Triangle inequality - class-VIII
| Description: triangle inequality | |
| Number of Questions: 50 | |
| Created by: Jayanti Mahajan | |
| Tags: construction of parallel lines and triangles inequalities triangle and its properties complex numbers maths geometry congruency of triangles triangles verification of the relation between the angles and sides of a triangle |
The points $\left( 0,\dfrac { 8 }{ 3 } \right),(1,3)$ and $(82,30)$ are the vertices of:
In $\Box PQRS$, $PQ+QR+RS+SP> PR+QS$.
If $\left| z+4 \right| \le 3$, then the maximum value of $\left| z+4 \right| $ is
The triangle inequality theorem states that
State the following statement is True or False
It is possible to have a triangle of sides $3,4,8$
State the following statement is True or False
The triangle inequality theorem states that the sum of the lengths of the $2$ sides of a triangle is equal than the third side of the triangle
State whether the following statement is True or False.
It is possible to have a triangle of sides $8,10,14$.
A triangle cannot be drawn with the following three sides:
The complex number z having least positive argument which satisfies the condition $|z - 25i| \le 15$ is:
If $|z^2-3|=3|z|$, then the maximum value of |z| is
If $z$ is a complex number satisfying the equation $\left| z+i \right| +\left| z-i \right| =8$, on the complex plane then maximum value of $\left| z \right| $ is
$\begin{array} { l } { \text { If } z _ { 1 } \text { and } z _ { 2 } \text { are complex numbers, then } \left| z _ { 1 } + z _ { 2 } \right| ^ { 2 } = \left| z _ { 1 } \right| ^ { 2 } + \left| z _ { 2 } \right| ^ { 2 } \text { if and only if } z _ { 1 } \overline { z } _ { 2 } \text { is } } \ { \text { purely imaginary. } } \end{array}$
If $|z| < \sqrt 2-1$, then $|z^2+2z cos\alpha|$ is
If $P$ and $Q$ are represented by complex numbers $z _{1}$ and $z _{2}$ such that $\left| \dfrac { 1 }{ { z } _{ 1 } } +\dfrac { 1 }{ { z } _{ 2 } } \right| =\left| \dfrac { 1 }{ { z } _{ 1 } } -\dfrac { 1 }{ { z } _{ 2 } } \right| $ then the circumference of $\triangleOPQ(O is origin)$ is
The sum of all sides of a quadrilateral is lessthan the sum of its diagonals.
If $\left| {z - 1} \right| + \left| {z + 3} \right| \le 8$ then the range of values of $\left| {z - 4} \right|$
If $\left|z\right| <\sqrt{2} -1$, then $\left|z^2 + 2 z cos \alpha \right|$ is
If z be a complex number for which $|2z cos \theta + z^2| = 1$, then the minimum value of |z|
is ......................
$sin^{-1}\left { \frac{1}{i} (z-1)\right }$ ,Where Z is non - real, can be the angle of a triangle, if
Let $z$ be any point in $\displaystyle A\cap B\cap C$ and let $w$ be any point satisfying $\displaystyle \left | w-2-i \right |< 3.$ Then, $\displaystyle \left | z \right |-\left | w \right |+3$ lies between
If $z=a+ib$ where $a>0,b>0$, then
The minimum value of $\displaystyle \left | z-1 \right |+\left | z \right |$for complex values of z is
If $|z| < 4$, then $|iz+3-4i|$ is less then
If $\displaystyle \left | z-\frac{2}{z} \right |=1$, then the greatest value of $\left | z \right |$ is
If $\displaystyle \left | z \right |< \sqrt{3}-1 $ then $\displaystyle \left | z^{2}+2z\cos\alpha \right | $ is
If $|z-4+3i|\le 1$ and $m$ and $n$ are the least and greatest values of $|z|$ and $k$ is the least value of $\displaystyle \frac { { x }^{ 4 }+{ x }^{ 2 }+4 }{ x } $ on the interval $(0,\infty)$, then $k$ is equal to
The maximum value of $|z|$ when $z$ satisfies the condition $\displaystyle \left | z+\frac{2}{z} \right |=2$
If $\displaystyle z\epsilon C \; and \; \left | z+4 \right |\leq 3$ then the greatest value of $\left | z+1 \right |$ is
If $\left| z - \displaystyle \frac{1}{z}\right| = 1$ then
The maximum value of |z| where z satisfies the condition $\displaystyle \left | z + \frac{2}{z} \right | = 2$ is
If $|z| \leq 1$ then the minimum and maximum value of |z - 3| are
lf $|\mathrm{z} _{1}|=2,\ |\mathrm{z} _{2}|=3$, then $|\mathrm{z} _{1}+\mathrm{z} _{2}+5+12\mathrm{i}|$ is less than or equal to
A point M is taken inside a parallelogram ABCD, then area of $\displaystyle \Delta AMD,$ $\displaystyle \Delta AMB,$ $\displaystyle \Delta AMC$ can take which of of the following values, respectively.
The complex number $z$ satisfies the condition $\left|\displaystyle {z}-\frac{25}{z}\right|=24$. Then the maximum distance from the origin to the point '$z$' in the argand plane is
If $|z+4|\leq 3$, then the maximum value of $|{z}+1|$ is
A point $'z'$ moves on the curve $|z - 4 - 3i| = 2$ in an argand plane. The maximum and minimum values of $|z|$ are
If $|{z _1}| = |{z _2}| = |{z _3}| = 1$ and ${z _1} + {z _2} + {z _3} = 0$ then the area of the triangle whose vertices are $z _1, z _2, z _3$ is
Statement 1: $|z _1-a| < a, |z _2-b| < b, |z _3-c| < c$, where a, b, c are positive real numbers, then $|z _1+z _2+z _3|$ is greater than $2|a+b+c|$.
Statement 2: $|z _1\pm z _2| \leq |z _1|+|z _2|$.
$z _0$ is a root of the equation $z^n cos \theta _o+z^{n-1} cos\theta _1+....+z cos\theta _{n-1}+cos\theta _n=2$, where $\theta, \epsilon R$, then
If $\displaystyle |Z - \frac {4}{Z}| = 2$, then the maximum value of $\displaystyle |Z|$ is equal to
The maximum value of $\left| z \right| $ when $z$ satisfies the condition $\displaystyle \left| z+\dfrac { 2 }{ z } \right| =2$ is
If the complex number z satisfies the condition |z| $\geq$ 3, then the least value of $\displaystyle \left | z + \frac{1}{z} \right |$ is equal to.
Let $\left| { z } _{ r }-r \right| \le r$, for all $ r = 1, 2, 3, ..., n.$ Then $\left| \sum _{ r=1 }^{ n }{ { z } _{ r } } \right| $ is less than
If $Re(z)$ is a positive integer, then value of the $|1+z+...+z^n|$ cannot be less than
If $z _{1},\ z _{2}--,\ z _{n}$ are complex numbers such that $|z _{i}|<\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{d}\lambda _{i}>0$ for $i=1,2,---n$ and $\lambda _{1}+\lambda _{2}+--+\lambda _{n}=1$ then $|\lambda _{1}z _{1}+\lambda _{2}z _{2}+--+\lambda _{n}\mathrm{z} _{1}|?$
If $\left | z-i \right |\leq 2$ and $z _{0}=13+5i$, then the maximum value of $\left | iz+z _{0} \right |$ is