solid cylinder of mass 20 kg, has length 1 metre and radius 0.5m. then its momentum of inertia in kg m² about its geometrical axis is
(a) 2.5
(b) 5
(c) 1.5
(d) 3

Answer: (a) 2.5

Question 8.
A particle moves on a circular path with decreasing speed. Choose the correct statement.
(a) Angular momentum remains constant.
(b) Acceleration is towards the center.
(c) Particle moves on a spiral path with decreasing radius.
(d) The direction of angular momentum remains constant.

Answer: (d) The direction of angular momentum remains constant.

Question 9.
The M.I. of uniform circular disc about a diameter is I. its M.I. about an axis perpendicular to its plane passing through a point on its rim will be
(a) 4 I
(b) 6 I
(c) 8 I
(d) 9 I

Answer: (b) 6 I

Question 10.
Which is the wrong relation from the following?
(a) t = I a
(b) F = ma
(c) L = I w
(d) I = t a

Answer: (d) I = t a

Question 11.
A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected?
(a) Moment of inertia
(b) Angular momentum
(c) Angular velocity
(d) Rotational kinetic energy

Answer: (b) Angular momentum

Question 12.
A particle moves on a circular path with decreasing speed. Choose the correct statement.
(a) Angular momentum remains constant.
(b) Acceleration is towards the center.
(c) Particle moves on a spiral path with decreasing radius.
(d) The direction of angular momentum remains constant.

Answer: (d) The direction of angular momentum remains constant.

Question 13.
A body of M.I. 3 kg m² rotating with an angular velocity 2 rad/s has the same K.E. as a mass of 12 kg moving with a velocity of
(a) 1 m/s
(b) 2 m/s
(c) 4 m/s
(d) 8 m/s

Answer: (a) 1 m/s

Question 14.
A hollow cylinder and a solid cylinder having different mass diameter are released from rest simultaneously from the of an inclined plane. Which will reach the bottom first?
(a) solid cylinder
(b) cant be determined without knowing their masses
(c) hollow cylinder
(d) cant be determined without knowing their diameters

Answer: (a) solid cylinder

Question 15.
Which is the wrong relation from the following?
(a) t = I a
(b) F = ma
(c) L = I w
(d) I = t a

Answer: (d) I = t a

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In This Post we are  providing Chapter-6 Work , Energy and Power 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 WORK, ENERGY AND POWER

Question 1: Which of the following must be known in order to determine the power output of an automobile?

• a) Work performed and elapsed time of work
• b) Force exerted and distance of motion
• c) Mass and amount of work performed
• d) Final velocity and height

Answer: Work performed and elapsed time of work

Question 2: A vehicle is moving with a uniform velocity on a smooth horizontal road, then power delivered by its engine must be

• a) increasing
• b) zero
• c) uniform
• d) decreasing

Answer: increasing

Question 3: How much water, a pump of 2 kW can raise in one minute to a height of 10 m, take g = 10 m/s²?

• a) 1200
• b) 100
• c) 2000
• d) 1000

Answer: 1200

Question 4: The engine of a vehicle delivers constant power. If the vehicle is moving up the inclined plane then, its velocity

• a) must remain constant
• b) must increase
• c) must decrease
• d) may increase, decrease or remain same

Answer: must remain constant

Question 5: A body projected vertically from the earth reaches a height equal to earth’s radius before returning to the earth. The power exerted by the gravitational force is greatest

• a) at the instant just before the body hits the earth
• b) at the highest position of the body
• c) it remains constant all through
• d) at the instant just after the body is projected

Answer: at the instant just before the body hits the earth

Question 6: When the force retards the motion of body, the work done is

• a) negative
• b) zero
• c) positive
• d) None of these

Answer: negative

Question 7: A man pushes a wall and fails to displace it, he does

• a) no work at all
• b) positive but not maximum work
• c) negative work
• d) maximum positive work

Answer: no work at all

Question 8: A boy carrying a box on his head is walking on a level road from one place to another is doing no work. This statement is

• a) correct
• b) incorrect
• c) partly correct
• d) cannot say

Answer: correct

Question 9: No work is done if

• a) All of these
• b) force and displacement are mutually perpendicular
• c) force is zero
• d) displacement is zero

Answer: All of these

Question 10: A particle is taken round a circle by application of force. The work done by the force is

• a) Zero
• b) positive non–zero
• c) negative non–zero
• d) None of these

Answer: Zero

Question 11:  Assertion : The work done in moving a body over a closed loop is zero for every force in nature.

