Square Identity MCQ Quiz - Objective Question with Answer for Square Identity - Download Free PDF
Last updated on Jun 5, 2025
Latest Square Identity MCQ Objective Questions
Square Identity Question 1:
The value of [(.253*.253-.253*.067+.067*.067)/(.253*.253*.253+.067*.067*.067)] is:
Answer (Detailed Solution Below)
Square Identity Question 1 Detailed Solution
Given:
Formula used:
Calculation:
Let a = 0.253 and b = 0.067
⇒
⇒
⇒
∴ The value of the given expression is 3.125.
Square Identity Question 2:
If a + b = 12 and 4ab = 140, then what is the value of a2 + b2?
Answer (Detailed Solution Below)
Square Identity Question 2 Detailed Solution
Given:
If a + b = 12 and 4ab = 140
Formula used:
(a + b)2 = a2 + b2 + 2ab
Calculation:
(a + b)2 = 122
⇒ 144 = a2 + b2 + 2ab
Since, 4ab = 140
⇒ ab = 35
⇒ 144 = a2 + b2 + 2 × 35
⇒ 144 = a2 + b2 + 70
⇒ a2 + b2 = 74
∴ The correct answer is option 2.
Square Identity Question 3:
Simplify (5z - 7y)2 + (7z + 5y)2 - 49z2
Answer (Detailed Solution Below)
Square Identity Question 3 Detailed Solution
Given:
Simplify (5z - 7y)2 + (7z + 5y)2 - 49z2
Formula used:
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
Calculation:
(5z - 7y)2 + (7z + 5y)2 - 49z2
⇒ (25z2 - 2 × 5z × 7y + 49y2) + (49z2 + 2 × 7z × 5y + 25y2) - 49z2
⇒ 25z2 - 70zy + 49y2 + 49z2 + 70zy + 25y2 - 49z2
⇒ 25z2 + 49z2 - 49z2 + 49y2 + 25y2
⇒ 25z2 + 74y2
∴ The correct answer is option (4).
Square Identity Question 4:
If x = 4 + √6 and y = 4 - √6 then the value of x2 + y2 is:
Answer (Detailed Solution Below)
Square Identity Question 4 Detailed Solution
Given:
If x = 4 + √6 and y = 4 - √6
Formula used:
x2 + y2 = (x + y)2 - 2xy
Calculation:
x = 4 + √6 and y = 4 - √6
x + y = (4 + √6) + (4 - √6) = 8
x × y = (4 + √6)(4 - √6) = 42 - (√6)2 = 16 - 6 = 10
⇒ x2 + y2 = (8)2 - 2 × 10
⇒ x2 + y2 = 64 - 20
⇒ x2 + y2 = 44
∴ The correct answer is option (3).
Square Identity Question 5:
Simplify
Answer (Detailed Solution Below)
Square Identity Question 5 Detailed Solution
Given:
Formula used:
Calculation:
⇒
⇒
⇒
⇒ 3.92
⇒
∴ The correct answer is option (2).
Top Square Identity MCQ Objective Questions
Simplify:
Answer (Detailed Solution Below)
Square Identity Question 6 Detailed Solution
Download Solution PDFCalculations:
√(36x² - 108x + 81)
=√[(6x)² - 2 × 6 × 9x + (9)²]
= √[6x - 9]²
= 6x - 9
Hence, The Required value is 6x - 9.
If a + b = 5 and ab = 6, then find 3(a2 + b2).
Answer (Detailed Solution Below)
Square Identity Question 7 Detailed Solution
Download Solution PDFGiven:
a + b = 5 and ab = 6
Concept used:
a2 + b2 = (a + b)2 - 2ab
Calculation:
3(a2 + b2)
⇒ 3{(a + b)2 - 2ab}
⇒ 3{52 - 2 × 6}
⇒ 39
∴ The required value is 39.
The value of [(.253*.253-.253*.067+.067*.067)/(.253*.253*.253+.067*.067*.067)] is:
Answer (Detailed Solution Below)
Square Identity Question 8 Detailed Solution
Download Solution PDFGiven:
Formula used:
Calculation:
Let a = 0.253 and b = 0.067
⇒
⇒
⇒
∴ The value of the given expression is 3.125.
If a + b = 12 and 4ab = 140, then what is the value of a2 + b2?
