Write a Pythagorean triplet whose one member is 15.
If 51x3 is a multiple of 9, where x is a digit, then what is the value of x?
Show that -1728 is a perfect cube. Also, find the number whose cube is -1728.
Leela invited some friends for tea on her birthday. Her mother placed some plates and some puris on a table to be served. If Leela places 4 puris in each plate 1 plate would be left empty. But if she places 3 puris in each plate 1puri would be left. Find the number of plates and number of puris on the table.
Take a clock and fix its minute hand at 12.
Record the angle turned through by the minute hand from its original position and the time that has passed, in the following table:
Time Passed (T)
Angle turned (A) (in degree)
What do you observe about T and A? Do they increase together? Is \(T\over A\) same every time?
Is the angle turned through by the minute hand directly proportional to the time that has passed? Yes; From the above table, you can also see
T1 : T2 = A1 A2, because
T1 : T2 = 15 30= 1 :2
A1 : A2 = 90 180 = 1 :2
Check if T2: T3 = A2 A3 and T3 : T4 = A3 : A4
You can repeat this activity by choosing your own time interval.
Complete the following crossword puzzle using the given direction.
(1) The product of number by itself two times, is called its _______
(2) If three numbers a, band c are such that a2 + b2= c2 then they are called _____ Triplets.
(3) A number is a when it is a product of the same two numbers.
Down: (4) The numbers 2n, n2-1 and n2 + 1 where n is a natural number show Pythagorean______.
(5) Finding is the inverse operation of squaring a number.
(6) A number which divides a _______ given number exactly is called a or divisor of that number.
Find the length of the diagonal BD when, the area of the quadrilateral is 32 cm2.
A mixture of paint is prepared by mixing 1 part of green pigments with 6 parts of the base. In the following table, find the parts of base needed to be added.
Parts of green pigment
Parts of base
A machine fills 540 bottles in six hours. How many bottles will it fill in five hours?