Download App

STD 11 - rectangular cartensian co-ordinates — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - rectangular cartensian co-ordinates1 Mark
MCQ
Let $A=\left(a_1, a_2\right)$ and $B=\left(b_1, b_2\right)$ be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between $A$ and $B$ ?
  • A
    $\sqrt{65}$
  • B
    $\sqrt{7} \overline{4}$
  • ✓
    $\sqrt{8 \overline{3}}$
  • D
    $\sqrt{9} \overline{7}$
✓

Answer

Correct option: C.
$\sqrt{8 \overline{3}}$
c
(c)

Given,

$A=\left( a _1, a_2\right), B=\left(b_1, b_2\right)$, where $a_1, a_2, b_1, b_2$ are integers.

Distance between $A B$

$=\sqrt{\left(b_1-a_1\right)^2+\left(b_2-a_2\right)^2}$

$\therefore A B=\sqrt{\text { sum of squares of two number }}$

$\sqrt{65}=\sqrt{64+1}$, it is possible.

$\sqrt{74}=\overline{\sqrt{49+2}}$, it is also possible.

$\sqrt{97}=\sqrt{81+16}$, it is also possible.

$83$ is not a sum of squares of two number.

Hence, option $(c)$ is correct.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 11 - rectangular cartensian co-ordinates→STD 11 - rectangular cartensian co-ordinates — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The equation of the circle passing through $(2, 0)$ and $(0, 4)$ and having the minimum radius is:
→
In a cinema hall, the charge per person is $₹ 200$. On the first day, only $60 \%$ of the seats were filled. The owner decided to reduce the price by $20 \%$ and there was an increase of $50 \%$ in the number of spectators on the next day. The percentage increase in the revenue on the second day was
→
Equation of directrix for parabola $y^2=12 x$ is :
→
The equation of the circle which intersects circles ${x^2} + {y^2} + x + 2y + 3 = 0$, ${x^2} + {y^2} + 2x + 4y + 5 = 0$and ${x^2} + {y^2} - 7x - 8y - 9 = 0$ at right angle, will be
→
If $0\,<\,x\,<\,1$ and $y=\frac{1}{2} x^{2}+\frac{2}{3} x^{3}+\frac{3}{4} x^{4}+\ldots$, then the value of $\mathrm{e}^{1+y}$ at $\mathrm{x}=\frac{1}{2}$ is:
→
Let $A$ be a set containing $10$ distinct elements. Then the total number of distinct functions from $A$ to $A$, is
→
The number of all possible triplets $(a_1 , a_2 , a_3)$ such that $a_1+ a_2 \,cos \, 2x + a_3 \, sin^2 x = 0$ for all $x$ is
→
If the points $A(3,{\rm{ }}4),\,B(7,{\rm{ }}7),\,C(a,{\rm{ }}b)$ be collinear and $AC = 10$, then $(a,{\rm{ }}b)$=
→
Let $P (3\, sec\,\theta , 2\, tan\,\theta )$ and $Q\, (3\, sec\,\phi , 2\, tan\,\phi )$ where $\theta + \phi \, = \frac{\pi}{2}$ , be two distinct points on the hyperbola $\frac{{{x^2}}}{9} - \frac{{{y^2}}}{4} = 1$ . Then the ordinate of the point of intersection of the normals at $P$ and $Q$ is
→
If ${^\text{n}}\text{C}_{\text{r}}+{^\text{n}}\text{C}_{\text{r+1}}={^\text{n+1}}\text{C}_{\text{x}},$ is then $x:$
→