May 2026

Describe the following set in Roster form : (i) {x:x is a letter before e in the English alphabet}. (ii) {x∈N : x^2 < 25}. (iii) {x∈N : x is a prime number, 10 < x < 20}. (iv) {x∈N : x = 2n, n∈N}. (v) {x∈R:x greater than x}. (vi) {x:x is a prime number which is a divisor of 60}. (vii) {x: x is a two digit number such that the sum of its digits is 8). (viii) The set of all letters in the word ‘Trigonometry’. (ix) The set of all letters in the word ‘Better’.

Leave a Comment / Educational /

Describe the Following Sets in Roster Form Describe the Following Sets in Roster Form Question Roster Form (i) \[ \{x:x \text{ is a letter before e in the English alphabet}\} \] \[ \{a,b,c,d\} \] (ii) \[ \{x\in N:x^2

Describe the following set in Roster form : (i) {x:x is a letter before e in the English alphabet}. (ii) {x∈N : x^2 < 25}. (iii) {x∈N : x is a prime number, 10 < x < 20}. (iv) {x∈N : x = 2n, n∈N}. (v) {x∈R:x greater than x}. (vi) {x:x is a prime number which is a divisor of 60}. (vii) {x: x is a two digit number such that the sum of its digits is 8). (viii) The set of all letters in the word ‘Trigonometry’. (ix) The set of all letters in the word ‘Better’. Read More »

If A = {0,1,2,3,4,5,6,7,8,9,10}, then insert the appropriate symbol ∈ or ∉ in each of the following. i. 4…A ii. -4….A iii. 12….A iv. 9…A v. 0…A vi. -2….AIf A = {0,1,2,3,4,5,6,7,8,9,10}, then insert the appropriate symbol ∈ or ∉ in each of the following. i. 4…A ii. -4….A iii. 12….A iv. 9…A v. 0…A vi. -2….A

Leave a Comment / Educational /

Insert the Appropriate Symbol ∈ or ∉ Insert the Appropriate Symbol ∈ or ∉ If \[ A=\{0,1,2,3,4,5,6,7,8,9,10\}, \] then insert the appropriate symbol \[ \in \text{ or } \notin \] in each of the following. Question Answer i. \(4\ …\ A\) \[ 4 \in A \] ii. \(-4\ …\ A\) \[ -4 \notin A \]

If A = {0,1,2,3,4,5,6,7,8,9,10}, then insert the appropriate symbol ∈ or ∉ in each of the following. i. 4…A ii. -4….A iii. 12….A iv. 9…A v. 0…A vi. -2….AIf A = {0,1,2,3,4,5,6,7,8,9,10}, then insert the appropriate symbol ∈ or ∉ in each of the following. i. 4…A ii. -4….A iii. 12….A iv. 9…A v. 0…A vi. -2….A Read More »

Which of the following collections are sets? Justify your answer: (i) A collection of all natural numbers less than 50. (ii) The collection of good hockey players in India. (iii) The collection of all girls in your class. (iv) The collection of most talented writers of India. (v) The collection of difficult topics in mathematics. (vi) The collection of novels written by munshi Prem Chand. (vii) The collection of all months of a year beginning with the letter J. (viii) The collection of all questions in this chapter. (ix) A collection of most dangerous animals of the world. (x) The collection of prime integers.

Leave a Comment / Educational /

Which of the Following Collections are Sets? Which of the Following Collections are Sets? Collection Set / Not a Set Reason (i) A collection of all natural numbers less than 50. Set The collection is well-defined. (ii) The collection of good hockey players in India. Not a Set The word “good” is not well-defined. (iii)

Which of the following collections are sets? Justify your answer: (i) A collection of all natural numbers less than 50. (ii) The collection of good hockey players in India. (iii) The collection of all girls in your class. (iv) The collection of most talented writers of India. (v) The collection of difficult topics in mathematics. (vi) The collection of novels written by munshi Prem Chand. (vii) The collection of all months of a year beginning with the letter J. (viii) The collection of all questions in this chapter. (ix) A collection of most dangerous animals of the world. (x) The collection of prime integers. Read More »

What is the difference between a collection and a set ? Give reasons to support your answer ?

