Correct Answer: 24 cm

Solution : Let $r{_1}$​ and $r{_2}$​ be the radii of the two circles, and let $d$ be the distance between their centres. In this case:
$d=r{_1}​+r{_2}$​
Given that the radii are 18 cm and 8 cm, we have:
$d=18+8=26$ cm
Now, the direct common tangent is

Correct Answer: Percentage

Solution : The correct option is Percentage.

The amount of moisture in the air as compared to the greatest amount that the air may contain at a particular temperature is known as relative humidity, which is stated as a percentage. A relative humidity of 50%, for instance,

Correct Answer: 5% loss

Solution : Given,
A girl purchases 9 mangoes for Rs. 90 and sells 10 mangoes for Rs. 95.
⇒ Cost Price of each mango = $\frac{90}{9} =\text{Rs. }10$
And Selling Price of each mango = $\frac{95}{10} = \text{Rs. }9.5$
Loss percentage = $\frac{10-9.5}{10}\times 100 = 5\%$

Correct Answer: $\frac{m^{2}-1}{n^{2}-1}$

Solution : $\sin A = m\sin B$--------------(i)
$\tan A = n\tan B$
$\frac{\sin A}{\cos A}$ = $n\frac{\sin B}{\cos B}$------------------(ii)
Substituting $\sin B$ from equation (i),
⇒ $\cos B$ = $\frac{n}{m}$$\cos A$----------(iii)
Squaring both sides of equation (i),
⇒ $\sin^{2} A$ = $m^{2}\sin^{2}B$
⇒ 1–$\cos^{2} A$ = $m^{2}(1–\cos^{2}

Correct Answer: Rs. 140

Solution : Let the marked price of the shirt be Rs. $x$.
Price after 15% discount $= x - 0.15x = 0.85x$
So, $0.85x = 119$
$\therefore x = 140$
Hence, the correct answer is Rs. 140.

Correct Answer: Lead

Solution : The correct option is - Lead.

Gelena, commonly known as galena, is a mineral composed primarily of lead sulfide (PbS). It is one of the most important ores of lead and is widely distributed throughout the world.

Correct Answer: cast

Solution : The correct option to fill in the blank is the fourth option.

The word cast in this context means getting rid of or disposing of old clothes. Cast off is the correct phrasal verb to use when indicating the act of discarding something.

Therefore, the

Correct Answer: $25\sqrt{2}$ sq. cm

Solution :
$AD = AB \sin 45^\circ$
$= 10\times\frac{1}{\sqrt2}$
$= 5\sqrt2$ cm
$\therefore$ Area of $\triangle ABC = \frac{1}{2}\times BC \times AD$
$=\frac{1}{2}\times 10 \times 5\sqrt2$
$= 25\sqrt2$ sq. cm
Hence, the correct answer is $25\sqrt2$ sq. cm.

Correct Answer: Arteries

Solution : The correct option is Arteries.

A sphygmomanometer is a medical instrument used to determine blood pressure. Blood pressure refers to the force applied by the blood on the walls of arteries while flowing through them. This device comprises an inflatable cuff that is put

Correct Answer: 22°

Solution : According to the question,
PS × PR = PQ × PT
⇒ $\frac{PQ}{PS}$ = $\frac{PR}{PT}$
⇒ ST || QR
 $\angle$ Q = $\angle$ PST = 96° (corresponding angles between two parallel lines)
Since $\angle$ PST = $\angle$ PRQ + 34°
⇒ 96° = $\angle$ PRQ