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When a charged particle moves in uniform circular motion inside a uniform magnetic field \(\overrightarrow{B}\) in a plane perpendicular to \(\overrightarrow{B}\) the centripetal force is the magnetic force on the particle. As in any UCM, this magnetic force is constant in magnitude and perpendicular to the velocity of the particle.

Magnetic Resonance Imaging (MRI) is a noninvasive imaging technology that produces three dimensional detailed anatomical images. Although MRI does not emit the ionizing radiation that is found in X-ray imaging, it does employ a strong magnetic field, e.g., medical MRIs usually have strengths between 1.5 T and 3 T.

The 21.1 T superconducting magnet at Maglab (Florida, US) is the world’s strongest MRI scanner used for Nuclear Magnetic Resonance (NMR) research. Since its inception in 2004, it has been continually conducting electric current of 284 A by itself. Because it is superconducting, the current runs through some 152 km of wire without resistance, so no outside energy source is needed. However, 2400 litres of liquid helium is cycled to keep the magnet at a superconducting temperature of 1.7 K. Even when not in use this magnet is kept cold; if it warms up to room temperature, it takes at least six weeks to cool it back down to operating temperature. The 45 T Hybrid Magnet of the Lab (which combines a superconducting magnet of 11.5 T with a resistive magnet of 33.5 T) is kept at 1.8 K using 2800 L of liquid helium and 15142 L of cold water.

Triangle, rectangle circle etc.

(c) two-dimensional

Number of faces in a cuboid are 6.

Number of vertices in a cuboid are 8.

An example of three dimensional figure is cuboid.

The plane figures having two measurements, length and breadth, are called two dimensional shapes.

Figure (i) and (ii) and Polyhedron. Figure (i) is made by combination of Cuboid and Pyramid.

Figure (ii) is made by combination of Prism and Pyramid.

Number of edges in a triangular prism = 9 and number of faces in a triangular prism = 5.

Cuboid, sphere, cylinder etc.

Number of faces in a cube 6.

A prism is a polyhedron whose base and top are congruent polygons and whose other faces, i.e., lateral faces are parallelogram in shapes.

Yes, It can be a cube. But it can be a cuboid also.

Faces = 8 

Vertices = 8 

using Eulers formula, 

F + V – E = 2 

8 + 8 – E = 2 

-E = 2 – 16 E= 14

(i) No. 

(ii) Yes. 

(iii) Yes.

A polyhedron having a polygonal base and triangular sides with a common vertex, is called a pyramid.

Yes, a square prism is same as a cube.

Number of faces (F) = 5
Number of Edges (E) = 9
Number of Vertices (V) = ?

We know by Euler’s formula
F + V = E + 2
5 + V = 9 + 2
5 + V = 11
V = 11 – 5
V = 6
∴Number of vertices = 6

Number of vertices (V) = 9
Number of faces (F) = 9
To Find : Number of edges.

Euler’s formula : 

V + F = E + 2
Then, 9 + 9 = E + 2
or 9 + 9 – 2 = E
Hence, E = 16

Since, F + V = E + 2

As 10 + 15 ≠ 20 + 2

∴ A polyhedron cannot have 10 faces, 20 edges and 15 vertices.

A polyhedron is said to be regular if its faces are made up of regular polygons and the same number of faces meet at each vertex.

Number of faces = 8

Number of vertices = 16

Number of edges = 26

Using Euler’s formula

F + V – E

⇒ 8 + 16 – 26 ≠ -2

⇒ -2 ≠ 2

No, a polyhedron cannot have 8 faces, 26 edges and 16 vertices.

Number of vertices (V) = 10, Number of edges (E) =16, Number of faces (F) = ?

Euler formula 

V + F = E + 2

⇒ 10 + F = 16 + 2

or F = 16 + 2 – 10 = 8

Take x and the height and 3x as the base of the triangular field

We know that

Area of triangle = ½ × b × h

By substituting the values

Area of triangle = ½ × x × 3x

So we get

Area of triangle = 3/2 x²

1 hectare = 1000 sq. metre

It is given that

Cost of sowing the field per hectare = ₹ 58

Total rate of sowing the field = ₹ 783

So we can find the total cost by

Total cost = Area of the field × ₹ 58

By substituting the values

(3/2) x² × (58/10000) = 783

By cross multiplication

x² = (783/58) × (2/3) × 10000

On further calculation

x² = 90000

By taking the square root

x = √90000

So we get

x = 300 m

Base = 3 × 300 = 900 m

Therefore, base = 900 m and height = 300 m.

