Correct Answer: 12

Solution : Let the number of sides be $n$.
Then, number of diagonals of the polygon = $\frac{n(n-3)}{2}$
So, $\frac{n(n-3)}{2}=54$
⇒ $n^2-3n=108$
⇒ $n^2-3n-108=0$
⇒ $(n-12)(n+9)=0$
⇒ $n$ =12, the negative value is rejected.
Hence, the correct answer is 12.

Correct Answer: 168

Solution : Education = 6% 
Health = 4%
According to the question
Total expenditure for education and health  = 6% + 4% = 10%
= 10% of 1680
= $\frac{10 \times 1680}{100}$
= 168
Hence, the correct answer is 168.

Correct Answer: Tuesday

Solution : Given: 
18th October 2006 =  Wednesday.

In a normal year, we have one odd day; in a leap year, we have two odd days. So, the total odd days –
18th October 2000 to 18th October 2001→1 odd day
18th October 2001 to 18th October

Correct Answer: evaporative cooling

Solution : The correct option is evaporative cooling.

The cooling provided by a desert cooler is based on the evaporative cooling principle. This process involves the evaporation of water into the surrounding air, which causes cooling. Desert coolers work well in hot, dry locations where

Correct Answer: Futile search

Solution : The correct choice is the fourth option.

The idiom "wild goose chase" means a completely useless search and a waste of time.

This makes the fourth option, which states "futile search", the appropriate meaning of the given idiom.

Correct Answer: Colomn

Solution : The first option is correct.

The incorrectly spelled word is colomn. The correct spelling is column. The error involves replacing "o" with "u," referring to a vertical pillar or post typically used for support.

The meanings of the other options are as follows:

Correct Answer: $5\sqrt3$ metres

Solution : Given: A person observes that the angle of elevation at the top of a pole of height 5 metres is 30°.
We know the formula, $\tan\theta = \frac{\text{Height}}{\text{Base}} = \frac{\text{Height of tower}}{\text{Distance of person from pole}}$

In $\triangle ACB$, $\tan\ 30°=\frac{AB}{BC}$
⇒ $\tan30° =

Correct Answer: 20 seconds

Solution : Distance to be covered = 150 m
Relative speed = 36 – 9 = 27 km/hr = 27 × $\frac{5}{18}$ = $\frac{15}{2}$ m/s
$\therefore$ Time = $\frac{\text{length of the train}}{\text{Relative Speed}}$ = $\frac{150}{\frac{15}{2}}$ = 20 seconds
Hence, the correct answer is 20 seconds.

Correct Answer: 1232 cm³

Solution : Given: Area of the base of a cone = 154 cm²
Curved surface area of cone = 550 cm²
We know that,
Area of the base of the cone with radius $r=\pi r^2$
⇒ $\pi r^2 = 154$
⇒ $\frac{22}{7}\times r^2

Correct Answer: INR 5,160

Solution : Total sales of vanilla flavour = INR 3,300
16.5% of the total sales of ice cream flavours = 3300
1% of total sale of ice cream flavours = $\frac{3300}{0.165}$ = 20000
Total sales of chocolate flavour = 25.8% of 20000 = 5160
Hence, the