Correct Answer: 5100

Solution : Multiply the given numbers by 3 and then add 6 to the resultant number to obtain the next number (pattern starting from 18).

(18 × 3) + 6 = 54 + 6 = 60
(60 × 3) + 6 = 180 + 6 = 186

Correct Answer: $\frac{x}{2y}$

Solution : $\frac{1}{8}\left\{\left(x+\frac{1}{y}\right)^2-\left(x-\frac{1}{y}\right)^2\right\}$
$=\frac{1}{8}(x^2 +\frac{1}{y^2} + 2×x×\frac{1}{y} - x^2 - \frac{1}{y^2} + 2×x×\frac{1}{y})$
$=\frac{1}{8}(\frac{4x}{y})$
$=\frac{x}{2y}$
Hence, the correct answer is $\frac{x}{2y}$.

Correct Answer:

Solution : As per the mirror image properties, closer things appear close to the mirror in the reflection.
Here, according to the information provided, the mirror is placed on the right side of the figure (on Line MN). So, the left side of the reflected image will appear

Correct Answer: K B O F Y K O

Solution : Given:
F _ _ Y _ _ K B _ O F _ B Y _

To fill the series we have to divide the series – F _ _ Y _ / _ K B _ O /

Correct Answer: 8000

Solution : The total number of children in areas P and Q together = Number of children in area P + number of children in area Q
= 20% of 10,000 + 30% of 20,000
= $\frac{20}{100}\times10000+\frac{30}{100}\times 20000$
= $2000+6000$
= $8000$
Hence, the correct answer is

Correct Answer: –16

Solution : (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2xz
⇒ 2(xy + yz + zx) = (x + y + z)² – (x² + y² + z²)
⇒

Correct Answer: The usage of chemicals, insecticides and pesticides

Solution : The fourth option is the correct choice.

The change from "use" to "usage" is a subtle improvement, making the sentence more formal and grammatically accurate. Usage is a noun, while use can function as both a verb and a

Correct Answer: Mulk Raj Anand

Solution : The correct answer is Mulk Raj Anand.

"Coolie", a novel by Mulk Raj Anand, initially published in 1936, marked his second literary work and solidified his status as a prominent English author in India. It presents a scathing critique of British colonial rule

Correct Answer: 8

Solution : Given:
$3^{11}+3^{12}+3^{13}+3^{14}$
= $3^{11}(1+3+3^2+3^3)$
= $3^{11}(40)$
Since 40 is divisible by 8,
Therefore, the above expression is also divisible by 8.
Hence, the correct answer is 8.

Correct Answer: 285

Solution : The number of natural numbers less than 1000 that are divisible by 5. 
$⇒\left\lfloor\frac{999}{5}\right\rfloor = 199$
The number of natural numbers less than 1000 that are divisible by 7. 
$⇒\left\lfloor\frac{1000}{7}\right\rfloor = 142$
However, we've double-counted numbers that are divisible by both 5 and 7, i.e.,