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State the AAA-similarity criterion.
Find the sum of all integers between $84$ and $719$, which are multiples of $5$.
→$\triangle PQR \sim \triangle PAB , m \angle P =60^{\circ}, PQ =6 cm, PR =4 cm$. Construct $\triangle PAB$, if $PQ : PA =3: 2$.
→A merchant borrows Rs.1000 and agrees to repay its interest Rs.140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by Rs.10. Find the amount of the first first instalment.
The length of an arc of a circle, subteding an angle of 54° at the centre is 16.5cm. Calculate the radius, circumference and area of the circle. $\Big[\text{Use }\pi=\frac{22}{7}\Big]$
→Solve the following equations by using the method of completing the square:
$3x^2 - 2x - 1 = 0$
→$3x^2 - 2x - 1 = 0$
Two chords AB and CD of a circle intersect at a point P outside the ciecle. Prove that.
→- $\triangle\text{PAC}\sim\triangle\text{PDB}$
- $\text{PA}.\text{PB}=\text{PC}.\text{PD}$
Solve the following quadratic equation.
5m2 + 2m + 1 = 0
5m2 + 2m + 1 = 0
Solve the following system of equations by the method of cross-multiplication:
$\text{ax}+\text{by}=\frac{\text{a}+\text{b}}{2}$
$3\text{x}+5\text{y}=4$
→$\text{ax}+\text{by}=\frac{\text{a}+\text{b}}{2}$
$3\text{x}+5\text{y}=4$
Product of Pragati’s age 2 years ago and 3 years hence is 84. Find her present age.