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

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

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

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

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,

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

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, 

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.

Correct Answer: Epistasis

Solution : The correct option is - Epistasis.

The term "epistasis" refers to a situation in which the expression of one gene is altered (e.g., hidden, inhibited, or suppressed) by the expression of one or more other genes. Epistasis is classified as either recessive or dominant.

Correct Answer: $2\sqrt{3} \mathrm{~cm}$

Solution :
PQ = 6 cm
The centroid divides the median in the ratio 2 : 1.
Since all the centres lie at the same point L, PL is also the circumradius of Equilateral Triangle PQR.
We know, Circumradius of an equilateral triangle = $\frac{\text{Side of