Answer (Detailed Solution Below)
Square Identity Question 9 Detailed Solution
Download Solution PDFGiven:
If a + b = 12 and 4ab = 140
Formula used:
(a + b)2 = a2 + b2 + 2ab
Calculation:
(a + b)2 = 122
⇒ 144 = a2 + b2 + 2ab
Since, 4ab = 140
⇒ ab = 35
⇒ 144 = a2 + b2 + 2 × 35
⇒ 144 = a2 + b2 + 70
⇒ a2 + b2 = 74
∴ The correct answer is option 2.
Square Identity Question 10:
Which of the following can be the value of k, if
Answer (Detailed Solution Below)
Square Identity Question 10 Detailed Solution
Given:
(88 ÷ 8 × k - 3 × 3) / (62 - 7 × 5 + k2) = 1
Formula used:
Equation: Numerator = Denominator
Calculations:
Numerator: 88 ÷ 8 × k - 3 × 3
⇒ 11k - 9
Denominator: 62 - 7 × 5 + k2
⇒ 36 - 35 + k2
⇒ 1 + k2
Setting the equation:
11k - 9 = 1 + k2
⇒ k2 - 11k + 10 = 0
Using the quadratic formula:
k = (-b ± √(b2 - 4ac)) / (2a)
Where a = 1, b = -11, c = 10
⇒ k = (11 ± √((-11)2 - 4 × 1 × 10)) / (2 × 1)
⇒ k = (11 ± √(121 - 40)) / 2
⇒ k = (11 ± √81) / 2
⇒ k = (11 ± 9) / 2
Values of k:
⇒ k = (20 / 2) = 10
⇒ k = (2 / 2) = 1
∴ The possible values of k are 10 and 1.
Square Identity Question 11:
Simplify:
Answer (Detailed Solution Below)
Square Identity Question 11 Detailed Solution
Calculations:
√(36x² - 108x + 81)
=√[(6x)² - 2 × 6 × 9x + (9)²]
= √[6x - 9]²
= 6x - 9
Hence, The Required value is 6x - 9.
Square Identity Question 12:
If a + b = 5 and ab = 6, then find 3(a2 + b2).
Answer (Detailed Solution Below)
Square Identity Question 12 Detailed Solution
Given:
a + b = 5 and ab = 6
Concept used:
a2 + b2 = (a + b)2 - 2ab
Calculation:
3(a2 + b2)
⇒ 3{(a + b)2 - 2ab}
⇒ 3{52 - 2 × 6}
⇒ 39
∴ The required value is 39.
Square Identity Question 13:
Simplify
Answer (Detailed Solution Below)
Square Identity Question 13 Detailed Solution
Given:
Expression =
Formula used:
The given expression can be simplified by using the identity for the sum of squares and products:
Here, a = 1.5, b = 2.5, and c = 3.5.
Calculations:
⇒
⇒
Using formula,
⇒
⇒
(a + b + c) = 1.5 + 2.5 + 3.5 = 7.5
The value of the given expression is 7.5.
Square Identity Question 14:
If a2 + b2 = 148 and ab = 54 , then find the value of
Answer (Detailed Solution Below)
Square Identity Question 14 Detailed Solution
Given:
a2 + b2 = 148
ab = 54
Formula used:
(a + b)2 = a2 + b2 + 2ab
(a - b)2 = a2 + b2 - 2ab
Calculations:
(a + b)2 = 148 + 2 × 54
⇒ (a + b)2 = 148 + 108 = 256
(a - b)2 = 148 - 2 × 54
⇒ (a - b)2 = 148 - 108 = 40
⇒
⇒
Verification of options:
Option 1:
Option 2:
Option 3:
Option 4:
∴ The correct answer is option (1).
Square Identity Question 15:
If x = 4 + √6 and y = 4 - √6 then the value of x2 + y2 is:
Answer (Detailed Solution Below)
Square Identity Question 15 Detailed Solution
Given:
If x = 4 + √6 and y = 4 - √6
Formula used:
x2 + y2 = (x + y)2 - 2xy
Calculation:
x = 4 + √6 and y = 4 - √6
x + y = (4 + √6) + (4 - √6) = 8
x × y = (4 + √6)(4 - √6) = 42 - (√6)2 = 16 - 6 = 10
⇒ x2 + y2 = (8)2 - 2 × 10
⇒ x2 + y2 = 64 - 20
⇒ x2 + y2 = 44
∴ The correct answer is option (3).