Consider a rectangle ABCD having 5,7,6,9 points in the interior o… - Vidyadip

MCQ

Consider a rectangle $ABCD$ having $5,7,6,9$ points in the interior of the line segments $AB,CD , BC , DA$ respectively. Let $\alpha$ be the number of triangles having these points from different sides as vertices and $\beta$ be the number of quadrilaterals having these points from different sides as vertices. Then $(\beta-\alpha)$ is equal to :

A
$795$
B
$1173$
C
$1890$
✓
$717$

✓

Answer

Correct option: D.

$717$

d
$\alpha=$ Number of triangles

$\alpha=5 \cdot 6 \cdot 7+5 \cdot 7 \cdot 9+5 \cdot 6 \cdot 9+6 \cdot 7 \cdot 9$

$\quad=210+315+270+378$

$\quad=1173$

$\beta=$ Number of Quadrilateral

$\beta=5 \cdot 6 \cdot 7 \cdot 9=1890$

$\beta-\alpha=1890-1173=717$

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 - 6. permutation and combination→STD 11 - 6. permutation and combination — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

$\sec^2\text{x}=\frac{4\text{xy}}{(\text{x}+\text{y})^2}$ is true if and only if

If $\alpha=\lim _{x \rightarrow 0^{+}}\left(\frac{e^{\sqrt{\tan x}}-e^{\sqrt{x}}}{\sqrt{\tan x}-\sqrt{x}}\right)$ and $\beta=\lim _{x \rightarrow 0}(1+\sin x)^{\frac{1}{2} \cot x}$ are the roots of the quadratic equation $a x^2+b x-\sqrt{e}=0$, then 12 $\log _e(a+b)$ is equal to.............

The middle term in the expansion of$\Big(1+\frac{1}{\text{x}^{2}}\Big)\big(1+\text{x}^{2}\big)^{\text{n}}$ is:

The coefficient of ${x^7}$ in the expansion of ${\left( {\frac{{{x^2}}}{2} - \frac{2}{x}} \right)^8}$ is

Point at lines $3 y+x-10=0$ and $2 x-5 y+13=0$ is:

The standard deviation of some temperature data in $^\circ C$ is $5.$ If the data were converted into $^\circ F,$ the variance would be:

What is the value of the limit $ \text{f(x)} = \text{x}2+\sqrt{2\text{x}}\sqrt{\text{x}2}−4\text{x}$ if $x$ approaches infinity?

The focal distance of a point on the parabola ${y^2} = 16x$ whose ordinate is twice the abscissa, is

The number of rectangles that you can find on a chess board is:

Circles are drawn on chords of the rectangular hyperbola $ xy = c^2$ parallel to the line $ y = x $ as diameters. All such circles pass through two fixed points whose co-ordinates are :