Cubic Identity MCQ Quiz - Objective Question with Answer for Cubic Identity - Download Free PDF
Last updated on Jun 12, 2025
Latest Cubic Identity MCQ Objective Questions
Cubic Identity Question 1:
Find the value of \(\rm \frac{1.2\times 1.2\times 1.2-0.2\times 0.2\times 0.2}{1.2\times 1.2+1.2\times 0.2+0.2\times 0.2}\)
Answer (Detailed Solution Below)
Cubic Identity Question 1 Detailed Solution
Given:
Find the value of \(\rm \frac{1.2\times 1.2\times 1.2-0.2\times 0.2\times 0.2}{1.2\times 1.2+1.2\times 0.2+0.2\times 0.2}\)
Formula used:
(a3 - b3) / (a2 + ab + b2) = a - b
Where, a = 1.2 and b = 0.2
Calculations:
(1.2 × 1.2 × 1.2 - 0.2 × 0.2 × 0.2) / (1.2 × 1.2 + 1.2 × 0.2 + 0.2 × 0.2)
⇒ (1.23 - 0.23) / (1.22 + 1.2 × 0.2 + 0.22)
⇒ (1.2 - 0.2)
⇒ 1
∴ The correct answer is option 2.
Cubic Identity Question 2:
Simplify.
\(\frac{(232)^3+(140)^3+(353)^3-3\times232\times140\times353}{(232)^2+(140)^2+(353)^2-232\times140-140\times353-353\times232}\)
Answer (Detailed Solution Below)
Cubic Identity Question 2 Detailed Solution
Given:
\(\frac{(232)^3+(140)^3+(353)^3-3\times232\times140\times353}{(232)^2+(140)^2+(353)^2-232\times140-140\times353-353\times232}\)
Formula used:
a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
Calculation:
\(\frac{(232)^3+(140)^3+(353)^3-3\times232\times140\times353}{(232)^2+(140)^2+(353)^2-232\times140-140\times353-353\times232}\)
Using the formula:
a = 232, b = 140, c = 353
Numerator: (232)3 + (140)3 + (353)3 - 3×232×140×353
Denominator: (232)2 + (140)2 + (353)2 - 232×140 - 140×353 - 353×232
Using the formula, we get:
Numerator: (232 + 140 + 353)( (232)2 + (140)2 + (353)2 - 232×140 - 140×353 - 353×232)
⇒ (232 + 140 + 353) = 725
∴ The correct answer is option (2).
Cubic Identity Question 3:
Simplify:
\(\frac{(7.3)^3 - (4.7)^3}{(7.3)^2 + 7.3 \times 4.7 + (4.7)^2}\)
Answer (Detailed Solution Below)
Cubic Identity Question 3 Detailed Solution
Given:
We are asked to simplify the expression:
\( \frac{(7.3)^3 - (4.7)^3}{(7.3)^2 + 7.3 \times 4.7 + (4.7)^2} \)
Formula used:
\( a^3 - b^3 = (a - b)(a^2 + ab + b^2) \)
Calculations:
Multiply the numerator and denominator by (7.3 - 4.7)
The expression will become:
\( \frac{(7.3)^3 - (4.7)^3}{(7.3)^2 + 7.3 \times 4.7 + (4.7)^2} \) × \(\frac{(7.3 - 4.7)}{(7.3 - 4.7)}\)
The denominator will become, \({(7.3)^3 - (4.7)^3}\)
Hence,
\( \frac{(7.3)^3 - (4.7)^3}{(7.3)^3 - (4.7)^3} \) × (7.3 - 4.7)
⇒(7.3 - 4.7)
⇒2.6
Option 3 is the correct answer.
Cubic Identity Question 4:
If \(\frac{3(16^3 - 6^3)}{16^2 + 6^2 + Q} = 30\), then find the value of Q.
Answer (Detailed Solution Below)
Cubic Identity Question 4 Detailed Solution
Formula used:
BODMAS
Calculation:
According to question,
⇒ \(\frac{3(16^3 - 6^3)}{16^2 + 6^2 + Q} = 30\)
⇒ \(\frac{3(4096 - 216)}{256 + 36 + Q} = 30\)
⇒ \(\frac{3(3880)}{292 + Q} = 30\)
\((11,640)= 30 (292 + Q)\)
⇒ 11,640 = 8,760 + 30Q
⇒11,640 - 8,760 = 30Q
⇒ 2,880 = 30Q
⇒ Q = 2,880/ 30 = 96
∴ The value of Q is 96.
