If x% of y is 150 and y% of z is 300, then the relation between x and z is:
From the given data, \(\frac{x}{100}y=150\Rightarrow xy=15000\) and \(\frac{y}{100}z=300\Rightarrow yz=30000\). Dividing the two, \(\frac{xy}{yz}=\frac{15000}{30000}\Rightarrow\frac{x}{z}=\frac{1}{2}\), so \(z=2x\).
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and height of the cone is equal to its radius. Then the volume of the solid is:
If \(1+\cfrac{5x}{1-\cfrac{1}{2+\cfrac{2x}{1-x}}}=3\), then the value of 'x' is:
In the following figure \(\angle a+\angle b=?\), when \(l\parallel m\):

The word "Mathematics" is derived from the following Greek words:
(a) Techne
(b) Arsmathematica
(c) Manthanein
If \(a^2+\frac{1}{9^2}=\frac{7}{3}\), then what is the value of \(\left(a^3-\frac{1}{a^3}\right)\)?
The total surface area of a hemisphere is \(462 \text{ cm}^2\). The diameter of this hemisphere is:
What is the purpose of formative evaluation in mathematics?
Which of the following is least appropriate about the nature of mathematics?
Statement I:
Mathematical concepts are hierarchical
Statement II:
Mathematics in inclusive as it always includes social subjectivites
Statement III:
Logical reasoning plays as important role in mathematics
If \(A:B:C = 2:3:4\) then \(\dfrac{A}{B} : \dfrac{B}{C} : \dfrac{C}{A}\) is equal to:
A 240 m long train crosses a platform that is twice its length in 5 min. What is the speed of the train?
| List-I (Relief Materials) | List-II (Color Code) |
| A. Shelter | I. Yellow |
| B. Clothes | II. Khaki |
| C. Food | III. Red |
| D. Medicine | IV. Brown |
Which of the following is NOT a state function or state variable in a thermodynamic system?