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 $S=\left\{\sin ^2 2 \theta:\left(\sin ^4 \theta+\cos ^4 \theta\right) x^2+(\sin 2 \theta) x+\right.$ $\left(\sin ^6 \theta+\cos ^6 \theta\right)=0$ has real roots $\}$. If $\alpha$ and $\beta$ be the smallest and largest elements of the set $S$, respectively, then $3\left((\alpha-2)^2+(\beta-1)^2\right)$ equals....................
Let $S=\left\{\sin ^2 2 \theta:\left(\sin ^4 \theta+\cos ^4 \theta\right) x^2+(\sin 2 \theta) x+\right.$ $\left(\sin ^6 \theta+\cos ^6 \theta\right)=0$ has real roots $\}$. If $\alpha$ and $\beta$ be the smallest and largest elements of the set $S$, respectively, then $3\left((\alpha-2)^2+(\beta-1)^2\right)$ equals....................
- [JEE MAIN 2024]
The number of distinct real roots of $x^4-4 x^3+12 x^2+x-1=0$ is
The number of distinct real roots of $x^4-4 x^3+12 x^2+x-1=0$ is
- [IIT 2011]
The number of real solutions of the equation $|x{|^2}$-$3|x| + 2 = 0$ are
The number of real solutions of the equation $|x{|^2}$-$3|x| + 2 = 0$ are
- [IIT 1989]
In the real number system, the equation $\sqrt{x+3-4 \sqrt{x-1}}+\sqrt{x+8-6 \sqrt{x-1}}=1$ has
In the real number system, the equation $\sqrt{x+3-4 \sqrt{x-1}}+\sqrt{x+8-6 \sqrt{x-1}}=1$ has
- [KVPY 2012]
If $a < 0$ then the inequality $a{x^2} - 2x + 4 > 0$ has the solution represented by
If $a < 0$ then the inequality $a{x^2} - 2x + 4 > 0$ has the solution represented by