Correct Answer: $\frac{4}{9}$

Solution :
AB : PQ = 2 : 3
As $\triangle$ABC is similar to $\triangle$PQR,
$\frac{AB}{PQ}$ = $\frac{BC}{QR}$ = $\frac{CA}{RP}$ = $\frac{AD}{PS}$ = $\frac{BD}{QS}$ = $\frac{DC}{SR}$ = $\frac{2}{3}$
$(\frac{BD}{QS})^2$ = $(\frac{2}{3})^2$ = $\frac{4}{9}$
Hence, the correct answer is $\frac{4}{9}$.

Correct Answer: 9592330

Solution : If the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or a number divisible by 11, then the given number is divisible by 11.
(a) For 9592450 = (9 + 9

Correct Answer: warily into bed

Solution : The first option is the correct answer.

The word warily means cautiously or with caution. It doesn't fit well in the context of the sentence. The intention seems to be to express extreme tiredness, and using warily suggests a cautious or suspicious action,

Correct Answer: (9, 90, 3)

Solution : Given:
(12, 313, 13), (11, 185, 8)

Add the square of the first and the third number to get the second number of the triad.
(12, 313, 13)→12² – 144; 13² – 169; 144 + 169 = 313
(11, 185, 8)→11² – 121;

Correct Answer: 1 and 0

Solution : Given: The expression px³ – qx² – 7x – 6 is completely divisible by x² – x – 6.
So, the roots of x² – x – 6 = 0 will also be the roots of px³ –

Correct Answer: 52

Solution : Given:
20 : 11 :: 102 : ?

Here, divide the first number by 2 and add 1 to it, to get the second number.
Like, 20 : 11; 20 ÷ 2 = 10, 10 + 1 = 11
Similarly, for 102 : ?; 102

Correct Answer: Jahangir 

Solution : The correct answer is Jahangir.

Mehr-un-Nissa, known as Noor Jahan, was the wife of Mughal Emperor Jahangir. Her influence was substantial in the 17th-century Mughal court, owing to her political acumen and cultural patronage. Noor Jahan left an indelible mark with her contributions to the

Correct Answer: Tanvi Shah

Solution : The correct option is Tanvi Shah.

Tanvi Shah is the first Indian female musician to win a Grammy Award. She won the award in 2010 for Best Song Written for Motion Picture, Television, or Other Visual Media for her Spanish lyrics for the

Correct Answer: 800

Solution : Let the speed of flight A be $x$ km/h and the speed of flight B be $y$ km/h.
$\frac{7200}{x} = \frac{7200}{y}$+1-------------------------------(i)
After engine trouble, speed of flight B = $x–\frac{x}{6} = \frac{5x}{6}$ and it takes 36 minutes more than flight A.
$\frac{7200}{x} = \frac{7200×6}{5y}–\frac{36}{60}$-------------------------(ii)
Equating

Correct Answer: 5

Solution : Given: a 7-digit number 54p3987 is divisible by 11
⇒ 5 + p + 9 + 7 – 4 – 3 – 8 = 0 or multiple of 11
⇒ 21 + p – 15 = 0 or multiple of 11
⇒ 6 + p