J P Mohindru and Bharat Mohindru Solutions for Chapter: Triangles, Exercise 9: NATIONAL TALENT SEARCH EXAMINATION (NTSE)

In the given Fig., $DE\parallel BC, AD=2.4 \mathrm{cm}, AE=3.2 \mathrm{cm} \mathrm{and} CE=4.8 \mathrm{cm}$. Then the value of $BD$ is equal to:

In the given figure, $DE$ is parallel to $BC$, $\frac{AD}{DB}=\frac{5}{3}$. If $AE=7.8 \mathrm{cm},$ the value of $EC$ is equal to: 

The sides of two similar triangles are in the ratio $4:9$. Areas of these triangles are in the ratio:

If $△ABC$ is right angled at $A$, then value of $\tan B\times \tan C$ is :

What value(s) of $x$ will make $DE\parallel AB$ in the following figure?

In the fig., if $\angle ADE=\angle B,$ such that $△ADE~△ABC$. If $AD=6.8 \mathrm{cm}, AE=8.6 \mathrm{cm}, BE=2.4 \mathrm{cm} \mathrm{and} BC=5.5 \mathrm{cm}$, find $DE$.

A ladder $10 \mathrm{m}$ long reaches a window $8 \mathrm{m}$ above the ground. If the distance of the foot of the ladder from the base of the wall is $k \mathrm{m}$, find the value of $k$.

A guy wire attached to a vertical pole of height $18 \mathrm{m}$ is $24 \mathrm{m}$ long and has a stake attached to the other end. If$k\sqrt{7} m$ far from the base of the pole should the stake be driven so that the wire will be taut, then find the value of $k$.