Correct Answer: 3 cm

Solution :
Given , AB = 8 cm
We know that the perpendicular from the centre of a circle to a chord bisects the chord.
AM = MB = $\frac{1}{2}×8=4$ cm
OA = 5 cm
From ∆ AOM,
OA² = OM² + AM²

Correct Answer: $\sqrt{3}$

Solution : Taking LCM of the given indices i.e., LCM of 2 and 3 is 6.
$\Rightarrow \sqrt[3]{2}=2^\frac{1}{3}=2^\frac{2}{6}=\sqrt[6]{2^2}=\sqrt[6]{4}$
$\Rightarrow \sqrt{3}=3^\frac{1}{2}=3^\frac{3}{6}=\sqrt[6]{3^3}=\sqrt[6]{27}$
Thus, $\sqrt{3}$ is greater.
Hence, the correct answer is $\sqrt{3}$.

Correct Answer: 187

Solution : List of all the prime numbers between 58 and 68
= 59, 61 and 67
Now, (59 + 61 + 67) = 187
Hence, the correct answer is 187.

Correct Answer: Leaves

Solution : The correct answer is Leaves.

Leaves are sometimes referred to as the "lungs of plants" because they serve an important role in gas exchange, which is analogous to the function of animal lungs. During photosynthesis, plants absorb carbon dioxide (CO₂) from the atmosphere

Correct Answer: price and output

Solution : The correct option is price and output.

A supply function is an economic term that, while leaving other variables constant, expresses the relationship between the cost of a good or service. It is common for the supply function to slope positively, indicating

Correct Answer: 500

Solution : Let $x$ be the initial value.
The number becomes 0.8$x$ after being reduced by 20%.
The number becomes 1.2 × (0.8$x$) = 0.96$x$ after increasing by 20%. This is 20 less than the initial number.
According to the question,
0.96$x$  =  $x$ – 20
⇒

Correct Answer: Brother

Solution : Given:
A + B ⇒ A is the sister of B
A – B ⇒ A is the husband of B
A × B ⇒ A is the son of B
A ÷ B ⇒ A is the mother of B

As per the given

Correct Answer: special status of Jammu and Kashmir State

Solution : The correct answer is the special status of Jammu and Kashmir State.

It allowed Jammu and Kashmir to have its constitution, flag, and legislative authority. The Indian constitution's "Temporary, Transitional and Special Provisions" Part XXI contains Article 370. It

Correct Answer: $\frac{11}{36}$

Solution : Given: $\sin\phi=\frac{5}{6}$.
Now, $\cot\phi \cdot \sin\phi \cdot \cos\phi$
= $\frac{\cos\phi}{\sin\phi}×\sin\phi×\cos\phi$
= $\cos^2\phi$
= $1–\sin^2\phi$
= $1–(\frac{5}{6})^2$
= $1–\frac{25}{36}$
= $\frac{11}{36}$
Hence, the correct answer is $\frac{11}{36}$.

Correct Answer: (4)

Solution : The correct choice is the fourth option, as there is no improvement in the sentence.

Auxiliary verbs are used to form the simple future tense. "Shall" is used in the first person and "will" is used for the second and third persons. Thus, the sentence