| 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] \[\Delta ABC\] is an isosceles, right triangle, right angled at C. Then, \[A{{B}^{2}}=2A{{C}^{2}}\]. |
| Reason [R] In a right angled triangle, the cube of the hypotenuse is equal to the sum of the squares of the other two sides. |
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 :
| In right angled \[\Delta ABC\], |
| \[A{{B}^{2}}=\text{ }A{{C}^{2}}+B{{C}^{2}}\] |
| [by Pythagoras theorem] |
| \[=A{{C}^{2}}+A{{C}^{2}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ \because \,\,BC=AC \right]\] |
| \[=2A{{C}^{2}}\] |
| \[\therefore A{{B}^{2}}=2A{{C}^{2}}\] |
| Hence, Statement I is true and Statement II is false. |
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