Correct Answer: $\frac{1}{2}\left(9 \sqrt{3}-\frac{11}{7}\right)$ unit$^2$

Solution :
Area of equilateral triangle = $\frac{\sqrt 3}{4}(side)^2$
$= \frac{\sqrt3}{4}(6)^2 = 9\sqrt{3}\ \mathrm{unit}^2$
Area of circle = $\pi r^2 = \pi\ \mathrm{unit^2}$ where $r$ = radius of circle = 1 unit.
Area of shaded region = $\frac{1}{2}$ Area of triangle - $\frac{1}{4}$ Area of circle
Area of shaded region = $\frac{9\sqrt{3}}{2} - \frac{\pi}{4}$
$= \frac{9\sqrt{3}}{2} - \frac{22}{7\times 4}$
$= \frac{9\sqrt{3}}{2} - \frac{11}{7\times 2}$
$= \frac{1}{2}\left(9 \sqrt{3}-\frac{11}{7}\right)$
Hence, the correct answer is $\frac{1}{2}(9 \sqrt{3}-\frac{11}{7})$ unit².

Correct Answer: 27

Solution : Total number of accountants working in the organization in the year 2019
= 35 – 0 + 26 – 16 + 15 – 5 + 20 – 38 + 14 – 24
= 27
Hence, the correct answer is 27.

Correct Answer: 5, 35

Solution : The pattern followed here is that when the second number is divided by the first number it gives the consecutive natural number of the first number.

Let's check the options —
First option: 3 – 12→12 ÷ 3 = 4
Second option: 2 – 6→6 ÷ 2 = 3
Third option: 6 – 42→42 ÷ 6 = 7
Fourth option: 5 – 35→35 ÷ 5 = 7 ≠ 6

Hence, the fourth option is correct.

Correct Answer: (5, 60)

Solution : Let's check the options –
First option: (7, 89); (7 × 12) + (7 – 2) = 84 + 5 = 89
Second option: (8, 102); (8 × 12) + (8 – 2) = 96 + 6 = 102
Third option: (5, 60); (5 × 12) + (5 – 2) = 60 + 3 = 63 ≠ 60
Fourth option: (6, 76); (6 × 12) + (6 – 2) = 72 + 4 = 76

So, the third option does not follow the logic and is different from the others. Hence, the third option is correct.

Correct Answer: 2

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

Explanation: The phrase, "the reason for his failure is because" is redundant. Both "the reason" and "because" convey the idea of causation. To correct this redundancy, we should use "the reason for his failure is that". In this case, using "that" results in a clearer and more concise sentence.

Therefore, the correct sentence should be: "The reason for his failure is that he did not work hard."

Correct Answer: no antibody

Solution : The correct option is no antibody.

Individuals with blood type AB do not naturally develop antibodies against the ABO blood group antigens. The four major blood types are A, B, AB, and O. Each blood type has different antigens on the surface of red blood cells, and people may have naturally occurring antibodies against antigens they don't have. Because type AB people have both A and B antigens on their red blood cells and do not normally create anti-A or anti-B antibodies, their plasma may be safely transfused to people with other blood types without provoking an immunological reaction.

Correct Answer: 3abc

Solution : Given: a + b + c = 0
a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)
⇒ a³ + b³ + c³ – 3abc = (0)(a² + b² + c² – ab – bc – ca)
⇒ a³ + b³ + c³ – 3abc = 0
⇒ a³ + b³ + c³ = 3abc
Hence, the correct answer is 3abc.

Correct Answer: Potable

Solution : The second option is the correct choice.

The meaning of the marked option is:

• Potable: Safe to drink; drinkable.

The meanings of the other options are:

• Delectable: Of food or drink delicious.
• Feasible: Possible to do easily or conveniently.
• Edible: Fit or suitable to be eaten.

Hence, the correct answer is potable.

Correct Answer: Indian National Congress

Solution : The correct answer is the Indian National Congress.

The Indian National Congress was established on December 28, 1885, and it was started by a retired British Civil Servant, A. O Hume. It was founded by a group of educated people in Bombay, with 72 founding members. The first president of the Indian National Congress was W. C. Banerjee. Mahatma Gandhi also became the President of this party in the 1924 session. Pandit Jawaharlal Nehru, the first prime minister of India, also belonged to this party.

Correct Answer: Khan Abdul Ghaffar Khan

Solution : The correct answer is Khan Abdul Ghaffar Khan.

The Red Shirt movement, also known as Khudai Khidmatgar (Persian for "Servants of God"), was founded in 1930 in India's North-West Frontier Province in support of the Indian National Congress. This organisation was formed under the leadership of Khan Abdul Ghaffar Khan, who was also known as "Bacha Khan" or "Frontier Gandhi." Khan Abdul Ghaffar Khan was a prominent leader and social reformer among the Pashtuns (Pathans) and played a significant role in the Indian independence movement.