Correct Answer: –6

Solution :

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
⇒ 6² = 38 + 2ab + 2bc + 2ca
⇒ (ab + bc + ca) = $\frac{(36 – 38)}{2}$
⇒ (ab +

Correct Answer: MJLO

Solution : Let's check each option –
First option: KNJZ; K + 3 = N; N – 4 = J; J – 10 = Z
Second option: FIEU; F + 3 = I; I – 4 = E; E – 10 = U
Third option: MJLO; M

Correct Answer: H. P. Blavatsky and Colonel Olcott

Solution : The correct answer is H. P. Blavatsky and Colonel Olcott.

The Theosophical Society, established in 1875 in New York City, is the organisational body of Theosophy, an esoteric new religious movement. Co-founded by Helena Blavatsky, a Russian mystic and

Correct Answer: alluring

Solution : The third option is the correct choice.

The word alluring conveys the idea of the shop window being attractive and enticing. This choice aligns with the context, which describes the shop window as displaying various captivating items such as magic balls, magic hens, wonderful cones,

Correct Answer: 9

Solution : HCF of 20, 30 and 40 = 10
Number of pieces from 20m long iron bar = $\frac{20}{10} = 2$
Number of pieces from 30m long iron bar = $\frac{30}{10} = 3$
Number of pieces from 40m long iron bar = $\frac{40}{10} = 4$
Total

Correct Answer: (6, 17, 30)

Solution : Given:
(14, 25, 38); (8, 19, 32)

The logic here is→(The second number – The first number) = 11; (The third number – The second number) = 13
(14, 25, 38)→25 – 14 = 11; 38 – 25 = 13
(8, 19, 32)→19

Correct Answer: blatent

Solution : The correct answer is the second option.

Explanation: The correct spelling is "blatant", not "blatent". The word "blatant" is an adjective used to describe something obvious, flagrant, or done without any attempt to conceal it. In the context of the sentence, it describes a disregard

Correct Answer: Fifth and Sixth

Solution : The correct option is the Fifth and Sixth

The term "rolling plan" typically refers to an economic planning approach where plans are continuously updated and modified rather than being fixed for a specific period, such as a five-year plan. The concept of the

Correct Answer: Mars

Solution : The correct answer is Mars.

Mars is not a Jovian planet. Mars is a terrestrial planet. The Jovian planets are Jupiter, Saturn, Uranus and Neptune. They orbit far from the sun. These planets have no solid surfaces and are essentially large balls of gas

Correct Answer: $0$

Solution : Given: $\frac{x}{(b–c)(b+c–2a)}=\frac{y}{(c–a)(c+a–2b)}=\frac{z}{(a–b)(a+b–2c)}$
Let $\frac{x}{(b–c)(b+c–2a)}=\frac{y}{(c–a)(c+a–2b)}=\frac{z}{(a–b)(a+b–2c)}=k$.
${x}=k{(b–c)(b+c–2a)}$ (equation 1)
${y}=k{(c–a)(c+a–2b)}$ (equation 2)
${z}=k{(a–b)(a+b–2c)}$ (equation 3)
Adding equations 1, 2, and 3 respectively, we get,
$x+y+z=k{(b–c)(b+c–2a)}+k{(c–a)(c+a–2b)}+k{(a–b)(a+b–2c)}$
$x+y+z=k[(b–c)(b+c–2a)+(c–a)(c+a–2b)+(a–b)(a+b–2c)]$
$x+y+z= k[b^2+bc–2ab–bc–c^2+2ac+c^2+ac–2bc–ac–a^2+2ab+a^2+ab–2ac–ab–b^2+2bc)$
$x+y+z$ = 0
Hence, the correct answer is 0.