If the radius of a right circular cylinder is decreased by \(10\%\) and the height is increased by \(20\%\), then the percentage increase/decrease in its volume is:
Decrease by 2.8%
Volume of a cylinder is proportional to r^2 h. New volume factor = (0.9)^2 * (1.2) = 0.81 * 1.2 = 0.972, i.e. 97.2% of the original volume, which is a decrease of 2.8%.
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:
If x% of y is 150 and y% of z is 300, then the relation between x and z 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:
| 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?