It's a Question of your Career!

Correct Answer: $\frac{\sqrt{b^2-a^2}}{a}$

Solution : Given,
$\operatorname{cosec} \theta=\frac{b}{a}$
⇒ $\sin\theta=\frac ab$
We have to find the value of $\frac{\sqrt{3} \cot \theta+1}{\tan \theta+\sqrt{3}}$
We know, $\cot\theta=\frac{\cos\theta}{\sin\theta}$ and $\tan\theta=\frac{\sin\theta}{\cos\theta}$
$\frac{\sqrt{3} \cot \theta+1}{\tan \theta+\sqrt{3}}=\frac{\sqrt3\times\frac{\cos\theta}{\sin\theta}+1}{\frac{\sin\theta}{\cos\theta}+\sqrt3}$
= $\frac{\cos\theta(\sqrt3\cos\theta+\sin\theta)}{\sin\theta(\sin\theta+\sqrt3\cos\theta)}$
= $\frac{\cos\theta}{\sin\theta}$
= $\frac{\sqrt{1-\sin^2\theta}}{\sin\theta}$ [As $\sin^2\theta+\cos^2\theta=1$]
= $\frac{\sqrt{1-(\frac ab)^2}}{\frac ab}$
= $\frac{\sqrt{b^2-a^2}}{a}$
Hence, the correct answer is

Correct Answer: indeed

Solution : The correct choice is the second option.

It is used to emphasise a statement, indicating that something is true or accurate. In the given sentence, it adds emphasis to the extraordinariness of the discovery.

The meanings of the other options are as follows:

• Novelly: It

Correct Answer: Two

Solution : Given:
Each vowel in the word CAPSULE is changed to the previous letter in the English alphabetical series and each consonant is changed to the following letter in the English alphabetical series.

In the newly formed word, Q is 3^rd from left and T

Correct Answer: 1527

Solution : The correct option is 1527.

On March 17, 1527, Babur triumphed over Rana Sanga in the Battle of Khanwa. An important military conflict known as the Battle of Khanwa occurred close to the town of Khanwa in modern-day Rajasthan, India. The triumph strengthened Babur's hold

Correct Answer: alludes

Solution : The correct choice is the first option.

Imply means to suggest, indicate, or express something indirectly without explicitly stating it. Alludes is the appropriate synonym, as it means to suggest or indirectly refer to something.

The meanings of the other options are as follows:

• Deceives:

Correct Answer: intestines

Solution : The correct option is - intestines

Entamoeba histolytica infects the human gastrointestinal tract, typically the large intestine (colon). It can be transmitted through the ingestion of contaminated food or water, or through close contact with infected individuals.

Correct Answer: IDMHDQNVCT

Solution : Given: 
TELEVISION is coded as UDMDWKQKMP
PUNISHMENT is coded as QTOHTJKGLV

Add and subtract 1 alternatively from the place values of the first 5 letters, and add and subtract 2 alternatively from the place values of the remaining letters.
Like, TELEVISION ⇒ T + 1

Correct Answer:

Solution : According to the given figures –
1. A figure at the centre rotates 90° in the anti-clockwise direction.
2. The letters are placed diagonally –
In Box 1, the letters M and N are placed diagonally in the southwest and northeast directions.
In Box 2, the

Correct Answer: 3

Solution : Given, $9+9^2+\ldots+9^{(2 n+1)}$ is divided by 6
Consider, $9+9^2+\ldots+9^{(2 n+1)}$
Here, for each term in the series, the remainder when divided by 6 is 3.
The sum of the remainder of each term = 3 + 3 + 3 + ............+ up to 2n +

Correct Answer: FPL

Solution : Given:
AKV : ZIS :: ? : ENI :: PQR : OOO

Subtract 1, 2, and 3 from the place value of the first, second and third letters respectively, to obtain the required missing term –
Like, AKV : ZIS→ A – 1 = Z;