Explore topic-wise InterviewSolutions in Current Affairs.

1. Borane – Boron hydride 

2. Boric acid – H₃BO₃ 

3. Borax – Na₂B₄O₇ .10H₂O 

4. Al₂O₃ – Amphoteric oxide

1. When water of moist air reacts with boron halide hydrogen chloride is formed which causes fumes,

2. BCl₃ + 3H₂O → H₃BO₃ + 3HCl

1. Diborane catches re spontaneously upon exposure to air. It burns in oxygen releasing an enormous amount of energy. 

B₂H6 + 3O₂ → B₂O₂ + 3H₂O; ∆H^Θ -1976 kJ mol^-1

2. Diborane is readily hydrolysed by water to give boric acid.

B₂H₆ (g) + 6H₂O(l) → 2B(OH)₃ (aq) + 6H₂(g)

Correct option: 1. Dermis

Healthy skin requires special care to maintain its health, elasticity, vibrancy and color.

a. Specialized dishes

In satellite kitchen Specialized dishes are prepared.

c. Thermal shocks

Chef coat should be made of cotton because it protect’s body by absorbing Thermal shocks.

(a) & (c)

(a) Increase in global temperature

(c) Increase in air pollution

The full form of EDII is Entrepreneurship Development Institute of India (EDII).

(a) Salmonella typhi

Typhoid is caused by Salmonella typhi.

(b) Hypertension

Sleep apnea is one of the symptoms of Hypertension.

(a) Madhumeh

Diabetes is commonly known as Madhumeh.

(b) 120 days

Life span of RBC is 120 days.

Correct option: a. White button mushroom

Correct option: c. Immature mango

Given:

Speed = y km/hr

Distance = x km

Time = z hours

Formula Used:

Speed = (Distance/Time)

Calculation:

y = x/z

If distance is constant 

Then, Speed ∝ 1/Time

So, x is constant

∴ y ∝ 1/z           

Given:

Distance travelled in the downstream = 20 km

And the time is taken to travel the distance in the downstream = 30 minutes.

Speed of the current = 10 km/hr

Formula used:

If x is the speed of the boat and y is the speed of the current, then

Downstream speed = x + y

1 hour = 60 minutes

Speed = distance/time

Calculation:

Let the speed of a boat be x km/hr and speed of the current be y km/hr

Downstream speed = (20)/(30/60)

⇒ 20 × 60/30

⇒ 40 km/hr

Downstream speed = x + y

⇒ 40 = x + y

⇒ 40 = x + 10

⇒ x = 40 - 10

⇒ x = 30 km/hr

∴ The speed of a boat is 30 km/hr

Concept:

Group: 

An algebraic set G* (G is set of numbers may be set of integers, * is any mathematical binary operation ) is called a group if 

- It is closed 

- It follows associate property

- It is having an identity in a group

- It is having inverse in group

Homomorphism 

Homomorphism is a mapping f from a group (G* ) and another group (G',o) where f(a*b) = f(a) of f(b).

Example:

We have one Group (R +) which is an additive group of real numbers, and then we have another group (R₀₊ ,× ), which is a group of whole numbers.

We have a mapping f(x) = e ^x

Then f(x₁ + x₂ ) = e (x₁ + x₂) = ex₁ .ex₂

Clearly, this satisfies the condition of the group (R0+,× ), So there is a homomorphism.

Isomorphism

Isomorphism is a type of homomorphism. 

Along with homomorphism, another characteristic is the mapping should be one to one and onto

One One mapping means, if f(a) = f(b), then a = b

It should be onto, which means every number in G, must have a reflection in G'.

In another word, we can say they must have a one-to-one correspondence between their elements. 

An example of Isomorphism mapping is 

f (Z + ) → f (3Z + ); f(x) = 3x

Where Z is a set of integer

If f(x₁) = f (x₂)

3 x₁ = 3 x₂

x₁ = x₂

Also, all elements of (Z + ) for the function will have the reflection in Z + 

Explanation:

From above concepts and given examples, we can conclude that the Two groups G and G' of the same order having one-to-one correspondence between their elements is called Isomorphisam. 

So, Isomorphism is the correct option

• Automorphism: It is the type of Isomorphic mapping done on same group. Here, in the question, it is given the mapping is between two different groups, so this cannot be the answer. 
• Endomorphism: Endomorphism is a type of homomorphism but within the same group.

p(1)=1²-1+1=1

Given 2x² - 3x - 1 = 0

x² - 3/2 x - 1/2 = 0

x² - 3/2 x = 1/2

x² - 3/2 x + (3/4)² = 1/2 + (3/4)²

\({{(x-3)}\over2}^2\) = 1/2 + 9/16

\({{(x-3)}\over2}^2\) = (8+9)/16

x - 3/2 = ±\(\sqrt{17}\)/4

x = +\(\sqrt{17}\)/4 + 3/2

⇒ \(\frac{(\sqrt{17}+ 6)}4\)

x = - \(\sqrt{17}\)/4 + 3/2

⇒ \(\frac{(-\sqrt{17}+ 6)}4\)