Question 1 :
A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a two-digit number.

Question 2 :
In $\triangle PQR,$ $PQ=4$ cm, $QR=3$ cm, and $RP=3.5$ cm. $\triangle DEF$ is similar to $\triangle PQR.$ If $EF=9$ cm, then what is the perimeter of $\triangle DEF\: ?$<br>

Question 3 :
A tree of height 24m standing in the middle of the road casts a shadow ofheight 16m. If at the same time a nearby pole of 48 m casts a shadow , whatwould the height of the shadow be?<br>

Question 4 :
D is the mid point of the base BC of a triangle ABC. DM and DN are perpendiculars on AB and AC respectively. If $DM=DN$, the triangle is

Question 5 :
In triangle ABC ; M is mid-point of AB, N mid-point of AC and D is any point in base BC. Then:

Question 6 :
Goldfish are sold at Rs.15 each. The rectangular coordinate graph showing the cost of 1 to 12 goldfish is:

Question 7 :
If the corresponding sides of two triangles are proportional, then the two&#160;triangles are similar by which test

Question 8 :
$4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>

Question 9 :
State true or false:<br/>In quadrilateral $ABCD$, its diagonals $AC$ and $BD$ intersect at point $O$, such that<br/>$\displaystyle \dfrac{OC}{OA}=\dfrac{OD}{OB}=\dfrac{1}{3}$, then$\triangle OAB \sim \triangle OCD$<br/>

Question 10 :
Two triangles are $ABC$ and $PQR$ are similar, then symbolically it is represented as:

Question 11 :
$\triangle ABC$ is similar to $\triangle XYZ$ by $SAS$ similarity. If in $\triangle ABC$&#160;$AB=12,BC=8,\angle B=60$<br/>and in $\triangle XYZ$ $XY=3$,$\angle Y=60$. Find the value of $YZ$

Question 12 :
In&#160;$\displaystyle \Delta ABC\sim \Delta DEF$ and their areas are&#160;$\displaystyle { 36cm }^{ 2 }$ and&#160;$\displaystyle { 64cm }^{ 2 }$ respectively.If side AB=3 cm. Find DE.

Question 13 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find&#160;$a$ when $c=25 \ cm$ and $b=7 \ cm$.

Question 14 :
Two polygons of the same number of sides are similar if all the corresponding interior angles are:<br/>

Question 15 :
State true or false:<br/>The ratio of the areas of two triangles of&#160;the same height is equal to the ratio of&#160;their bases.

Question 16 :
The area of two similar triangles ABC and PQR are $25\ cm^{2}\ \&amp; \&#160; 49\ cm^{2}$, respectively. If QR $=9.8$ cm, then BC is:<br/>

Question 17 :
The perimeters of two similar triangles are $25\;cm$ and $15\;cm$ respectively. If one side of first triangle is $9\;cm$, then the corresponding side of the other triangle is

Question 18 :
The corresponding sides of two similar triangles are in the ratio $2$ to $3$. If the area of the smaller triangle is $12$ the area of the larger is

Question 19 :
Triangle is equilateral with side$A$, perimeter $P$, area $K$ and circumradius $R$ (radius of the circumscribed circle). Triangle is equilateral with side $a$, perimeter $p$, area $k$, and circumradius $r$. If $A$ is different from $a$, then

Question 20 :
Consider the following statements:<br/>(1) If three sides of triangle are equal to three sides of another triangle, then the triangles are congruent.<br/>(2) If three angles of a triangle are respectively equal to three angles of another triangle, then the two triangles are congruent.<br/><br/>Of these statements,

Question 21 :
In$ \displaystyle \bigtriangleup $ ABC , angle C is a right angle, then the value of$ \displaystyle \tan A+ \tan B is $

Question 22 :
For two triangles, if sides of one triangle are proportional to the sides of other triangle, then their corresponding angles are equal and hence the two triangles are similar. This is called ___ similarity. &#160;&#160;<br/>

Question 23 :
A ladder $13m$ long rests against a vertical wall. If the foot of the ladder is $5m$ from the foot of the wall, find the distance of the other end of the ladder from the ground.

Question 24 :
It is given that $\triangle FED\sim \triangle STU$. Is it true to say that $\cfrac{DE}{UT}=\cfrac{EF}{TS}$?&#160;<br/>

Question 25 :
A line segment $DE$ is drawn parallel to base $BC$ of $\displaystyle \Delta ABC$ which cuts $AB$ at point<br/>$D$ and $AC$ at point $E$. If $AB=5 BD$ and $EC = 3.2$ cm. find the length of $AE$.<br/>

Question 26 :
The hypotenuse of a grassy land in the shape of a right triangle is $1$ meter more than twice the shortest side. If the third side is $7$ meters more than the shortest side, find the sides of the grassy land.

Question 27 :
The ratio of the areas of two similar triangles is equal to the <br>

Question 28 :
The ratio of the areas of two similar triangles is $25:16$. The ratio of their perimeters is ..............

Question 29 :
In $\Delta ABC,$ if $AB =6\sqrt{3}$ cm, $AC=12$ cm and $BC=6$ cm, then angle B is equal to:<br/>

Question 30 :
If the ratio of the corresponding sides of two similar triangles is 2:3 then the ratio of their corresponding altitude is

Question 33 :
The corresponding sides of two similar triangles are in the ratio $a : b$. What is the ratio of their areas?

Question 34 :
The base of a triangle is $80$, and one of the base angles is $60^{\circ}$. The sum of the lengths of the other two sides is $90$. The shortest side is

Question 35 :
In a right angled triangle $ABC,\,\angle B=90^{\circ}$ such that&#160;$AC=13\;cm,\;BC=5\;cm$. Then, find $AB$.

Question 36 :
$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta DEF$ are two similar triangles such that&#160;$\displaystyle \angle A={ 45 }^{ \circ &#160;},\angle E={ 56 }^{ \circ &#160;}$, then&#160;$\displaystyle \angle C$ =___.<br/>

Question 37 :
State true or false:<br/>In a trapezium ABCD, side AB is parallel to side DC; and the diagonals AC and BD intersect each other at point&#160;P, then<br/>$\displaystyle \Delta APB$ is similar to $\displaystyle \Delta CPD.$<br/><br/>

Question 38 :
Choose and write the correct alternative.<br>Out of the following which is aPythagorean triplet ?<br>

Question 39 :
Match the column.<br/><table class="wysiwyg-table"><tbody><tr><td>1. In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR},\angle A=\angle P$<br/></td><td>(a) AA similarity criterion&#160;</td></tr><tr><td>2.&#160;In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \angle A=\angle P,\angle B=\angle Q$<br/><br/></td><td>(b) SAS similarity criterion&#160;</td></tr><tr><td>3.&#160;In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$<br/>$\angle A=\angle P$<br/></td><td>(c) SSS similarity criterion&#160;</td></tr><tr><td>4. In&#160;$\displaystyle \Delta ACB,DE||BC$<br/>$\displaystyle \Rightarrow \frac{AD}{BD}=\frac{AE}{CE}$<br/></td><td>(d) BPT</td></tr></tbody></table>

Question 40 :
$\frac{a}{r}$, a, ar are the sides of a triangle. If the triangle is a right angled triangle, then $r^2$ is given by

Question 41 :
Let&#160;$\displaystyle \Delta XYZ$ be right angle triangle with right angle at Z. Let&#160;$\displaystyle A_{X}$ denotes the area of the circle with diameter YZ. Let&#160;$\displaystyle A_{Y}$ denote the area of the circle with diameter XZ and let&#160;$\displaystyle A_{Z}$ denotes the area of the circle diameter XY. Which of the following relations is true?