Correct Answer: 25

Solution : Given: ab + bc + ca = 12
(a + b + c) = 7
Squaring both sides, we get,
⇒ (a + b + c)² = 7² = 49
⇒ a² + b² + c² + 2(ab + bc

Correct Answer: –35

Solution : We know that, (A + B)³ = A³ + B³ + 3AB(A+B)
⇒ (–5)³ = A³ + B³ + 3 × 6(–5)
⇒ –125 = A³ + B³ – 90
$\therefore$ A³ + B³ =

Correct Answer: OUJ

Solution : Given:
PAL : RDP :: MRF : ?

Add the increasing order of the numbers, starting from 2 in the letters to get the required code.
Like, P + 2 = R; A + 3 = D; L + 4 = P
Similarly, M +

Correct Answer: 3616

Solution : Given: $\frac{(a+b+c)}{2}=16$
$⇒ a+b+c=32$
Also given $2ab+2 bc+2ca=120$
We know that, $(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca$
Putting the values we get:
⇒ $(32)^2=a^2+b^2+c^2+120$
⇒ $1024-120=a^2+b^2+c^2$
⇒ $a^2+b^2+c^2=904$
$\therefore 4(a^2+b^2+c^2)=4\times904=3616$
Hence, the correct answer is 3616.

Correct Answer: Rotavac

Solution : The correct option is Rotavac.

The World Health Organization (WHO) had pre-qualified Rotavac, India's first locally-made vaccine. Being pre-qualified entitles the vaccine to overseas sales to numerous South American and African nations. The vaccination was a part of India's national immunisation program and was

Correct Answer: 3

Solution : Let us assume $B$ as the speed of the boat in still water (m/s) and $S$ as the speed of the stream (m/s)
Effective speed upstream = (B – S) m/s
Effective speed downstream = (B + S) m/s
For upstream:
Distance = (B –

Correct Answer: tuut

Solution : Given:
_utt_tt_ttu_

To fill the series we have to divide the series→_ut / t_t / t_t / tu_
Let's check each option –
First option: uutt; uut / tut / ttt / tut (No repeated pattern has been found.)

Correct Answer: 67, 96, 57

Solution : Given: 
ROW

Number representations of each letter –
R→58, 67, 76, 85, 99
O→55, 69, 78, 87, 96
D→57, 66, 75, 89, 98

Let's check the options –
First option: 58, 66, 78; O and W cannot be represented by 66 and 78

Correct Answer: Santoor

Solution : The correct option is Santoor.

Pandit Shivkumar Sharma is remembered for his mastery of playing the santoor. The santoor is a traditional Indian musical instrument with origins in the Kashmir region, and Shivkumar Sharma has played a key role in popularising and elevating its

Correct Answer: Appropriate

Solution : The third option is the correct answer as "appropriate" is an adjective that describes something as suitable or fitting for a particular situation.

The meaning of the other options is:

Appropriately: Doing something in the right way or manner, fitting for the situation.

Suit