Correct Answer: $\frac{61}{3}+\frac{17}{3 \sqrt{5}}$

Solution : Given: $\sin A =\frac{2}{3}$
We know that $\sin A=\frac{\text{Perpendicular}}{\text{Hypotenuse}}=\frac{2}{3}$
We know, Hypotenuse² = Base² + Perpendicular²
⇒ Base = $\sqrt{3^2-2^2}=\sqrt5$
We know, $\cos A =\frac{\text{Base}}{\text{Hypotenuse}}=\frac{\sqrt{5}}{3}$
And,
⇒ $\tan A=\frac{\sin A}{\cos A}=\ \frac{2}{\sqrt{5}}$
Now,
$\left ( 7-\tan A \right )\left ( 3+\cos

Correct Answer: (1, 2, 16)

Solution : Given:
(6, 2, 96); (5, 6, 240)

Like, (6, 2, 96)→(6 × 2) × 8 = 96
(5, 6, 240)→(5 × 6) × 8 = 240

Let's check the options –
First option: (4, 1, 6)→(4 × 1) × 8 = 32 ≠

Correct Answer: 13 m

Solution : First, we will draw the diagram, as per the given instructions –

Here, A is the starting point and F is the finishing point.
AB = 29 m; BC = DE = 16 m; CD = BE = 17 m; DF = 21 m

Correct Answer: CEADFACEAE

Solution : Given:
AA_D_F_AC_E_A_ _D_F_ACD_F

To fill the series we have to divide the series – AA_D_F / _AC_E_ / A_ _D_F / _ACD_F

Let's check each option –
First option: CAFDFAACEE; AACDAF / FACDEF / AA A

Correct Answer: 24 cm

Solution :
As shown in the given figure,
Perpendicular drawn from the centre of a circle to the chord bisects the chord.
Therefore, AC = BC and $\angle$OCB = 90°
Thus, $\triangle$OCB is a right-angled triangle.
By Pythagoras Theorem,
$OB^2 = OC^2 + CB^2$
$⇒CB^2 =

Correct Answer: independent of the Legislature

Solution : The correct option is independent of the legislature.

The President of presidential governance is elected by the people in a separate election from the legislature. Regardless of parliamentary backing, the President has a term of four to five years. This separation

Correct Answer: XIFGERU

Solution : Given:
OBESITY is written as EBOHYTI. 

Change the position of the first and last three letters and write the opposite letter of the middle letter of OBESITY, to obtain the required code –

Thus, OBESITY is coded as EBOHYTI.
Similarly, follow the same pattern for

Correct Answer: increase

Solution : The second option is the correct choice.

Wane means to decrease or diminish in size, intensity, or power.
Increase, on the other hand, means to grow, expand, or become larger.

The meanings of the other words are:

Fall: It denotes a descent or drop from

Correct Answer: Bottom

Solution : The correct choice is the second option.

The term bottom refers to the lowest part or point, contrasting with the highest point represented by the apex. So, both nadir and bottom serve as antonyms for apex in different contexts.

The meanings of the other

Correct Answer: have been know the result

Solution : The error lies in the third option.

Explanation: The error lies in the use of the phrase "have been know". The correct form should be "have known" when expressing future perfect tense. The structure is "will have known", indicating that the