Given that,

Let the length of other parallel side of trapezium = x cm

Length of one parallel side of trapezium = 6 cm

Area of trapezium = 28 cm²

Length of altitude of trapezium = 4 cm

We know that,

Area of trapezium = 1/2 (Sum of lengths of parallel sides) × distance between parallel sides

i.e., Area of trapezium = 1/2 (Sum of sides) × distance between parallel sides

28 = 1/2 (6 + x) × 4

28 = (6 + x) × 2

(6 + x) = 28/2

(6 + x) = 14

x = 14 – 6

x = 8

∴ Length of the other parallel side of trapezium = 8 cm

Let altitude of the triangular field be h m

Then base of the triangular field is 3h m.

We know that area of triangle = ½ x b x h

Area of the triangular field = ½ (h x 3h) = 3h²/2 m² ……. (i)

The rate of cultivating the field is Rs 24.60 per hectare.

Therefore,

Area of the triangular field = 332.10 /24.60

= 13.5 hectare

= 135000 m² [Since 1 hectare = 10000 m²] …… (ii)

From equation (i) and (ii) we have,

3h²/2 = 135000 m²

3h² = 135000 x 2 = 270000 m²

h² = 270000/3

= 90000 m² 

= (300)²

h = 300 m

Hence, Height of the triangular field = 300 m and

Base of the triangular field = 3 x 300 m = 900 m

Given diagonal AC = 48 cm and diagonal BD = 32 m

Area of a quadrilateral = ½ (Product of diagonals)

= ½ (AC x BD)

= ½ (48 x 32) m²

= 768 m²

(a) Mercury 

(b) Silver, Copper

1. True

2. True

3. True

4. True

5. True

(a) Element: It is a substance that cannot be broken down into simpler substance by chemical means 

Ex. : Oxygen, Hydrogen, Gold & Helium.

(b) Compound A compound is a pure substance that is formed when the atoms of two or more elements combine chemically in definite proportions. 

Ex : H?0, NaCl.

(c) Metal A chemical element that is an effective conductor of electricity and heat can be defined as a metal. 

Ex.: Copper, Iron, Silver, etc

(d) Non-Metal Non-metal is an element that doesn’t have the characteristics of metal including, (i.e.) ability to conduct heat or electricity luster or flexibility. 

Ex. Carbon Iodine, Sulphur.

(e) Metalloid : Metalloid is a chemical element that exhibits some properties of metals and some of non-metals. Metalloids are generally semi- conductors. 

Ex. : Silicon. Arsenic, Antimony and Boron.

1. Gas at room temperature 

2. Graphite 

3. can be split into elements 

4. elements

Correct answer is (b) metal

1. atom 

2. CO₂ 

3. Graphite 

4. same 

5. Symbol 

6. 118 

7. simplest 

8. capital 

9. polyatomic molecule 

10. Nitrogen

A chemical formula is a symbolic representation of one molecule of an element or a compound.

Correct answer is (a) atom

Correct answer is (b) Molecule

Atom is the fundamental particle of an element.

Correct answer is (c) element

Correct answer is (c) Robertr boyle

Core of white matter in cerebellum is called as arbor vitae.

There are 31 pairs of spinal nerves in man.

The parts of brain which functions as endocrine glands are hypothalamus, pituitary body, pineal body.

The cyclotron frequency, or the magnetic resonance frequency, is the frequency of revolution of a charged particle of charge per unit mass \(\cfrac {q}{m}\) in a magnetic field of induction B inside a cyclotron. The cyclotron frequency, f = \(\cfrac{qB}{2\pi m}\). The frequency of the alternating voltage applied to the dees of the cyclotron should be equal to the cyclotron frequency.

The frequency of the alternating voltage between the dees of a cyclotron should be equal to the cyclotron frequency so that a positive ion exiting a dee always sees an accelerating potential difference to the other dee. This equality of the frequencies is called the resonance condition.

Correct option is (C) \(\cfrac{qBR}{m}\)

Correct option is A) proton

Molecular mass: Molecular mass or molecular weight refers to the mass of a molecule. It is calculated as the sum of the mass of each constituent atom multiplied by the number of atoms of that element in the molecular formula.

C) M – shell

Correct option is D) mass