Cubic Identity Question 5:
Simplify.
\(\frac{(232)^3+(140)^3+(353)^3-3\times232\times140\times353}{(232)^2+(140)^2+(353)^2-232\times140-140\times353-353\times232}\)
Answer (Detailed Solution Below)
Cubic Identity Question 5 Detailed Solution
Given:
\(\frac{(232)^3+(140)^3+(353)^3-3\times232\times140\times353}{(232)^2+(140)^2+(353)^2-232\times140-140\times353-353\times232}\)
Formula used:
a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
Calculation:
\(\frac{(232)^3+(140)^3+(353)^3-3\times232\times140\times353}{(232)^2+(140)^2+(353)^2-232\times140-140\times353-353\times232}\)
Using the formula:
a = 232, b = 140, c = 353
Numerator: (232)3 + (140)3 + (353)3 - 3×232×140×353
Denominator: (232)2 + (140)2 + (353)2 - 232×140 - 140×353 - 353×232
Using the formula, we get:
Numerator: (232 + 140 + 353)( (232)2 + (140)2 + (353)2 - 232×140 - 140×353 - 353×232)
⇒ (232 + 140 + 353) = 725
∴ The correct answer is option (2).
Top Cubic Identity MCQ Objective Questions
Simplify the following. 253 - 753 + 503
Answer (Detailed Solution Below)
Cubic Identity Question 6 Detailed Solution
Download Solution PDFGiven:
The number 253 - 753 + 503.
Calculation:
253 - 753 + 503
⇒ 15625 - 421875 + 125000
⇒ - 281250
∴ The required answer is - 281250.
Alternate MethodWe know that,
If a + b + c = 0, then a3 + b3 + c3 = 3abc
a = 25, b = -75 and c = 50
a + b + c = 25 -75 +50 = 0
253 - 753 + 503 = 3 × 25 × -75 × 50 = -281250
If x + y = 25 and xy = 20, then find the value of x3 + y3.
Answer (Detailed Solution Below)
Cubic Identity Question 7 Detailed Solution
Download Solution PDFx + y = 25 and xy = 20
Formula used:-
(x + y)3 = x3 + y3 + 3xy(x + y)
Calculation:-
⇒ 253 = x3 + y3 + 3 × 20×25
⇒ 15625 = x3 + y3 + 1500
⇒ x3 + y3 = 15625 − 1500 = 14125
∴ The required answer is 14125.
If b = 5, determine the value of an expression \(({5 \over b} + 5b)\) \(({25 \over b^2} - 25 + 25b^2)\) using an identity.
Answer (Detailed Solution Below)
Cubic Identity Question 8 Detailed Solution
Download Solution PDFb = 5
Formula used:-
A3 + B3 =(A + B) (A2 + B2 - AB)
Calculation:-
(5/b + 5b)(25/b2 - 25 +25b2)
⇒ (5/b)3 + (5b)3
Put the value of "b" in the above equation
⇒ (5/5)3 + (5 × 5)3
⇒ 1 + (25)3
⇒ 1 + 15625 = 15626
∴ The required answer is 15626.
Simplify the following.
\(\frac{762\times762\times762+316\times316\times316}{762\times762-762\times316+316\times316}\)
Answer (Detailed Solution Below)
Cubic Identity Question 9 Detailed Solution
Download Solution PDFGiven:
\(\frac{762\times762\times762+316\times316\times316}{762\times762-762\times316+316\times316}\)
Concept used:
a3 + b3 = (a + b)(a2 + b2 - ab)
Calculation:
\(\frac{762\times762\times762+316\times316\times316}{762\times762-762\times316+316\times316}\)
⇒ \(\frac{762^3+316^3}{762^2-762\times316+316^2}\)
⇒ \(\frac{(762+316)(762^2-762\times316+316^2)}{762^2-762\times316+316^2}\)
⇒ 762 + 316
⇒ 1078
∴ The required answer is 1078.
