| Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. |
| Assertion [A] The factor of |
| \[\frac{3}{2}{{x}^{2}}-8x-\frac{35}{2}\] is \[\frac{1}{2}\left( x-7 \right)\left( 3x+5 \right)\] |
| Reason [R] The factors are calculated by dividing the coefficients by 2 and expression is obtained by splitting the middle term |
A) A is true, R is true; R is a correct explanation for A.
B) A is true, R is true; R is not a correct explanation for A.
C) A is true; R is False.
D) A is false; R is true.
Correct Answer: C
Solution :
| The expression is calculated by splitting the middle term |
| Let be \[f\left( x \right)=\frac{3}{2}{{x}^{2}}-8x-\frac{35}{2}\] |
| \[=\frac{1}{2}\left[ 3{{x}^{2}}-16x-35 \right]\] |
| \[=\frac{1}{2}\left( 3{{x}^{2}}-21x+5x-35 \right)\] |
| \[=\frac{1}{2}\left[ 3x\left( x-7 \right)+5\left( x-7 \right) \right]\] |
| \[=\frac{1}{2}\left[ \left( 3x+5 \right)\left( x-7 \right) \right]\] |
| Assertion is true but Reason is false. |
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