Tag: maths

State the following statement is True or False
In a right angle triangle $ABC$ such as $AC=5 cm ,BC=2 cm$ , $\angle B=90^o$
Then the length of $AB$ after construction is $7$cm

For construction of a $\triangle PQR$, where $\displaystyle QR=6\ cm, PR=10\ cm$ and $\angle Q=90^{\circ}$, its steps for construction is given below in jumbled form. Identify the second step from the following.

1. At point $ Q $, draw an angle of $ {90}^{\circ} $.
2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass.
3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.
4. Join $P $ to $ Q $ . $ PQR $ is the required triangle. 
5. Draw the base side $ QR = 6\  cm $.

For construction of a $\triangle PQR$, when $\displaystyle QR=6\ cm, PR=10\ cm$ and $\angle Q=90^{\circ}$, its steps for construction is given below in jumbled form. Identify the fifth step from the following.

1. At point $ Q $, draw an angle of $ {90}^{\circ} $.
2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass.
3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.
4. Join $P $ to $ Q $ . $ PQR $ is the required triangle. 
5. Draw the base side $ QR = 6\  cm $.

For construction of a $\triangle PQR$, where $\displaystyle QR=6\ cm, PR=10\ cm$ and $\angle Q=90^{\circ}$, its steps for construction is given below in jumbled form. Identify the first step from the following.

1. At point $ Q $, draw an angle of $ {90}^{\circ} $.
2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass .
3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.
4. Join $P $ to $ Q $ . $ PQR $ is the required triangle. 
5. Draw the base side $ QR = 6\  cm $.

Construct a triangle $ABC$, in which $AB = 5.5 cm, AC = 6.5 cm$ and $\angle BAC = 70^{\circ}$.
Steps for its construction is given in a jumbled form.Identify its correct sequence.
1) At $A$, construct a line segment $AE$, sufficiently large, such that $\angle BAC$ at $70^\circ$, use protractor to measure $70^\circ$
2) Draw a line segment which is sufficiently long using ruler.
3) With $A$ as centre and radius $6.5cm$, draw the line cutting $AE$ at C, join $BC$, then $ABC$ is the required triangle.
4) Locate points $A$ and $B$ on it such that $AB = 5.5cm$.

Which of the following steps is INCORRECT, while constructing $\triangle$LMN, right angled at M, given that LN = 5 cm and MN = 3 cm?
Step 1. Draw MN of length 3 cm.
Step 2. At M, draw MX $\perp$ MN. (L should be some where on this perpendicular).
Step 3. With N as centre, draw an arc of radius 5 cm. (L must be on this arc, since it is at a distance of 5 cm from N).
Step 4. L has to be on the perpendicular line MX as well as on the arc drawn with centre N. Therefore, L is the meeting point of these two and $\triangle$LMN is obtained.

In a right-angled triangle, the square of the hypotenuse is equal to twice the product of the other two sides. One of the acute angles of the triangle is

Let $f\left( x \right) =1+\sqrt { x } $ and $g\left( x \right) =\dfrac { 2x }{ { x }^{ 2 }+1 } $, then

Let f(x) = ${ x }^{ 2 }\quad +\quad \frac { 1 }{ { x }^{ 2 } } \quad and\quad g(x)\quad =\quad -\quad \frac { 1 }{ x } ,\quad x\in R\quad -\quad \left{ -1,0,1 \right} \quad .If\quad h(x)\quad =\quad \frac { f(x) }{ g(x) } ,\quad then\quad the\quad local\quad minimum\quad value\quad of\quad h(x)\quad is\quad :$

A Cartesian plane consists of two mutually _____ lines intersecting at their zeros.