Reason : Work done depends on nature of force

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

Answer: Assertion is correct, reason is correct; reason is not a correct explanation for assertion

Question 12: If a motorcyclist skids and stops after covering a distance of 15 m. The stopping force acting on the motorcycle by the road is 100 N, then the work done by the motorcycle on the road is

• a) Zero
• b) 750J
• c) –1500 J
• d) 1500 J

Answer: Zero

Question 13: A ball moves in a frictionless inclined table without slipping. The work done by the table surface on the ball is

• a) zero
• b) positive
• c) negative
• d) None of these

Answer: zero

Question 14: A spring of spring constant 5 × 10³ N/m is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is

• a) 18.75 J
• b) 25.00 J
• c) 6.25 J
• d) 12.50 J

Answer: 18.75 J

Question 15: A boy pushes a toy box 2.0 m along the floor by means of a force of 10 N directed downward at an angle of 60º to the horizontal. The work done by the boy is

• a) 10 J
• b) 12 J
• c) 8 J
• d) 6 J

Answer: 10 J

In This Post we are  providing Chapter-5 Laws of Motion 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 LAWS OF MOTION

Question 1: Physical independence of force is a consequence of

• a) first law of motion
• b) third law of motion
• c) second law of motion
• d) all of these

Answer: first law of motion

Question 2: A reference frame attached to the earth

• a) cannot be an inertial frame because earth is revolving round the sun
• b) is an inertial frame by definition
• c) is an inertial frame because Newton’s laws are applicable
• d) is an inertial frame because the earth is rotating about its own axis

Answer: cannot be an inertial frame because earth is revolving round the sun

Question 3: The direction of impulse is

• a) same as that of the net force
• b) opposite to that of the net force
• c) same as that of the final velocity
• d) same as that of the initial velocity

Answer: same as that of the net force

Question 4: When a body is stationary

• a) the combination of forces acting on it balances each other
• b) the body is in vacuum
• c) the force acting on it is not in contact with it
• d) there is no force acting on it

Answer: the combination of forces acting on it balances each other

Question 5: When an elevator cabin falls down, the cabin and all the bodies fixed in the cabin are accelerated with respect to

• a) man standing on earth
• b) ceiling of elevator
• c) floor of elevator
• d) man standing in the cabin

Answer: man standing on earth

Question 6: A monkey is climbing up a rope, then the tension in the rope

• a) must be equal to the force applied by the monkey on the rope
• b) must be less than the force applied by the monkey on the rope.
• c) must be greater than the force applied by the monkey on the rope.
• d) may be equal to, less than or greater the force applied by the monkey on the rope.

Answer: must be equal to the force applied by the monkey on the rope

Question 7: If two masses (M & m) are connected on a horizontal plane and a force is applied on the combination, then the tension T depends on

• a) whether force is applied on M or m
• b) the force applied on the system
• c) Can’t be predicted.
• d) None of these

Answer: whether force is applied on M or m

Question 8: A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of 5 m/s², the reading of the spring balance will be

• a) 24 N
• b) 74 N
• c) 15 N
• d) 49 N

Answer: 24 N 

Question 9: Identify the correct statement from the following

• a) Friction does not depend on the area in contact
• b) Friction is always less than the applied force
• c) Friction depends on the volume of body
• d) Friction depends on the area of contact.

Answer: Friction does not depend on the area in contact

Question 10: The coefficient of static friction between two surfaces depends upon

• a) the normal reaction
• b) the shape of the surface in contact
• c) the magnitude of applied force
• d) None of these

Answer: the normal reaction

Question 11: If the applied force is doubled, then coefficient of friction is

• a) not changed
• b) tripled
• c) halved
• d) doubled

Answer: not changed

Question 12: Which of the following statements about friction is true?

• a) Kinetic friction is always greater than rolling friction
• b) Frictional force is proportional to the area of contact between the two surfaces
• c) Frictional force cannot accelerate a body
• d) Friction can be reduced to zero

Answer: Kinetic friction is always greater than rolling friction

Question 13: A block of mass 0.1kg is held against a wall applying a horizontal force of 5 N on the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of the frictional force acting on the block is:

• a) 0.98 N
• b) 4.9 N
• c) 0.49 N
• d) 2.5 N

Answer: 0.98 N

Question 14 : What are the effects if force is acting on a moving body in a direction perpendicular to the direction of motion

• a) The direction of motion changes
• b) All of these
• c) The acceleration changes uniformly
• d) The speed changes uniformly

Answer: The direction of motion changes

Question 15: On a banked road, which force is essential to provide the necessary centripetal force to a car to take a turn while driving at the optimum speed?

• a) Component of normal reaction
• b) Component of frictional force
• c) Both
• d) None of these

Answer: Component of normal reaction