Correct Answer: My sister said, "Let us go for a walk in the fresh air."

Solution : The correct option is the fourth option.

Direct speech involves quoting the exact words spoken by someone. When converting a sentence from indirect to direct speech, you generally:

• The reporting verb "suggested" is changed to "said". and the sentence should begin with let which is used in a sentence to express a suggestion or proposal.
• The connector "that" is removed.
• There would be no change in the reported clause because it is in the present tense.
• The words of the speaker are enclosed in the inverted commas.

Therefore, the converted sentence in direct speech would be: My sister said, "Let us go for a walk in the fresh air".

Correct Answer: by

Solution : The second option is the correct answer: by.

"At" typically indicates a specific location or time.
"By" often expresses a deadline or method.
"In" usually denotes a location within a space or a time frame.
"On" often indicates a surface or a specific date or day.

Therefore, the answer is "Naresh made a fortune by buying and selling used cars."

Correct Answer: $\frac{20}{39}$

Solution : $3 \tan \theta=2 \sqrt{3} \sin \theta$
⇒ $3 × \frac{\sin \theta}{\cos \theta} = 2 \sqrt{3} \sin \theta$
⇒ $\frac{3}{\cos \theta} = 2 \sqrt{3}$
⇒ $\cos \theta = \frac{3}{2 \sqrt{3}} = \frac{\sqrt3}{2}$
⇒ $\theta = 30^{\circ}$
Now, $\frac{\operatorname{cosec}^2 2 \theta+\cot ^2 2 \theta}{\sin ^2 \theta+\tan ^2 2 \theta}$
$=\frac{\operatorname{cosec}^2 (2 ×30^{\circ})+\cot ^2 (2 ×30^{\circ})}{\sin ^2 30^{\circ}+\tan ^2 (2× 30^{\circ})}$
$=\frac{\operatorname{cosec}^2 60^{\circ}+\cot ^2 60^{\circ}}{\sin ^2 30^{\circ}+\tan ^2 60^{\circ}}$
$=\frac{(\frac{2}{\sqrt3})^2+(\frac{1}{\sqrt3})^2}{(\frac{1}{2})^2+(\sqrt3)^2}$
$=\frac{(\frac{4}{3})+(\frac{1}{3})}{(\frac{1}{4})+3}$
$=\frac{(\frac{5}{3})}{(\frac{1+12}{4})}$
$= \frac{5×4}{3×13}$
$=\frac{20}{39}$
Hence, the correct answer is $\frac{20}{39}$.

Correct Answer: talked

Solution : The third option is correct.

In the given sentence, the phrase spoke about indicates a conversation or discussion on the topic of political unrest within the state.

Among the options provided:

• Expressed: This term denotes conveying thoughts or feelings but doesn't specifically imply a conversation or discussion. 
• Said: While it refers to verbal expression, it's a bit generic and doesn't specifically suggest a conversation or discussion involving multiple individuals. 
• Talked: This word best fits the context as it signifies a conversation or discussion among people about the political turmoil.
• Stated: It implies expressing something definitively or explicitly but doesn't strongly convey a conversation or discussion.

Therefore, the correct sentence is: They talked about the political turmoil in the state.

Correct Answer: (3)

Solution : The correct choice is the third option.

It should be "mother's milk" and not "mothers milk" as "mothers" is a plural form of "mother" and "mother's milk" means milk of a mother.

So, the correct sentence is: The only thing that endures and can sustain an infant till the stage it receives immunity comes from the consumption of the mother's milk.

Correct Answer: excretion

Solution : The correct option is - Excretion.

All embryos contain the allantois, which is also known as allantoic. A clear fluid is contained within the allantois, which resembles a hollow sac.  The allantois has two functions: collecting liquid waste from the embryo and exchanging gases that the embryo uses.  The chorionic membrane, amniotic membrane, and allantois all aid in the embryo's growth.

Correct Answer: Neither conclusion follows

Solution : The possible Venn diagram, according to the given statements is as follows –

Let's analyse the conclusions –
Conclusion (I): Some O is not Q – From the diagram, it is evident that there is no direct relation between O and Q. So, this conclusion does not follow.
Conclusion (II): All M are Q – From the Venn diagram, it is evident that some parts of the circles representing M lie outside the circle representing Q. So, it can be concluded that some M is Q.

So, neither conclusion follows. Hence, the fourth option is correct.

Correct Answer: $8 \frac{4}{17}\%$

Solution : P = INR 500 and INR 700
T = 4 years and 2 years 
R = same for both 
According to the question,
$280 = \frac{\text{500×R×4}}{100}$+$\frac{\text{700×R×2}}{100}$
⇒ $280 = \frac{\text{2000R}}{100}$+$\frac{\text{1400R}}{100}$
⇒ $ 280 = \frac{\text{3400R}}{100}$
⇒ $R = \frac{280}{34} = 8\frac{4}{17}$
Hence, the correct answer is $8 \frac{4}{17}\%$.

Correct Answer: No improvement required

Solution : The correct choice is the fourth option.

The sentence as it stands is grammatically correct and coherent. The reflexive pronoun "ourselves" is used appropriately here to indicate that individuals are sometimes the cause of their own poor health.

Therefore, in the given sentence, there is no improvement required.

Correct Answer: 3

Solution : Taking dice positions 1 and 2 with 1 as common face,

Moving clockwise from the common face with 1,

Pairs of opposite faces –

So, the face opposite to 1 is 3. Hence, the fourth option is correct.