Consider the following two statements
$I$. Any pair of consistent liner equations in two variables must have a unique solution.
$II$. There do not exist two consecutive integers, the sum of whose squares is $365$.Then,
Consider the following two statements
$I$. Any pair of consistent liner equations in two variables must have a unique solution.
$II$. There do not exist two consecutive integers, the sum of whose squares is $365$.Then,
- [KVPY 2018]
- A
both $I$ and $II$ are true
- B
both $I$ and $II$ are false
- C
$I$ is true and $II$ is false
- D
$I$ is false and $II$ is true
Similar Questions
Let $\alpha, \beta$ be two roots of the equation $x^{2}+(20)^{\frac{1}{4}} x+(5)^{\frac{1}{2}}=0$. Then $\alpha^{8}+\beta^{8}$ is equal to:
Let $\alpha, \beta$ be two roots of the equation $x^{2}+(20)^{\frac{1}{4}} x+(5)^{\frac{1}{2}}=0$. Then $\alpha^{8}+\beta^{8}$ is equal to:
- [JEE MAIN 2021]
The integer $'k'$, for which the inequality $x^{2}-2(3 k-1) x+8 k^{2}-7>0$ is valid for every $x$ in $R ,$ is
The integer $'k'$, for which the inequality $x^{2}-2(3 k-1) x+8 k^{2}-7>0$ is valid for every $x$ in $R ,$ is
- [JEE MAIN 2021]
Let $\alpha$ and $\beta$ be the two disinct roots of the equation $x^3 + 3x^2 -1 = 0.$ The equation which has $(\alpha \beta )$ as its root is equal to
Let $\alpha$ and $\beta$ be the two disinct roots of the equation $x^3 + 3x^2 -1 = 0.$ The equation which has $(\alpha \beta )$ as its root is equal to
Let $A=\left\{x \in(0, \pi)-\left\{\frac{\pi}{2}\right\}: \log _{(2 / \pi)}|\sin x|+\log _{(2 / \pi)}|\cos x|=2\right\}$ and $B=\{x \geq 0: \sqrt{x}(\sqrt{x}-4)-3|\sqrt{x}-2|+6=0\}$. Then $n(A \cup B)$ is equal to:
- [JEE MAIN 2025]
If $x$ is real, then the maximum and minimum values of expression $\frac{{{x^2} + 14x + 9}}{{{x^2} + 2x + 3}}$ will be
If $x$ is real, then the maximum and minimum values of expression $\frac{{{x^2} + 14x + 9}}{{{x^2} + 2x + 3}}$ will be