Correct Answer: –2

Solution : $\frac{3\left(\operatorname{cosec}^2 26^{\circ}-\tan ^2 64^{\circ}\right)+\left(\cot ^2 42^{\circ}-\sec ^2 48^{\circ}\right)}{\cot \left(22^{\circ}-\theta\right)-\operatorname{cosec}^2\left(62^{\circ}+\theta\right)-\tan \left(\theta+68^{\circ}\right)+\tan ^2\left(28^{\circ}-\theta\right)}$
$= \frac{3\left(\operatorname{sec}^2 64^{\circ}-\tan ^2 64^{\circ}\right)+\left(\cot ^2 42^{\circ}-\operatorname{cosec} ^2 42^{\circ}\right)}{\tan \left(68^{\circ}+\theta\right)-\operatorname{cosec}^2\left(62^{\circ}+\theta\right)-\tan \left(\theta+68^{\circ}\right)+\cot ^2\left(62^{\circ}+\theta\right)}$
$= \frac{3\left(1\right)+\left(\cot ^2 42^{\circ}-1-\cot ^2 42^{\circ}\right)}{-(\operatorname{cosec}^2\left(62^{\circ}+\theta\right)-\cot ^2\left(62^{\circ}+\theta\right))}$
$= \frac{3-1}{-1}$
$= -2$
Hence, the correct answer is –2.

Correct Answer: OUA

Solution : Given:
AEI, EIO, IOU, ?

Vowels are replaced with immediate next vowels according to the English alphabetical series and the order is –
A, E, I, O, U
AEI → The immediate next vowel of A is E, the Immediate next vowel of E is I, and the immediate next vowel of I is O → EIO
EIO → The immediate next vowel of E is I, the Immediate next vowel of I is O, and the immediate next vowel of O is U → IOU
IOU → The immediate next vowel of I is O, the Immediate next vowel of O is U, and the immediate next vowel of U is A → OUA

So, the required missing term in the series is OUA. Hence, the third option is correct.

Correct Answer: Full-service broker
 

Solution : The correct answer is (a) Full-service broker

A full-service broker is a type of broker that offers a wide range of services to clients, including investment advice, research, financial planning, and execution of orders on behalf of their clients. They provide personalized assistance and guidance to help clients make informed investment decisions. In addition to executing trades, they often offer comprehensive financial services, portfolio management, and recommendations based on their expertise and analysis of the market. Clients typically pay higher fees or commissions for the additional services and advice provided by full-service brokers.

Correct Answer: $1864.41 \text{ cm}^2$

Solution : The volume of a sphere, where $r$ is the radius.
$V = \frac{4}{3}\pi r^3$
The volume of a cone, where $r$ is the radius and $h$ is the height.
$V = \frac{1}{3}\pi r^2 h$
The volume of the three spheres is equal to the volume of the cone since the spheres are melted to form the cone. 
$⇒\frac{4}{3}\pi (10^3 + 8^3 + 6^3) = \frac{1}{3}\pi r^2 h$
$⇒\frac{4}{3}\pi (10^3 + 8^3 + 6^3) = \frac{1}{3}\pi (12)^2 h$
$⇒ 4(10^3 + 8^3 + 6^3) = (12)^2 h$
$⇒ 6912= 144 h$
$⇒h = 48 \text{ cm}$
Now, the slant height, $l = \sqrt{r^2 + h^2}= \sqrt{(12)^2 + (48)^2} = 49.477 \text{ cm}$
The curved surface area of a cone, where $l$ is the slant height of the cone. 
$= \pi r l= \pi ×(12)× (49.477)=1864.41 \text{ cm}^2$
Hence, the correct answer is $1864.41 \text{ cm}^2$.

Correct Answer: 247

Solution : Here, the given equations follows a pattern in which the first number and the middle number in LHS becomes the tens place digit and the hundreds place digit in the answer part in RHS respectively.

⇒ 9 x 7 x 4 = 794 

⇒ 3 x 4 x 6 = 436 

Following the same pattern in the unsolved equation, we get –

⇒ 4 x 2 x  7 = 247

Hence, option second is correct.

Correct Answer: Ashoka

Solution : The correct answer is Ashoka.

The last significant ruler of India's Mauryan dynasty was Ashoka. Following his victorious conquest of the Kalinga, he turned to Buddhism, gave up violent conquest and embraced a strategy he called "conquer by dharma," realising the carnage of the conflict.