Mathematics Questions and Answers – Identity

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Identity”.

1. Select the term which is not an identity.
a) (a + b)2 = a2 + b2
b) (a + b)2 = a2 + b2 + 2ab
c) (a – b)2 = a2 + b2 – 2ab
d) (a + 1)(a + 2) = a2 + 3a + 2
View Answer

Answer: a
Explanation: Identities are the special type of equations which are true for every value of the variables (a + 1)2 = a2 + b2 is only true for a = 1, b = 0; a = 0, b = 1.
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2. Find the value of (2a + 1)2 using standard identity.
a) 4a2 + 2 + 2a
b) 4a2 + 2 – 4a
c) 4a2 – 2 + 4a
d) 4a2 + 2 + 4a
View Answer

Answer: d
Explanation: Using the identity (a + b)2 = a2 + b2 + 2ab
⇒ (2a + 1)2 = (2a)2 + (1)2 + 2(2a)(1)
⇒ (2a + 1)2 = 4a2 + 2 + 4a.

3. Find the value of (m + 4n)2 using the standard identity.
a) m2 + 4n2 – 8mn
b) m2 + 16n2 + 4mn
c) m2 + 16n2 + 8mn
d) m2 + 4n2 + 8mn
View Answer

Answer: c
Explanation: We know that (a + b)2 = a2 + b2 + 2ab.
⇒ (m + 4n)2 = (m)2 + (4n)2 + 2(m)(4n)
⇒ (m + 4n)2 = m2 + 16n2 + 8mn.
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4. Calculate the value of (11x – 2y)2.
a) 121x2 + 4y2 – 22xy
b) 121x2 + 4y2 – 44xy
c) 121x2 + 4y2 + 44xy
d) 121x2 + 4y2 + 22xy
View Answer

Answer: b
Explanation: The expression is of the form (a – b)2 where, a = 11x and b = 2y and (a – b)2 = a2 + b2 – 2ab.
⇒ (11x – 2y) = (11x)2 + (2y)2 – 2(11x)(2y)
⇒ (11x – 2y) = 121x2 + 4y2 – 44xy.

5. Evaluate the value of (2q – 3p)2.
a) 4q2 + 9p2 + 12pq
b) 4q2 + 9p2 – 12pq
c) 4q2 + 9p2 + 6pq
d) 4q2 + 9p2 – 6pq
View Answer

Answer: b
Explanation: The expression is of the form (a – b)2 where, a = 2q and b = 3p and (a – b)2 = a2 + b2 – 2ab.
⇒ (2q – 3p)2 = (2q)2 + (3p)2 – 2(2q)(3p)
⇒ (2q – 3p)2 = 4q2 + 9p2 – 12pq.
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6. Using the standard identity, find the value of (3.9)2.
a) 15.11
b) 16.11
c) 15.21
d) 16.21
View Answer

Answer: c
Explanation: 3.9 can be written as (4 – 0.1) and (a – b)2 = a2 + b2 – 2ab.
⇒ (4 – 0.1)2 = (4)2 + (0.1)2 – 2(4)(0.1)
⇒ (4 – 0.1)2 = 16 + 0.01 – 0.8 = 15.21.

7. Find the value of (12.4)2.
a) 152.77
b) 153.66
c) 153.76
d)152.76
View Answer

Answer: c
Explanation: We can use the identity (a + b)2 = a2 + b2 + 2ab.
⇒ (12 + 0.4)2 = (12)2 + (0.4)2 + 2(12)(0.4)
⇒ (12 + 0.4)2 = 144 + 0.16 + 9.6 = 153.76.
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8. Using the standard identity, find the value of (2m + 2)(2m + 3).
a) 4m2 + 10m + 5
b) 4m2 + 10m + 6
c) 4m2 + 10m – 6
d) 4m2 + 10m – 5
View Answer

Answer: b
Explanation: The expression is of the form (x + a)(x + b). Now, (x + a)(x + b) = x2 + (a + b)x + ab.
⇒ (2m + 2)(2m + 3) = (2m)2 + (2 + 3)2m + (2)(3)
⇒ (2m + 2)(2m + 3) = 4m2 + 10m + 6.

9. Evaluate the value (x + 12)(x + 1).
a) x2 + 13x – 13
b) x2 + 13x + 13
c) x2 + 13x – 12
d) x2 + 13x + 12
View Answer

Answer: d
Explanation: The expression is of the form (x + a)(x + b). Now, (x + a)(x + b) = x2 + (a + b)x + ab.
⇒ (x + 12)(x + 1) = x2 + (12 + 1)x + 12(1)
⇒ (x + 12)(x + 1) = x2 + 13x + 12.
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10. Using the standard identity, find the value of 201 × 204.
a) 4104
b) 401004
c) 40104
d) 41004
View Answer

Answer: d
Explanation: 201 and 204 can be written as (200 + 1) and (200 + 4) respectively. (x + a)(x + b) = x2 + (a + b)x + ab
⇒ (200 + 1)(200 + 4) = (200)2 + (1 + 4)200 + (1)(4)
⇒ (200 + 1)(200 + 4) = 40000 + 1000 + 4 = 41004.

11. Calculate the value of 904 × 902.
a) 815408
b) 8105408
c) 810548
d) 81548
View Answer

Answer: a
Explanation: 904 and 902 can be written as (900 + 4) and (900 + 2) respectively. Also, (x + a)(x + b) = x2 + (a + b)x + ab.
⇒ (900 + 4)(900 + 2) = (900)2 + (4 + 2)900 + (2)4
⇒ (900 + 4)(900 + 2) = 810000 + 5400 + 8 = 815408.

12. Find the value of (10001 + 12)(10001 – 12).
a) 1000190857
b) 1000019857
c) 10019857
d) 100019857
View Answer

Answer: d
Explanation: We know that (a + b)(a – b) = a2 – b2.
⇒ (10001)2 – (12)2 = 100020001 – 144
⇒ (10001)2 – (12)2 = 100019857.

13. Find the value of (98)2 – (2)2.
a) 9600
b) 960
c) 96000
d) 900
View Answer

Answer: a
Explanation: a2 – b2 = (a + b)(a – b)
⇒ (98)2 – (2)2 = (98 + 2)(98 – 2)
⇒ (98)2 – (2)2 = 100(96) = 9600.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter