| DIRECTION: Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct answer (Only one option is correct) from the following - |
| Statement-1: Degree of the differential equation \[y=x\times \frac{dy}{dx}+\sqrt{1+{{\left( \frac{dt}{dx} \right)}^{2}}}\]is 2. |
| Statement-2: In the given equation the power of highest order derivative when expressed as a polynomials in derivatives is 2. |
A) Statement-1 is false, Statement-2 is true.
B) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
C) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
D) Statement-1 is true, Statement-2 is false.
Correct Answer: B
Solution :
\[y=x\frac{dy}{dx}=\sqrt{1+{{\left( \frac{dy}{dx} \right)}^{2}}}\] becomes \[({{x}^{2}}-1){{\left( \frac{dy}{dx} \right)}^{2}}-2xy\frac{dy}{dx}+({{y}^{2}}-1)=0,\]when expressed as a polynomial in derivatives.
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