If ^@\alpha^@ and ^@\beta^@ are the zeros of quadratic polynomial ^@x^2 + x + 2^@, find the value of ^@\dfrac{1}{ \alpha^3 } + \dfrac{1} { \beta^3 }^@.
If thrice the daughter's age in years is added to mother's age, the sum is 84. If thrice the mother's age is added to the daughter's age, the sum is 132. Find the age of mother and daughter.
The production of television sets in a factory increases uniformly by a fixed number every year. The factory produced ^@ 2262 ^@ television sets in the ^@ 3^{ rd } ^@ year and ^@ 4902 ^@ television sets in the ^@ 8^{ th } ^@ year. Find the production of television sets in the ^@ 5^{ th } ^@ year.
A lamp is ^@ 15.4 \space m ^@ above the ground. A boy ^@ 55 \space cm ^@ tall walks away from the base of this post at a speed of ^@ 1.7 \space m/s^@. Find the length of the shadow of the boy after ^@ 8 \space seconds ^@.
Let ^@D(11,10), E(9,12),^@ and ^@F(8,7)^@ be the mid points of the sides ^@BC, CA,^@ and ^@AB^@ respectively of a ^@\Delta{ABC}^@. Then, find the coordinates of the vertex ^@A^@.
A chord of a circle of radius ^@ 28 \space cm ^@ subtends a right angle at the center. Find the area of the corresponding major segment.^@ \bigg[\pi = \dfrac { 22 } { 7 }\bigg] ^@
A wooden toy rocket is in the shape of a cone mounted on a cylinder as shown in the figure.The height of the entire rocket is 35 cm, while the height of the conical part is 25 cm. The base of the conical portion has a diameter of 13 cm,which the base diameter of the cylinderical portion is 10 cm. If the conical portion is painted yellow , choose the area of the rocket painted with yellow colours.
Olivier and Vincent sit on the 6-member board of directors for company X. If the board is to be split up into two 3-person subcommittees, what is the percentage that Vincent and Olivier are included in the same sub-committee?
In this diagram, the triangle represents men, the square represents doctors and the circle represents employed. Find the number of men who are employed but not doctors.
France
