The perimeters of two similar triangles are ^@ 24 \space cm^@ and ^@72 \space cm^@ respectively. If one side of the first triangle is ^@10 \space cm^@, find the corresponding side of the second triangle.
The length of a string between a kite and a point on the ground is ^@ 77 \space m^@. If the string makes an angle ^@\theta^@ with the ground level such that ^@ \tan \theta = \dfrac { 9 } { 40 } ^@, then find the height of the kite from the ground. Assume that there is no slack in the string.
A circle is touching the side ^@ BC ^@ of ^@ \triangle ABC ^@ at ^@ P ^@ and touching ^@ AB ^@ and ^@ AC ^@ produced at ^@ Q ^@ and ^@ R ^@ respectively. Which of the following hold true?
A.
^@ AQ = \dfrac { 1 } { 4 } \text{(Perimeter of } \triangle ABC) ^@
B.
^@AQ = \text{ Perimeter of } \triangle ABC ^@
C.
^@ AQ = \dfrac { 1 }{ 2 } \text{(Perimeter of } \triangle ABC)^@
The radii of the ends of a frustum of a cone ^@13 \space cm^@ high are ^@ 26 \space cm ^@ and ^@ 13 \space cm ^@. Find its total curved surface area. (Take ^@ \pi = \dfrac { 22 } { 7 }^@)
Three coins are tossed simultaneously ^@ 400 ^@ times and it is found that three heads appeared ^@ 200 ^@ times, two heads appeared ^@ 140 ^@ times, one head appeared ^@ 40 ^@ times and no head appeared ^@ 20 ^@ times.
If three coins are tossed simultaneously at random, what is the probability of getting ^@ 0 \text { heads } ^@?
The sum of the 6th element and the 15th element of an arithmetic progression is -227. The sum of the 9th and the 18th element is -305. What is the value of the 27th term?
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