Leave a Comment / Educational /

Difference Between a Collection and a Set Difference Between a Collection and a Set What is the difference between a collection and a set? Give reasons to support your answer. Solution Collection Set A collection is simply a group of objects. A set is a well-defined collection of distinct objects. A collection may or may

What is the difference between a collection and a set ? Give reasons to support your answer ? Read More »

Statement-1 (Assertion): The value of {(0.027)^3 + (0.023)^3}/ {(0.027)^2 – (0.027)×(0.023) + (0.023)^2} is 0.05 Statement-2 (Reason): a^3 – b^3 = (a – b) (a^2 – ab + b^2)

Leave a Comment / Educational /

Assertion and Reason on {(0.027)³ + (0.023)³}/{(0.027)² − (0.027)(0.023) + (0.023)²} Assertion and Reason Question on Algebraic Identities Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. (a) Statement-1 is true, Statement-2 is true; Statement-2

Statement-1 (Assertion): The value of {(0.027)^3 + (0.023)^3}/ {(0.027)^2 – (0.027)×(0.023) + (0.023)^2} is 0.05 Statement-2 (Reason): a^3 – b^3 = (a – b) (a^2 – ab + b^2) Read More »

Statement-1 (Assertion): If a, b, c are all non-zero such that a + b + c = 0, then a^2/bc + b^2/ca + c^2/ab = 3 Statement-2 (Reason): If a + b + c = 9 and a^2 + b^2 + c^2 = 35, then ab + bc + ca = 23

Leave a Comment / Educational /

Assertion and Reason on a²/bc + b²/ca + c²/ab = 3 Assertion and Reason Question on Algebraic Identities Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. (a) Statement-1 is true, Statement-2 is true; Statement-2

Statement-1 (Assertion): If a, b, c are all non-zero such that a + b + c = 0, then a^2/bc + b^2/ca + c^2/ab = 3 Statement-2 (Reason): If a + b + c = 9 and a^2 + b^2 + c^2 = 35, then ab + bc + ca = 23 Read More »

Statement-1 (Assertion): If a + b + c = 5 and ab + bc + ca = 10, then a^3 + b^3 + c^3 – 3abc Statement-2 (Reason): a^3 + b^3 + c^3 – 3abc = (a + b + c) {(a + b + c)^2 – 3(ab + bc + ca)}

Leave a Comment / Educational /

Assertion and Reason on a³ + b³ + c³ − 3abc Assertion and Reason Question on Algebraic Identities Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. (a) Statement-1 is true, Statement-2 is true; Statement-2

Statement-1 (Assertion): If a + b + c = 5 and ab + bc + ca = 10, then a^3 + b^3 + c^3 – 3abc Statement-2 (Reason): a^3 + b^3 + c^3 – 3abc = (a + b + c) {(a + b + c)^2 – 3(ab + bc + ca)} Read More »

Statement-1 (Assertion): If 3x = a + b + c, then Statement-2 (Reason): (x – a)^3 + (x – b)^3 + (x – c)^3 = 3(x – a)(x – b)(x – c) If a + b + c = 0, then a^3 + b^3 + c^3 = 3abc

Leave a Comment / Educational /

Assertion and Reason on If 3x = a + b + c Then (x − a)³ + (x − b)³ + (x − c)³ = 3(x − a)(x − b)(x − c) Assertion and Reason Question on Algebraic Identities Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices

Statement-1 (Assertion): If 3x = a + b + c, then Statement-2 (Reason): (x – a)^3 + (x – b)^3 + (x – c)^3 = 3(x – a)(x – b)(x – c) If a + b + c = 0, then a^3 + b^3 + c^3 = 3abc Read More »

Statement-1 (Assertion): (a – b)^3 + (b – c)^3 + (c – a)^3 = 3(a – b)(b – c) (c – a) Statement-2 (Reason): If a + b + c = 0, then a^3 + b^3 + c^3 = 3abc

Leave a Comment / Educational /

Assertion and Reason on (a − b)³ + (b − c)³ + (c − a)³ Assertion and Reason Question on Algebraic Identities Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. (a) Statement-1 is true,

Statement-1 (Assertion): (a – b)^3 + (b – c)^3 + (c – a)^3 = 3(a – b)(b – c) (c – a) Statement-2 (Reason): If a + b + c = 0, then a^3 + b^3 + c^3 = 3abc Read More »

Which of the following is a factor of (x + y)^3 – (x^3 + y^3) ?

Leave a Comment / Educational /

Factor of (x + y)³ − (x³ + y³) Factor of (x + y)³ − (x³ + y³) Which of the following is a factor of \[ (x+y)^3-(x^3+y^3)? \] (a) \(x^2+y^2+2xy\) (b) \(x^2+y^2-xy\) (c) \(xy^2\) (d) \(3xy\) Solution \[ (x+y)^3=x^3+y^3+3xy(x+y) \] Therefore, \[ (x+y)^3-(x^3+y^3)=3xy(x+y) \] Hence, \[ \boxed{(d)\ 3xy} \] Next Question / Full Exercise

Which of the following is a factor of (x + y)^3 – (x^3 + y^3) ? Read More »