If ^@ \alpha ^@ and ^@ \beta ^@ are the zeros of polynomial ^@ x^2 + x-2,^@ find a polynomial whose zeros are ^@ \dfrac{ \alpha^2 }{ \beta^2 } ^@ and ^@ \dfrac{ \beta^2 }{ \alpha^2 }. ^@
A boy can row ^@40{\space} km ^@ downstream in ^@6{\space} hours^@ and ^@14{\space} km^@ upstream in ^@8 {\space}hours^@. Find the speed of the boy in still water.
The production of washing machines in a factory increases uniformly by a fixed number every year. The factory produced ^@ 2014 ^@ washing machines in the ^@ 3^{ rd } ^@ year and ^@ 3830 ^@ washing machines in the ^@ 7^{ th } ^@ year. Find the production of washing machines in the first ^@ 7 ^@ years.
A ladder ^@ 29 \space m^@ long just reaches the top of a building ^@20 \space m^@ high from the ground. Find the distance of the foot of the ladder from the building.
The coordinates of one end point of a diameter ^@AB^@ of a circle are ^@A(4,2)^@ and the coordinates of the center of the circle are ^@C(-1,4)^@. Find the coordinates of ^@B^@.
A rope is tightly stretched and attached from top of a vertical tower to the ground. The angle made by rope with ground is ^@ 30^\circ. ^@ If length of the rope is ^@ 6 \space m ^@, find height of the tower.
A circle is inscribed in a ^@ \triangle ABC ^@, touching ^@ BC, CA, ^@ and ^@ AB ^@ at points ^@ P, Q, ^@ and ^@ R ^@ respectively. If ^@ AB = 12 \space cm, AQ = 9 \space cm ^@ and ^@ CQ = 7 \space cm ^@ then find the length of ^@ BC ^@.
Find the difference between the area of a regular hexagonal plot each of whose side is ^@ 58 \space m ^@ and the area of the circular swimming tank inscribed in it. ^@ \bigg[π = \dfrac { 22 } { 7 } \text { and } \sqrt { 3 } = 1.732 \bigg]^@
There are a total of 16 chocolates - 4 each in the flavors of cherry, orange, banana and grape. There are also 5 children. If each child is allowed to choose their own favorite flavor, what is the probability that all of them will get flavors of their choice?
Oman
