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JIPMAT 2021 (QA) PYQs

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JIPMAT 2021

Algebra
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Identities

Conceptual

The value of (25.7322−15.7322)(25.732^{2} - 15.732^{2}) is

✅ Correct Option: 3
Using a2−b2=(a+b)(a−b)a^2 - b^2 = (a+b)(a-b):
=(25.732+15.732)(25.732−15.732)= (25.732 + 15.732)(25.732 - 15.732) \newline =41.464×10= 41.464 × 10 \newline =414.64= 414.64
Therefore, 25.7322−15.7322=414.6425.732^2 - 15.732^2 = 414.64

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Which of the following is the value of mm for which the polynomial x4+10x3+25x2+15x+mx^4 + 10x^3 + 25x^2 + 15x + m is exactly divisible by x+7x+7?

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(4.53−3.07)2(3.07−2.15)(2.15−4.53)+(3.07−2.15)2(2.15−4.53)(4.53−3.07)+(2.15−4.53)2(4.53−3.07)(3.07−2.15)\frac{(4.53-3.07)^2}{(3.07-2.15)(2.15-4.53)} + \frac{(3.07-2.15)^2}{(2.15-4.53)(4.53-3.07)} + \frac{(2.15-4.53)^2}{(4.53-3.07)(3.07-2.15)} is simplified to

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