Correct Answer: 273

Solution : The ratio of 2nd : 3rd = 9 : 13
And the ratio of 1st : 3rd = 2:7
3rd number is common in both ratios, so to make the value equal, we need to multiply by 7 in 9 : 13 and by 13 in 2 : 7.
We get 1st : 2nd : 3rd = 26 : 63 : 91
Let the 1st, 2nd and 3rd number be 26x, 63x, and 91x.
According to the question,
26x + 63x + 91x = 540
⇒ 180x = 540
$\therefore$ x = 3
Thus, the 3rd number = (91 × 3) = 273
Hence, the correct answer is 273.

Correct Answer: $h(\cot\alpha+\cot\beta)$

Solution :
$AD=h$ unit
In $\Delta ADB$,
$\tan\alpha=\frac{AD}{BD}$
$⇒\tan\alpha=\frac{h}{BD}$
$⇒BD=h\cot\alpha$ --------------------------------------(1)
In $\Delta ADC$,
$\tan\beta=\frac{AD}{DC}$
$⇒\tan\beta=\frac{h}{DC}$
$⇒DC=h\cot\beta$ -------------------------------------(2)
Now $BC=BD+DC$
$⇒BC=h\cot\alpha+h\cot\beta$
$\therefore BC=h(\cot\alpha+\cot\beta)$
Hence, the correct answer is $h(\cot\alpha+\cot\beta)$.

Correct Answer: varied

Solution : The third option is the correct choice.

In the context of posters, the sentence discusses the different purposes or uses of posters, which can range from cautionary messages to advertising sales or events. Varied means diverse or having a wide range of different kinds, which fits well in this context.

The meanings of the other options are as follows:

• Little: It means a small amount, not much, or a small degree of something.

• Much: It means a large amount or a high degree of something.

• Similar: It denotes having qualities or characteristics that are alike or resemble each other.

Correct Answer: (2)

Solution : The error lies in the second part of the sentence.

The sentence contains an error in verb tense consistency. The verb form has should be changed to had to maintain the past tense consistency since the sentence is referring to a past event. Moreover, childish should be replaced with childlike, as childish means silly, whereas childlike means having the good qualities, such as innocence, associated with a child.

Therefore, the correct sentence is: "It was only when they met that they found he had a childlike simplicity in him".

Correct Answer: $\frac{3}{5}< \frac{2}{3}< \frac{11}{15}$

Solution : Given: The numbers are $\frac{2}{3}, \frac{3}{5}, \frac{11}{15}$.
To find the greatest fraction, we have to find the LCM of denominators.
LCM of denominators $=$ LCM $(3, 5, 15) = {(3×5)} = 15$
We have to make all denominators the same for comparison,
$ ⇒\frac{2}{3}\times \frac{5}{5} = \frac{10}{15} $
$ ⇒\frac{3}{5}\times \frac{3}{3} = \frac{9}{15} $
$ ⇒\frac{11}{15}\times \frac{1}{1} = \frac{11}{15} $
Now, by comparing numerators $(9<10<11)$.
So, we can say $\frac{3}{5}< \frac{2}{3}<\frac{11}{15}$.
Hence, the correct answer is $\frac{3}{5}< \frac{2}{3}<\frac{11}{15}$.

Correct Answer: Nephew

Solution : As per the given information, the family tree will be as follows –

Here, the quadrilateral represents the male, and the circular figure represents the female in the figure.

So, from the above family tree, Rajiv is the nephew of Sunil. Hence, the first option is correct.

Correct Answer: 6

Solution : According to the question, we have to determine the common region between cardboard and box but this region should not be common to white. In the diagram, the shaded part represents the region common to both cardboard and boxes only.

The number of cardboard boxes that are not white is 6. Hence, the first option is correct.

Correct Answer: Panch Mahal

Solution : The correct answer is Panch Mahal.

One of Fatehpur Sikri's most well-known structures is the Panch Mahal, also known as the Dream in Stone. It was constructed by Akbar. Akbar ordered the construction of the Panch Mahal, also known as the "Five Level Palace".The fact that this building, made of Sikri sandstone, is close to the Zenana quarters lends support to the idea that it was used for recreation and relaxation.

Correct Answer: 2

Solution : The correct option is the second option.

The original sentence has an error with the pronoun. "Me" should be replaced with "my". Here, "my" is used as a possessive adjective to indicate ownership or possession of the action, which is leaving the payment until next year.

Therefore, the correct sentence is," "Do you mind my leaving this payment until next year?"

Correct Answer: Rs. 8835

Solution : The customer purchases an article worth Rs. 10000 using a credit card.
After a flat discount of Rs. 500 the price of the article
= (10000 – 500)
= Rs. 9500
After a further discount of 7%, the price of the article becomes,
= $9500×(\frac{100-7}{100})$
= Rs. 8835
Hence, the correct answer is Rs. 8835.