The value of \(\frac{1.6\times1.6\times1.6-0.6\times0.6\times0.6}{1.6\times1.6+1.6\times0.6+0.6\times0.6}\) is:
Answer (Detailed Solution Below)
Cubic Identity Question 10 Detailed Solution
Download Solution PDFGiven:
\(\frac{1.6\times1.6\times1.6-0.6\times0.6\times0.6}{1.6\times1.6+1.6\times0.6+0.6\times0.6}\)
Concept used:
a3 - b3 = (a - b)(a2 + b2 + ab)
Calculation:
\(\frac{1.6\times1.6\times1.6-0.6\times0.6\times0.6}{1.6\times1.6+1.6\times0.6+0.6\times0.6}\)
⇒ \(\frac{1.6^3-0.6^3}{1.6^2+1.6\times0.6+0.6^2}\)
⇒ \(\frac{(1.6-0.6)(1.6^2+1.6\times0.6+0.6^2)}{1.6^2+1.6\times0.6+0.6^2}\)
⇒ 1.6 - 0.6
⇒ 1
∴ The required answer is 1.
Find the value of the following expression.
123 + (-8)3 + (-4)3
Answer (Detailed Solution Below)
Cubic Identity Question 11 Detailed Solution
Download Solution PDFCalculation:
123 + (-8)3 + (-4)3
⇒ 1728 - 512 - 64
⇒ 1152
∴ The simplified value is 1152.
Cubic Identity Question 12:
Simplify the following. 253 - 753 + 503
Answer (Detailed Solution Below)
Cubic Identity Question 12 Detailed Solution
Given:
The number 253 - 753 + 503.
Calculation:
253 - 753 + 503
⇒ 15625 - 421875 + 125000
⇒ - 281250
∴ The required answer is - 281250.
Alternate MethodWe know that,
If a + b + c = 0, then a3 + b3 + c3 = 3abc
a = 25, b = -75 and c = 50
a + b + c = 25 -75 +50 = 0
253 - 753 + 503 = 3 × 25 × -75 × 50 = -281250
Cubic Identity Question 13:
If x + y = 25 and xy = 20, then find the value of x3 + y3.
Answer (Detailed Solution Below)
Cubic Identity Question 13 Detailed Solution
x + y = 25 and xy = 20
Formula used:-
(x + y)3 = x3 + y3 + 3xy(x + y)
Calculation:-
⇒ 253 = x3 + y3 + 3 × 20×25
⇒ 15625 = x3 + y3 + 1500
⇒ x3 + y3 = 15625 − 1500 = 14125
∴ The required answer is 14125.
Cubic Identity Question 14:
If b = 5, determine the value of an expression \(({5 \over b} + 5b)\) \(({25 \over b^2} - 25 + 25b^2)\) using an identity.
Answer (Detailed Solution Below)
Cubic Identity Question 14 Detailed Solution
b = 5
Formula used:-
A3 + B3 =(A + B) (A2 + B2 - AB)
Calculation:-
(5/b + 5b)(25/b2 - 25 +25b2)
⇒ (5/b)3 + (5b)3
Put the value of "b" in the above equation
⇒ (5/5)3 + (5 × 5)3
⇒ 1 + (25)3
⇒ 1 + 15625 = 15626
∴ The required answer is 15626.
Cubic Identity Question 15:
Simplify the following.
\(\frac{762\times762\times762+316\times316\times316}{762\times762-762\times316+316\times316}\)
Answer (Detailed Solution Below)
Cubic Identity Question 15 Detailed Solution
Given:
\(\frac{762\times762\times762+316\times316\times316}{762\times762-762\times316+316\times316}\)
Concept used:
a3 + b3 = (a + b)(a2 + b2 - ab)
Calculation:
\(\frac{762\times762\times762+316\times316\times316}{762\times762-762\times316+316\times316}\)
⇒ \(\frac{762^3+316^3}{762^2-762\times316+316^2}\)
⇒ \(\frac{(762+316)(762^2-762\times316+316^2)}{762^2-762\times316+316^2}\)
⇒ 762 + 316
⇒ 1078
∴ The required answer is 1078.