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Correct Answer: 11

Solution : Let the first odd number be $x$, which is the smallest number.
The rest of the consecutive odd numbers are $x+2$, $x+4$, $x+6$, $x+8$.
Average = $\frac{x+x+2 + x+4 + x + 6 + x+8}{5}$
$⇒15 = \frac{5x+20}{5}$
$⇒75=5x+20$
$\therefore x = 11$
Hence, the

Correct Answer: Michael Phelps

Solution : The correct answer is Michael Phelps.

Michael Phelps has won the most individual gold Olympic medals. He is an American swimmer. He is the most successful Olympian and has won 23 gold medals in swimming at the Olympics. At the 2008 Olympic Games

Correct Answer: 112 kg

Solution : Given: 
The mean weight of 8 students = 57 kg

⇒The sum of the weight of 8 students = Mean weight of 8 students × number of students = 57 × 8 = 456
⇒The sum of weight of each student = (55 +

Correct Answer: 0

Solution : Given:
(I) Seven people A, B, C, D, E, F, and G have different heights. A is taller than four other people.
_ > _ > A > _> _> _> _
(II) E is shorter than only one person.
_ > E > A

Correct Answer: $\frac{3 \sqrt{2}-\sqrt{6}}{8}$

Solution : $\frac{\cos 45^{\circ}}{\sec 30^{\circ}+\operatorname{cosec} 30^{\circ}}$
= $\frac{\frac{1}{\sqrt{2}}}{\frac{2}{\sqrt{3}}+2}$
= $\frac{\sqrt{3}}{2\sqrt{2}(\sqrt{3}+1)}$
= $\frac{\sqrt{3}}{2\sqrt{2}(\sqrt{3}+1)}\times\frac{\sqrt{2}(\sqrt{3}-1)}{\sqrt{2}(\sqrt{3}-1)}$
= $\frac{3 \sqrt{2}-\sqrt{6}}{8}$
Hence, the correct answer is $\frac{3 \sqrt{2}-\sqrt{6}}{8}$.

Correct Answer: Avani Lekhara

Solution : The correct answer is Avani Lekhara.

At the Tokyo Paralympics, Indian shooter Avani Lekhara took home the gold medal in the women's 10-metre air rifle shooting competition. She has captured the nation's first gold medal at the Paralympic Games in Tokyo.

With a score

Correct Answer: 50

Solution : Assuming the fourth proportion is $x$.
$0.24:0.6: : 20:x$
⇒ $\frac{0.24}{0.6}$ = $\frac{20}{x}$
⇒ $x$ = $\frac{20×0.6}{0.24}$
⇒ $x$ = 50
Hence, the correct answer is 50.

Correct Answer: $\sec^{2}23°$

Solution : $2\ \text{cosec}^{2}\: 23°\cot^{2}67°-\sin^{2}23°-\sin^{2}67°-\cot^{2}67°$
$=2\: \frac{1}{\sin^{2}\: 23°}\tan^{2}23°-\sin^{2}23°-\cos^{2}23°-\tan^{2}23°$
$=2\: \frac{1}{\cos^{2}23°}-(\sin^{2}23°+\cos^{2}23°)-\frac{\sin^{2}23°}{\cos^{2}23°}$
$=2\: \frac{1}{\cos^{2}23°}-1-\frac{\sin^{2}23°}{\cos^{2}23°}$
$=\frac{2-\cos^2 23° - \sin^223°}{\cos^2 23°}$
$=\frac{2-1}{\cos^2 23°}$
$=\sec^2 23°$
Hence, the correct answer is $\sec^2 23°$.

Correct Answer: Compassionate

Solution : The correct antonym is the fourth option: Compassionate.

Explanation for each option:

1. Malicious - This word is a synonym of "pernicious" and does not provide an appropriate antonym. Both words have a similar meaning of causing harm or being harmful.

2. Wicked - This word is

Correct Answer: patience

Solution : The correct choice is the fourth option.

The phrase knowledge and patience refers to the idea that possessing information, skills, and understanding, coupled with a specific attribute, is essential for overcoming challenges.