The word "Mathematics" is derived from the following Greek words: (a) Techne (b) Arsmathematica (c) Manthanein
(b) and (c)
Reference texts commonly trace the term to the Greek roots "Techne" (art or craft) and "Manthanein" (to learn), while "Ars Mathematica" is a later Latin phrase rather than a Greek word. This makes option (B), combining (c) and (a), the more defensible pick on etymological grounds, though the source booklet marks option (D). The discrepancy is flagged here for editorial review.
If the polynomial 3x² − x³ − 3x + 5 is divided by another polynomial x − 1 − x², the remainder comes out to be 3, the quotient polynomial is:
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:
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:
The sum of three numbers is 124. If the ratio between the first and the second is 2 : 3 and between the second and the third is 7 : 9, then the third number is:
15 men or 18 women can complete a piece of work in 45 days. If 5 men and 6 women work together then the work will be completed in:
A 240 m long train crosses a platform that is twice its length in 5 min. What is the speed of the train?
Why is error analysis important?
The speed of a train is 46 km/hr. If the length of the train is 805 m, then how much time will train take to cross a man standing on the platform?
Rajan purchased two ceiling fans at the rate Rs 2,500 each. Out of which one fan was sold at 15% profit and other was sold at 8% loss. How much profit or loss percentage is obtained in the whole transaction?
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :