Correct Answer: 3

Solution :
The diameters of the two circles are 12 cm and 20 cm.
The distance between their centres is 16 cm.
According to the diagram,
The two circles are touching each other externally.
So, the number of common tangents will be 3.
Hence, the correct answer

Correct Answer: got permission

Solution : The correct choice is the third option.

The original sentence contains an unnecessary article "a" before "permission". In English, when referring to the concept of permission, the noun "permission" is typically used without an article, as it is not a countable

Correct Answer: Pyrex glass

Solution : The correct answer is Pyrex glass.

Glasses are formed of silica. Although glass do not have any sharp melting point but it melts slowly because of heat. Because of this phenomenon glasses of windows become thick at bottom and thin at upper portion. Pyrex

Correct Answer: (3)

Solution : The correct choice is the third option.

Explanation:

There is an error in the comparison structure. When comparing two actions or preferences, the verb "prefer" is followed by the preposition "to" and not "than". 

Therefore, the correct sentence is: On a holiday, I prefer

Correct Answer: no smoke without fire

Solution : The most appropriate idiomatic expression to fill in the blank is the first option.

This expression means that there is usually a reason or cause behind a rumour or accusation. In the context of the sentence, it suggests that there might be

Correct Answer: His father praised him.

Solution : The correct choice is the fourth option.

Active voice emphasises the doer of the action, while passive voice emphasises the receiver. To convert passive to active, we make the subject perform the action and rephrase the verb.

The structure of the

Correct Answer: 9

Solution : TP = 12 cm
PB = $x$ + 7 cm
PA = $x$ cm
TP$^{2}$ = PA $\times$ PB
⇒ $12^{2} = x \times (x + 7)$
⇒ $144 = x^{2} + 7x$
⇒ $ x^{2} + 7x-144=0$
⇒ $(x-9)(x+16) = 0$
⇒ $x =

Correct Answer: 2

Solution : Taking dice positions 1 and 3 with 2 as the common face,

Moving clockwise from the common face with 2,

So, pairs of opposite faces are –

So, the face opposite to the one containing 3 is 2. Hence, the second option is correct.

Correct Answer: 5

Solution : Given: The unit digit of the sum of the first 111 whole numbers.
The sum of first 111 whole numbers = 0 + 1 + 2 + 3 +.........+ 109 + 110
Using formula of sum of A.P. = $\frac{n}{2}[a+l]$
Where $a$ is the first

Correct Answer: (3)

Solution : The sentence can be improved using the third option.

The third option, "agonises me most", is correct because it places the verb "agonises" in its appropriate position in the sentence. The word order in this option is grammatically sound and idiomatic, effectively expressing that the