Three points (p + 1, 1), (2p + 1, 3) and (2p + 2, ;2p) are collin… - Vidyadip

MCQ

Three points $(p + 1,{\rm{ }}1)$, $(2p + 1,{\rm{ }}3$) and $(2p + 2,\;2p)$ are collinear, if $p =$

A
$-1$
B
$1$
✓
$2$
D
$0$

✓

Answer

Correct option: C.

$2$

c
(c) $\left| {\,\begin{array}{*{20}{c}}{p + 1}&1&1\\{2p + 1}&3&1\\{2p + 2}&{2p}&1\end{array}\,} \right| = 0$

$ \Rightarrow \,\,(p + 1)\,(3 - 2p) + 1(2p + 2 - 2p - 1)$

$ + 1\,[(2p)\,(2p + 1) - 3\,(2p + 2)] = 0$

$ \Rightarrow \,\,p = 2$.

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 "MCQ" from rectangular cartensian co-ordinates→rectangular cartensian co-ordinates — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Equation of vertical line to the right of y-axis at 5 units from y-axis is:

Consider all natural number whose decimal expansion has only the even digits $0,2,4,6,8$. Suppose these are arranged in increasing order. If $a _n$ denotes the $n$th number in this sequence, then $\frac{\lim _{n \rightarrow \infty} \log a_n}{\log n}$ equals

A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 soldiers there is one captain. The number of captains in the group is:

The geometric series $a + ar + ar^2 + ar^3 +..... \infty$ has sum $7$ and the terms involving odd powers of $r$ has sum $'3'$, then the value of $(a^2 -r^2)$ is -

The tangents to the parabola $y^2 = 4ax$ makes angle $\theta _1$ and $\theta _2$ with the positive $x-$ axis. Then, the locus of their point of intersection if $cot\, \theta _1 + cot\, \theta _2 = c$ is

Solution of $|\text{x} – 1|\geq|\text{x}-3| $ is:

Let $\left(5, \frac{a}{4}\right)$, be the circumcenter of a triangle with vertices $A(a,-2), B(a, 6)$ and $C\left(\frac{a}{4},-2\right)$. Let $\alpha$ denote the circumradius, $\beta$ denote the area and $\gamma$ denote the perimeter of the triangle. Then $\alpha+\beta+\gamma$ is

If a secretary and a joint secretary are to be selected from acommittee of 11 members, then in how many ways can they be selected:

The value of $x$ in the expression ${[x + {x^{{{\log }_{10}}}}^{(x)}]^5}$, if the third term in the expansion is $10,00,000$

By mathamatical induction $n\left(n^2-1\right)$ is divisible by: