There are two numbers. If four times the larger of two numbers is divided by the smaller one, we get 8 as quotient and 12 as remainder. If five times the smaller of two numbers is divided by the larger one, we get 2 as quotient and 11 as remainder. Find the numbers.
Sum of ^@n^@ terms of three ^@A.P.^@ are ^@S _1^@, ^@S _2^@, ^@S _3^@ respectively. If first term of each progression is ^@1^@ and common differences are ^@1^@, ^@2^@, ^@3^@ respectively, then ^@S _1 + S _3 = ^@
In a trapezium ^@ ABCD^@ , ^@O ^@ is the point of intersection of ^@AC^@ and ^@BD^@. ^@AB || CD^@ and ^@AB = 2 \times CD^@. If the area of ^@\Delta AOB = 80 \space cm^2^@, find the area of ^@\Delta COD^@.
If ^@ cot \theta = \dfrac { b } { a } ^@, find the value of ^@ \sqrt { \dfrac { a {\space} tan \theta - b {\space} cos \theta} { a {\space} tan\theta + b{\space} cos\theta }} ^@ .
The difference between circumference and diameter of a circular plot is ^@ 27 \space m^@. Find the area of the circular plot. ^@ \left( \text{Assume } \pi = \dfrac{ 22 }{ 7 } \right) ^@
A tent is in form of a right circular cylinder and cone as shown in the picture. The radius of cone and cylinder is 4 meters. The height of cylinder and cone are 8 meters and 3 meters respectively. Find the outer surface area of the tent. (Assume π =
There is a cylindrical compass holder of height ^@ 12 \space cm^@ and diameter ^@ 16 \space cm^@. Now the compass holder is cut into two pieces such that the height of the new compass holder is reduced to ^@ \left(\dfrac{ 3 }{ 4 } \right)^{th} ^@ of the height. The diameter of the new compass holder remains the same. If the new compass holder is filled with water up to the brim, then find the amount of water held in liters. (Where ^@ \pi = 3.14 ^@)
Nepal
