Correct Answer: 0.5

Solution : Given expression,
$(\frac{\sec \theta-1}{\sec \theta+1})^n=\operatorname{cosec} \theta-\cot \theta$
Considering L.H.S.,
We know, $\sec\theta=\frac{1}{\cos\theta}$
= $\left\{\frac{\frac{1}{\cos\theta}-1}{\frac{1}{\cos\theta}+1}\right\}^n$
= $\left\{\frac{1-\cos\theta}{1+\cos\theta}\right\}^n$
Multiplying and dividing by $1-\cos\theta$, we get,
= $\left\{\frac{1-\cos\theta}{1+\cos\theta}\times\frac{1-\cos\theta}{1-\cos\theta}\right\}^n$
= $\left\{\frac{(1-\cos\theta)^2}{1-\cos^2\theta}\right\}^n$
= $\left\{\frac{(1-\cos\theta)^2}{\sin^2\theta}\right\}^n$
Now consider R.H.S,
$\operatorname{cosec} \theta-\cot \theta$
We know, $\operatorname{cosec} \theta=\frac{1}{\sin\theta}$ and $\cot\theta=\frac{\cos\theta}{\sin\theta}$
= $\frac{1}{\sin\theta}-\frac{\cos\theta}{\sin\theta}$
= $\frac{1-\cos\theta}{\sin\theta}$

Correct Answer: 72.5%

Solution : Given: In a survey, 200 respondents were asked whether they owned a vehicle or not.
The percentage of respondents who do not own a car
$=\frac{\text{Total respondents who do not own a car}}{\text{Total respondents}}×100=\frac{30+50 + 20 + 45}{200}\times 100=\frac{145}{200}=72.5\%$
Hence, the correct answer is 72.5%.

Correct Answer: LZA

Solution : Given:
GDM : ROX :: AOP : ?

Add 11 to the place value of each letter of GDM to obtain the required code –
G + 11 = R; D + 11 = O; M + 11 = X
Thus, GDM is coded as

Correct Answer: Mitochondria

Solution : The correct answer is Mitochondria.

The cell organelle that appears as rounded or sausage-shaped structures under electron microscopy, measuring about 0.5–1.0 μm in diameter and 2–8 μm in length, is the mitochondrion. Mitochondria are responsible for energy production within the cell through the process of

Correct Answer: 5, 3, 1, 4, 2

Solution : Given:
1. Star  2. Satellite  3. Galaxy  4. Planet  5. Universe

These all are geographical objects. First comes the Universe which consists of galaxies. Galaxies consist of stars. Then Planets are followed by stars and finally Satellites are followed by Planets.

Correct Answer: for example

Solution : The correct choice is the first option.

The phrase "for example" is used to introduce an instance or illustration that supports or exemplifies the preceding statement. In this context, the previous sentence mentions that not all swan species are white. The phrase "for

Correct Answer: (2)

Solution : The sentence can be improved using the second option "credulous".

The word "credulous" means "ready to believe too easily". In this sentence, it is used to describe Manoj's tendency to believe everything he is told, even if it is not true.

The meanings of the

Correct Answer: 1

Solution : Check divisibility by 11
⇒ Sum of digits in odd places – Sum of digits in even places = 0 or multiple of 11.
⇒ (3 + N) – 4 = 0
⇒ N = 1
Hence, the correct answer is 1.

Correct Answer: Portuguese

Solution : The correct answer is Portuguese.

Vasco da Gama was the first European to reach India in 1498. He reached Calicut via the Atlantic Sea in the Calicut region of India. The first to come to India as traders were the Portuguese, and they were followed

Correct Answer: $\sqrt{\frac{1-\sin 2 A}{\cos 2 A}}$

Solution : Given expression,
$\sqrt{\frac{1-\tan A}{1+\tan A}}$
= $\sqrt{\frac{1-\frac{\sin A}{\cos A}}{1+\frac{\sin A}{\cos A}}}$
= $\sqrt{\frac{\cos A-\sin A}{\cos A+\sin A}}$
Multiplying and dividing by $\sqrt{\cos A-\sin A}$
$\sqrt{\frac{\cos A-\sin A}{\cos A+\sin A}}\times\sqrt{\frac{\cos A-\sin A}{\cos A-\sin }}$
= $\sqrt{\frac{(\cos A-\sin A)^2}{(\cos A+\sin A)(\cos A-\sin A)}}$