Correct Answer: 9

Solution : Sum of all interior angles = $14×90^{\circ}$ = $1260^{\circ}$
Let the number of sides of the polygon be $n$.
⇒ $1260^{\circ}$ = $(n-2)×180^{\circ}$
⇒ $(n-2)$ = $\frac{1260}{180}$
⇒ $(n-2)$ = $7$
⇒ $n$ = $2+7$ = $9$
Hence, the correct answer is 9.

Correct Answer: Rohit Dahiya

Solution : The correct answer is Rohit Dahiya.

Rohit Dahiya won bronze medals on the final day of the World Championship 2022 in Sofia, Bulgaria. He defeated his opponent, Ukraine's Ruslan Abdiiev, in the 82 kg. India ended the World U20 Wrestling Championships 2022 with sixteen medals, which comprised one gold, four silvers, and eleven bronze medals.

Correct Answer: Kerala

Solution : The correct option is Kerala.

The Indian Navy Sailing Championship 2022, celebrating both Azadi ka Amrit Mahotsav, and Khelo India, was held at the picturesque Indian Naval Academy (INA) in Ezhimala, Kerala, from October 18th to 21st, 2022. This premier sailing event saw nearly 100 yachtsmen and women from all three Indian Naval Commands compete in three formats (Fleet Racing, Match Racing, and Team Racing) across five different boat classes.

Correct Answer: 4 : 21

Solution :
AD : DB = 2 : 3
Let AD =$2x$
DB = $3x$
Now, the ratio of the area of the similar triangle is equal to the square of the ratio of their corresponding sides.
Hence, in similar $\triangle ABC$ and $\triangle ADE$
$\frac{\text{Area of}\triangle ABC}{\text{Area of}\triangle ADE}=\frac{AB^2}{AD^2}$
⇒ $\frac{\text{Area of}\triangle ABC}{\text{Area of}\triangle ADE}=\frac{(5x)^2}{(2x)^2} = \frac{25}{4}$
Let the area of$\triangle ABC$ be 25k and the area of $\triangle ADE$ be 4k
$\therefore$ Area of quadrilateral BDEC = Area of $\triangle ABC-$Area of $\triangle ADE$
= 25k – 4k = 21k
The ratio of the area of $\Delta ADE$ and the area of quadrilateral BDEC = 4 : 21.
Hence, the correct answer is 4 : 21.

Correct Answer: 2

Solution : The appropriate answer is option "enjoying" because ''sat'' is an  intransitive verb  followed by the adverb" ''there'' "we need a gerund to indicate what we were doing while we sat there  i.e. ''enjoying''.

Therefore, the correct statement should be "We sat there enjoying the view.". 

Correct Answer: certain

Solution : The most appropriate antonym of the word "suspicious" in the given sentence is the first option.

Explanation for each option:

1. "Certain" - This is the correct antonym for "suspicious" as it represents a lack of doubt or uncertainty, which contrasts with being suspicious.

2. "Problematic" - This word is not an antonym but relates to the issue with the web server, and it does not contrast with "suspicious".

3. "Submit" - It is a verb with several meanings, often relating to yielding to authority, presenting something for consideration.

4. "Portal" - It commonly refers to an entry point, whether physical, digital, or conceptual, providing access to something else.

So, the correct sentence would be: "Although the web server was problematic, Sudha was certain that she will submit her form on the portal by evening."

Correct Answer: Gujarat

Solution : The correct option is Gujarat.

On October 2, 1869, in Porbandar, a coastal settlement in the Indian state of Gujarat, Mahatma Gandhi was born. Gandhi went on to play a significant role in the campaign for Indian independence from British colonial control and is admired all over the world for his nonviolent resistance tenets, which he called "Satyagraha."

Correct Answer: 49

Solution : Given:
01 : 36 :: 02 : ?

Like, 01 : 36→1 + 5 = 6² = 36
Similarly, for 02 : ?→2 + 5 = 7² = 49

So, 02 is related to 49. Hence, the second option is correct.

Correct Answer: $\frac{20}{3}\ \text{cm}$

Solution :
Join OP and OT.
Let OT intersect PQ at a point R.
Then, TP = TQ (The lengths of tangents drawn from an external point to a circle are equal) and $\angle$PTR = $\angle$QTR.
⇒ TR $\perp$ PQ and TR bisect PQ.
⇒ PR = RQ = 4 cm
OP = 5 cm
So, OR² = OP² – PR² = $\sqrt{5^2-4^2}=\sqrt{9}=3$ cm
Let TP = $x$ cm
and TR = $y$ cm
From right ΔTRP, we get,
TP² = TR² + PR²
⇒ $x$² = $y$² + 16
⇒ $x$² − $y$² = 16-------------------------(i)
From right ΔOPT, we get
TP² + OP² = OT²
⇒ $x$² + 5² = ($y$ + 3)² [$\because$ OT² = (OR + RT)² ]
⇒ $x$² − $y$² = 6$y$ − 16------------------(ii)
From (i) and (ii), we get,
6$y$ − 16 = 16
⇒ 6$y$ = 32
⇒ $y$ = $\frac{16}{3}$
Putting the value of $y$ in equation (i), we get,
$x$² $=16 + (\frac{16}{3})^2=16+\frac{256}{9}=\frac{400}{9}=\frac{20}{3}\ \text{cm}$
Hence, the correct answer is $\frac{20}{3}\ \text{cm}$.

Correct Answer: queue

Solution : The correct choice is the first option.

Explanation:

In the context of people waiting in line, the term commonly used is queue.

Therefore, the complete sentence is: Anders couldn't get to the bank until just before it closed, so of course the queue was endless.