Correct Answer: $\cos A$

Solution : $\frac{\cos (\pi-A) \cdot \cot \left(\frac{\pi}{2}+A\right) \cos (-A)}{\tan (\pi+A) \tan \left(\frac{3 \pi}{2}+A\right) \sin (2 \pi-A)}$
$=\frac{-\cos A \ \cdot (-\tan A) \ \cdot \cos A}{\tan A \ \cdot (-\cot A) (-\sin A)}$
$= \frac{\cos^2 A \ \cdot \tan A}{\sin A}$
$= \frac{\cos^2 A \ \cdot

Correct Answer: Phylum annelida

Solution : The correct option is Phylum annelida.

Annelida is an animal phylum that comprises segmented worms. These worms are distinguished by their body segments, known as metameres, which are connected by septa (dividing walls). Annelids live in a variety of environments, including marine, freshwater, and

Correct Answer: 160

Solution :
Given: $DE\parallel BC$ and $DE = 6\text{ cm}$, $BC = 8\text{ cm}$, and area of ($\triangle ADE) = 90 \text{ cm}^2$
Since $DE\parallel BC$, $\triangle ADE$ and $\triangle ABC$ are similar.
So, $\frac{(Area \ of \ \triangle ADE)}{(Area \ of \  \triangle ABC)} = \frac{DE^2}{BC^2}$

Correct Answer: $3$

Solution : Given:
$\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=3$
Take $a=(\sqrt{5+x}+\sqrt{5-x})$, $b=(\sqrt{5+x}-\sqrt{5-x}), m=3$ and $n=1$.
Applying the rule of componendo and dividendo,
$\frac{a}{b}=\frac{m}{n}$ ⇒ $\frac{a+b}{a-b}=\frac{m+n}{m-n}$
Now, $\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=3$
⇒ $\frac{\sqrt{5+x}+\sqrt{5-x}+\sqrt{5+x}-\sqrt{5-x}}{\sqrt{5+x}+\sqrt{5-x}- \sqrt{5+x}+\sqrt{5-x}}=\frac{3+1}{3-1}$
⇒ $\frac{\sqrt{5+x}+\sqrt{5+x}}{\sqrt{5-x}+\sqrt{5-x}}=\frac{4}{2}$
⇒ $\frac{2\sqrt{5+x}}{2\sqrt{5-x}}=\frac{4}{2}$
⇒ $\frac{\sqrt{5+x}}{\sqrt{5-x}}=2$
Squaring both sides, we get,
⇒ $\left(\frac{\sqrt{5+x}}{\sqrt{5-x}}\right)^{2}=2^{2}$
⇒ $\frac{5+x}{5-x}=4$
⇒ $5+x=20-4x$
⇒ $5x=15$
$\therefore x=3$
Hence,

Correct Answer: 1 - c

2 - a

3 - b

Solution : The correct option is -1 - c, 2 - a. 3 - b

Radha Reddy is the famous exponent of the classical dance Kuchipudi, which originated in Andhra Pradesh. Padma Subrahmanyam is an Indian classical Bharatanatyam

Correct Answer: eye

Solution : The correct answer is the eye.

The eye of the storm is a tranquil region in the middle of a cyclone. A cyclone's eye is an area of generally calm weather near the centre of a powerful tropical cyclone. The eyewall, a ring of towering

Correct Answer: Sultan Muhammad Ghori

Solution : The correct answer is Sultan Muhammad Ghori.

A Chahamana, Prithviraj III (1168–1192), became a Chauhan ruler later on. He governed the areas that surrounded Delhi and Ajmer. In 1191, he vanquished the Afghan invader, Sultan Muhammad Ghori. However, Ghori overcame him just

Correct Answer: to detect antibodies and hormones present in the blood samples

Solution : The correct option is to detect antibodies and hormones present in the blood samples.

Radioimmunoassay (RIA) is a laboratory technique used for measuring the concentration of specific substances in biological samples, such as blood, urine, or

Correct Answer: Rs. 1,800

Solution : Let the original price of the chair be Rs. Q.
The original price of the table = Rs. (3900 – Q)
According to the question,
Q × 16% + (3900 – Q) × 8% = 540
⇒ 16Q + 3900 × 8 – 8Q

Correct Answer: step-wise migration

Solution : The correct option is - step-wise migration

Migration that takes place in steps, such as relocating to a town that is larger than the one where one grew up but not immediately to one of the metropolitan regions, is referred to as "step wise