| Statement 1: The value of the product \[(4{{a}^{2}}+3b)(4{{a}^{2}}+3b)\] at \[a=1\] and \[b=2\] is 100. |
| Statement II: Value of \[\frac{{{(997+496)}^{2}}-{{(997-496)}^{2}}}{997\times 496}\] is 2. |
A) Both Statement - I and Statement - II are true.
B) Statement - I is true but Statement - II is false
C) Statement - I is false but Statement- II is true
D) Both Statement - I and Statement - II are false.
Correct Answer: B
Solution :
Statement I: \[(4{{a}^{2}}+3b)(4{{a}^{2}}+3b)\] \[={{(4{{a}^{3}}+3b)}^{2}}\] \[=16{{a}^{4}}+9{{b}^{2}}+24{{a}^{2}}b\] When \[a=1,b=2\] \[=16{{(1)}^{4}}+9{{(2)}^{2}}+24\times {{(1)}^{2}}\times 2\] \[=16+36+48=100\] Statement II: \[\frac{{{(997+496)}^{2}}-{{(997-496)}^{2}}}{997\times 496}\] \[{{(997)}^{2}}+{{(496)}^{2}}+2\times 997\times 496\] \[=\frac{-{{(997)}^{2}}-{{(496)}^{2}}+2\times 997\times 496}{997\times 496}\] \[=\frac{4\times 997\times 496}{997\times 496}=4\]
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