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(c) initial state

There are 3 parts in specification

(b) final state

(d) be equal

Answer is (c) 5 and 5

(i) A = {2, -2, 3} and B = {1, -4} 

A x B = {2,-2, 3} x {1,-4} 

= {(2, 1), (2, -4)(-2, 1) (-2, -4) (3, 1) (3,-4)} 

A x A = {2,-2, 3} x {2,-2, 3} 

= {(2, 2)(2, -2)(2, 3)(-2, 2) (-2, -2)(-2, 2) (3,-2) (3,3)} 

B x A = {1,-4} x {2,-2, 3} 

= {(1, 2)(1, -2)( 1, 3)(-4, 2) (-4,-2)(-4, 3)}

(ii) A = B = {p, q} 

A x B = {p, q) x {p, q} 

= {(p,p),(p,q)(q,p)(q,q)} 

A x A = {(p,q) x (p,q)} 

= {(p,p)(p,q)(q,p)(q,q)}

B x A = {p,q} x {p,q} 

= {(p,p)(p,q)(q,p)(q,q)}

(iii) A = {m, n} x B = Φ 

Note: B = Φ or {} 

A x B = {m, n} x { } 

= { } 

A x A = {(m, n) x (m, n)} = {(m, m)(w, w)(n, m)(n, n)} 

B x A = { } x {w, n} 

= { }

A = {1, 2, 3}, B = {2, 3, 5, 7} 

A x B = {(1, 2), (1, 3), (1, 5), (1, 7), (2, 2), (2, 3), (2, 5), (2, 7), (3, 2), (3, 3), (3, 5), (3, 7)} 

B x A = {(2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (5, 1), (5, 2), (5, 3), (7, 1), (7, 2) , (7, 3)}

1. Propulsion of rockets is based on the law of conservation of linear momentum as well as Newton’s III law of motion. 

2. Rockets are filled with fuel (either liquid or solid) in the propellant tank. When the rocket is fired, this fuel is burnt and hot gas is ejected with high speed from the nozzle of the rocket, producing a huge momentum. 

3. To balance this momentum, an equal and opposite reaction force is produced in the combustion chamber, which makes the rocket project forward.

4. While in motion, the mass of the rocket gradually decreases, until the fuel is completely burnt out. 

5. Since there is no net external force acting on it, the linear momentum of the system is conserved. 

6. The mass of the rocket decreases with altitude, which results in the gradual increase in the velocity of the rocket. 

7. At one stage, it reaches a velocity, which is sufficient to just escape from the gravitational pull of the Earth. This velocity is called escape velocity.

B x A = {(-2, 3) (-2, 4) (0, 3) (0, 4) (3, 3) (3,4)} 

A = {3,4} 

B = {-2,0,3}

(b) Pseudo code cannot be executed by the computer directly.

Reference variable in C++ is alias for existing variable. They store nothing but the address of the variable used at the time of its declaration. It is important to assign the reference variable at the time of declaration, else it will show an error.

Linear Momentum.

Trash is the equivalent of Recycle bin of windows OS. All the deletted files and folders are moved here.

At the bottom of the screen is a horizontal bar called the taskbar. This bar contains (from left to right) the Start button, shortcuts to various programs, minimized programs and in the extreme right comer you can see the system tray which consist of volume control, network, date and time etc. Next to the Start button is the quick Launch Toolbar which contains task for frequently used applications.

Wordpad is an in-built word processor application in Windows OS to qreate and manipulate text documents.
In order to create files in wordpad you need to follow the steps given below.

1. Click Start → All Programs → Accessories → Wordpad or Run → type Wordpad, click OK. Wordpad window will be opened.

2. Type the contents in the workspace and save the file using File → Save or Ctrl + S.

3. Save As dialog box will be opened.

4. In the dialog box, select the location where you want to save the file by using look in drop down list box.

5. Type the name of the file in the file name text box.

6. Click save button.

The default desktop background, or wallpaper, belonging to the default Ubuntu 16.04 theme known as Ambiance.

(b) low pressure and high temperature

(a) translational kinetic energy

The correct answer is (c) T.

(b) By Concave mirror

In the plane mirror, the left part appears as right in the image and the right part appears as left in the image. This event is called lateral transformation.

The difference between concave and convex mirror is

Shaving mirror – concave mirror. Car headlight mirror – concave mirror. Searchlight mirror – concave mirror. Driving mirror – convex mirror. Dentist’s inspection mirror – concave mirror. Torch mirror – concave mirror. Staircase mirror in a double-decker bus – convex mirror. Make-up mirror – concave mirror. Solar furnace mirror – concave mirror. Satellite TV dish – concave mirror. Shop security mirror – convex mirror. 

(i) Atomicity of the gas molecule.

(ii) Shape of the molecule.

(iii) Temperature of gas.

P = 2/3 E. The K.E. of water molecules gas partly converted into the binding energy of the ice.

(a) Our image will be diminished, virtual and erect. This is because when the object lies anywhere between the pole and inifinity, the concave mirror forms a diminished, virtual and erect image. 

(b) Our image will be enlarged, virtual and erect. This is because when the object lies within the focus of a concave mirror, it forms an enlarged, virtual and erect image. 

Correct answer is (a) zero

We have R = {(a,b) :a ≤ b²} , where a, b ∈ R 

For reflexivity, we observe that 1/2 ≤ (1/2)² is not true. 

