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 […]

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

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

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

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

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,

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

If x/y + y/x = −1, Find the Value of x³ − y³ If x/y + y/x = −1, Find the Value of x³ − y³ If \[ \frac{x}{y}+\frac{y}{x}=-1 \quad (x,y\ne0), \] then the value of \[ x^3-y^3 \] is (a) \(1\) (b) \(-1\) (c) \(0\) (d) \(\frac{1}{2}\) Solution \[ \frac{x}{y}+\frac{y}{x}=-1 \] Multiplying by \(xy\):

If x³ − 3x² + 3x + 7 = (x + 1)(ax² + bx + c), Find a + b + c If x³ − 3x² + 3x + 7 = (x + 1)(ax² + bx + c), Find a + b + c If \[ x^3-3x^2+3x+7=(x+1)(ax^2+bx+c), \] then \[ a+b+c= \] (a) \(4\) (b)

If (x + y)³ − (x − y)³ − 6y(x² − y²) = ky³, Find k If (x + y)³ − (x − y)³ − 6y(x² − y²) = ky³, Find k If \[ (x+y)^3-(x-y)^3-6y(x^2-y^2)=ky^3, \] then \[ k= \] (a) \(1\) (b) \(2\) (c) \(4\) (d) \(8\) Solution \[ (x+y)^3=x^3+3x^2y+3xy^2+y^3 \] \[ (x-y)^3=x^3-3x^2y+3xy^2-y^3 \]