Correct Answer: 20%

Solution : Let the original radius be $r$.
New radius $=r+\frac{20}{100} \times =1.2r$
Old circumference $=2\pi r$
New circumference $=2 \pi \times 1.2r=2.4\pi r$
Increase in circumference $=2.4\pi r - 2 \pi r=0.4\pi r$
$\therefore$ Percentage increase in circumference $=\frac{0.4 \pi r}{2\pi r} \times 10=20\%$
Hence, the

Correct Answer: have borne

Solution : The third option is the correct choice.

Explanation: The original sentence contains a subject-verb agreement error. The subject "efforts" is plural; therefore, the verb should also be plural. The corrected verb form is "have borne", which maintains agreement with the plural subject "efforts".

The

Correct Answer: a - (iii), b - (i), c - (iv), d - (ii)

Solution : The correct options are a - (iii), b - (i), c - (iv), and d - (ii).

The Kalahari Desert is a vast semi-arid sandy savanna in Southern Africa that covers a considerable portion

Correct Answer: Leonardo da Vinci

Solution : The correct option is Leonardo da Vinci.

One of the best-known pieces of art in the world is Leonardo da Vinci's painting of the Last Supper, an Italian Cenacolo. At a table marking the Jewish holiday of Passover, The Last Supper shows

Correct Answer: $\frac{25}{12}$

Solution : Given: $\operatorname{cos} \theta=\frac{4}{5}$
We know that, $\operatorname{sin} \theta=\sqrt{1-\operatorname{cos}^2 \theta}$
$⇒\operatorname{sin} \theta=\sqrt{1-(\frac{4}{5})^2}$
$⇒\operatorname{sin} \theta=\sqrt{1-\frac{16}{25}}$
$⇒\operatorname{sin} \theta=\sqrt{\frac{9}{25}}=\frac{3}{5}$
Now, $\operatorname{cot} \theta+\tan \theta$
$= \frac{\operatorname{cos} \theta}{\operatorname{sin} \theta}+\frac{\operatorname{sin} \theta}{\operatorname{cos} \theta}$
Putting the values, we get:
$=\frac{\frac{4}{5}}{\frac{3}{5}}+\frac{\frac{3}{5}}{\frac{4}{5}}$
$=\frac{4}{3}+\frac{3}{4}$
$=\frac{16+9}{12}$
$=\frac{25}{12}$
Hence, the correct answer is $\frac{25}{12}$.

Correct Answer: (28, 21, 3528)

Solution : Given:
(13, 7, 546); (14, 15, 1260)

Here, (13, 7, 546)→(13 × 7) × 6 = 546
(14, 15, 1260)→(14 × 15) × 6 = 1260

Let's check the options –
First option: (28, 21, 3528)→(28 × 21) × 6 = 3528
Second

Correct Answer: eluded

Solution : The correct choice is the third option.

Elude means to escape or evade, especially in a cunning or skilful manner. It helps in conveying the intended meaning that fortune escaped him due to his ill luck.

The meanings of the other options are

Correct Answer: Tippani

Solution : The correct option is Tippani.

Tippani is a traditional folk dance form that originates in the state of Gujarat. It is often performed during various cultural and festive occasions in the region. The dance is characterised by bright and vivacious motions and the rhythmic usage

Correct Answer: 8.16%

Solution : Let the amount lent be Rs. 100.
We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
Simple Interest for first 6 months = $\frac{100\times 8\times \frac{1}{2}}{100}$ = Rs. 4
Increased principal = Rs. 104
Simple Interest for next 6 months = $\frac{104\times 8\times \frac{1}{2}}{100}$

Correct Answer: 57

Solution : Given Ratio = $\frac{1}{3}:\frac{1}{4}:\frac{1}{5}:\frac{1}{6}$
LCM of (3, 4, 5, 6) = 60.
So, the new ratio becomes
= $\frac{60}{3}:\frac{60}{4}:\frac{60}{5}:\frac{60}{6}$ = 20 : 15 : 12 : 10
Therefore, the minimum number of pens that a person should have = 20 + 15 + 12 +10