So, R is not reflexive as (1/2, 1/2) ∉ R 

For symmetry, we observe that − 1 ≤ 3² but 3 > (−1)² 

∴ (−1, 3) ∈ R but (3, −1) ∉R. 

So, R is not symmetric. 

For transitivity, we observe that 2 ≤ (−3)² and −3 ≤ (1)² but 2 > (1)² 

∴ (2, − 3) ∈ R and (−3,1) ∈ R but (2, 1) ∉ R. So, R is not transitive. 

Hence, R is neither reflexive, nor symmetric and nor transitive.

The Taxi driver travelled with highest speed. 

How do we say? Let us calculate how long they travelled in One Hour? 

Distance travelled by the Car in One Hour = 80 km (160 ÷ 2) 

Distance travelled by the Bus in One Hour = 50 km (200 ÷ 4) 

Distance travelled by the Truck in One Hour = 60 km (300 ÷ 5)

Have you found out? say now. 

Fastest Taxi, Slowest Bus

I think you should solve this question by yourself. I'm giving you some simple tricks to find out whether the given equation perform SHM or not. Follow this :

Any equation performing a simple harmonic motion has two properties that can be used to determine the nature. 

1. Relation between acceleration and displacement of the object assumed to be undergoing an SHM.
2. SHM usually involves conservation of energy.

An object is undergoing simple harmonic motion (SHM) if;

• the acceleration of the object is directly proportional to  its displacement from its equilibrium position.
• the acceleration is always directed towards the equilibrium position.

The simple harmonic differential equation is

d²x/dt²=−ω²x

a=-w²x

Where x is the displacement from initial position, its double differentiation is acceleration and ω is the angular frequency.

If the equation obeys this differential equation then you have a simple harmonic function.

Simplest way to recognize whether a function is SHM or not, check whether the function consists of a sine or a cosine term or not.

If it consists any sine or cosine term it will surely be simple harmonic.

<FRAMESET>tag and <FRAME>tag 

Attributes of <FRAMESET>

• Rows: Used to divide screen in row wise 
• Cols: Used to divide screen in column wise 
• Attributes of <FRAME>
• SRC: Species name of web page to be loaded in Frame 
• NAME: Gives a name for the frame.

Eg. <FRAMESET Rows= “50%,*”>

<FRAME SRC= “page1.htm”>

<FRAME SRC= “page2.htm”>

</FRAMESET>

1. Src: It specie the URL of the document to be loaded in the frame.

2. Scrolling: It indicates scroll bar is to be shown in the frame or not, values are yes, no or auto 

3. Noresize: It stops the resizing of the frame, no value is to be assigned. 

4. Margin width and Margin height: It sets the horizontal and vertical margins, values are in pixels. 

5. Name: It gives a name for the frame. 

6. Target: It species the target frame.

The attributes are 

1. Border: It can act in <Table>tag and in <Frameset> tag. 

2. Bgcolor: It can act in <Table> and in <Body>tag

3. Type: It can act in <OL> and in <Input>tag.

Phosphorous or Gallium

Radon is radioactive element

There are Six(6) sphere.

Option : (c) Fe³⁺

Option : (c) Os

Option : (a) they show variable oxidation states

• All the transition elements are metals. 
• They are hard, lustrous, malleable, ductile and they have high tensile strength. 
• They have high melting points and boiling points. 
• Their metallic character is due to vacant or partially filled (n – 1) d-orbitals, and they involve both metallic and covalent bonding. 
• Since the strength of metallic bonds depends upon the number of unpaired electrons, it increases up to middle i.e., up to (n – 1 )d⁵, hence accordingly melting points and boiling points also increase. 
• After (n – l)d⁵ configuration, the electrons start pairing, hence the metallic strength, melting points and boiling points decrease with the increase in atomic number. 

Option : (c) 14

Option : (c) d-electron

1. Position of Lanthanoids in the periodic table : Group – 3; Period – 6. 

2. They interrupt the third transition series of t/-block elements (i.e. 5 d series) in the sixth period. 

3. They are 14 elements from ₅₈Ce to ₇₁Lu and their position is in between La and Hf. Since they follow lanthanum, they are called lanthanoids.

4. They are called 4f-series elements and for the convenience, they are placed separately below the main periodic table.

5. The actual position of lanthanoids is in between Lanthanum (Z = 57) and Hafnium (Z = 72).

6. Their position is justified due to following reasons :

• All these elements have the same electronic configuration in ultimate and penultimate shells, one electron in 5d-orbital and two electrons in 6s-orbital.
• Group valence of all lanthanoids is 3.
• All lanthanoids from ₅₈Ce to ₇₁Lu have similar physical and chemical properties. 

Option : (c) Ag

Option : (d) 6d

Option : (c) Thorium

• There are some properties similarity between transition and inner transition metals.
• They are placed between s and p-block elements. 
• They are metals with filling of inner suhshells in their electronic configuration. 
• They show variable oxidation slates.  
• They show magnetism. 
• They form coloured compounds. 
• They have catalytic property.

The factors on which the colour of transition metal ion depends are as follows :

• The presence of incompletely filled dorbitals in metal ions. (The compounds with the configuration d° and d’0 are colourless.)
• The presence of unpaired electrons in d-orbitals. 
• d → d transitions of electrons due to absorption of radiation in the visible region. 
• Nature of groups (anions) (or ligands) linked to the metal ion in the compound or a complex. 
• Type of hybridisation in metal ion in the complex. 
• Geometry of the complex of the metal ion.