MCQ
$110$ triangles can be formed by joning $10$ points as vertices in which $n$ points are collinear. Then the value of $n$ is
  • $5$
  • B
    $6$
  • C
    $3$
  • D
    $4$

Answer

Correct option: A.
$5$
a
$^{10}C_3 - ^nC_3 = 110$
$n = 5$

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

Similar questions

The minimum value of $z=2 x+4 y$ subject to constraints $x+2 y \geq 10,3 x+y \geq 10, x \geq 0,$ $y \geq 0$ is $....$
$\frac{2^{3}-1^{3}}{1 \times 7}+\frac{4^{3}-3^{3}+2^{3}-1^{3}}{2 \times 11}+$$\frac{6^{3}-5^{3}+4^{3}-3^{3}+2^{3}-1^{3}}{3 \times 15}+\ldots .+$ $\frac{30^{3}-29^{3}+28^{3}-27^{3}+\ldots+2^{3}-1^{3}}{15 \times 63}$is equal to.
If ${{2x + 3} \over {(x + 1)(x - 3)}} = {a \over {x + 1}} + {b \over {(x - 3)}}$, then $a + b$
Let $f: R \rightarrow R$ be a twice differentiable function such that $f( x + y )=f( x ) f( y )$ for all $x , y \in R$. If $f^{\prime}(0)=4 a$ and $f$ staisfies $f^{\prime \prime}( x )-3 a f^{\prime}( x )-f( x )=0$, $a>0$, then the area of the region
$R =\{( x , y ) \mid 0 \leq y \leq f( ax ), 0 \leq x \leq 2\}$ is :
Let $A =$ $ \left[ {\begin{array}{*{20}{c}}1&2&2\\2&1&2\\2&2&1\end{array}}\right]$ , then
If the system of equation $2x + 3y =\, -1; 3x + y = 2; \lambda x + 2y = \mu $ is consistent, then
The length of the chord joining the points in which the straight line $\frac{x}{3} + \frac{y}{4} = 1$ cuts the circle ${x^2} + {y^2} = \frac{{169}}{{25}}$ is 
The co-ordinates of the point from where the tangents are drawn to the circles ${x^2} + {y^2} = 1$, ${x^2} + {y^2} + 8x + 15 = 0$ and ${x^2} + {y^2} + 10y + 24 = 0$ are of same length, are
The ${n^{th}}$ term of an $A.P.$ is $3n - 1$.Choose from the following the sum of its first five terms
The locus of the centre of a circle which cuts orthogonally the circle ${x^2} + {y^2} - 20x + 4 = 0$ and which touches $x = 2$ is