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Question : If $a \cot \theta+b \operatorname{cosec} \theta=p$ and $b \cot \theta+a \operatorname{cosec} \theta=q$, then $p^2-q^2$ is equal to ____.

Option 1: $b^2-a^2$

Option 2: $a^2-b^2$

Option 3: $b-a$

Option 4: $a^2+b^2$

Team Careers360 23rd Jan, 2024

Correct Answer: $b^2-a^2$


Solution : $a \cot \theta+b \operatorname{cosec} \theta=p$
$b \cot \theta+a \operatorname{cosec} \theta=q$
So, $p^2-q^2$
= $(a \cot \theta+b \operatorname{cosec} \theta)^2 - (b \cot \theta+a \operatorname{cosec} \theta)^2$
= $a^2 \cot^2 \theta+b^2 \operatorname{cosec}^2 \theta + 2×a \cot \theta×b \operatorname{cosec} \theta$ – $(b^2 \cot^2 \theta+a^2 \operatorname{cosec}^2\theta+2×b \cot \theta×a \operatorname{cosec} \theta)$

17 Views

Question : Direction: If SPANK is coded as PSNAK, then THROW is coded as?

Option 1: HTWOR

Option 2: HTWRO

Option 3: HTROW

Option 4: HTORW

Team Careers360 23rd Jan, 2024

Correct Answer: HTORW


Solution : Given:

SPANK → PSNAK

In the coded language,

S ⇔ P; A ⇔ N

Similarly, THROW will be coded as:

T ⇔ H; R ⇔ O

THROW → HTORW

Hence, the fourth option is correct.

19 Views

Question : Which one of the following is also called a 'power house' of the cell?

Option 1: Golgi body

Option 2: Mitrochondria

Option 3: Ribosome

Option 4: Lysosome

Team Careers360 23rd Jan, 2024

Correct Answer: Mitrochondria


Solution : The correct answer is Mitrochondria.

The Mitrochondria is also known as the cell's powerhouse. Mitochondria are organelles found in every eukaryotic cell. They are in charge of turning food into energy in the form of ATP, the cell's primary energy currency.

8 Views

Question : If $\small a^{4}+1=\left [\frac{a^{2}}{b^{2}}\right ]\left (4b^{2}-b^{4}-1\right),$ then what is the value of $a^{4}+b^{4}?$

Option 1: 2

Option 2: 16

Option 3: 32

Option 4: 64

Team Careers360 24th Jan, 2024

Correct Answer: 2


Solution : Given: $a^{4}+1=\frac{a^{2}}{b^{2}}( 4b^{2}-b^{4}-1)$
⇒ $\frac{(a^{4}+1)}{a^2}=\frac{1}{b^{2}}( 4b^{2}-b^{4}-1)$
⇒ $a^2+\frac{1}{a^2}=4 -b^2-\frac{1}{b^2}$
⇒ $a^2+\frac{1}{a^2}+2+b^2+\frac{1}{b^2} +2 =0$
⇒ $(a-\frac{1}{a})^2+(b-\frac{1}{b})^2=0$
So, $(a-\frac{1}{a})^2=0 \;$and$\; (b-\frac{1}{b})^2=0$
⇒ $a-\frac{1}{a}=0 \; $ and$\; b-\frac{1}{b}=0$
⇒ $a=\frac{1}{a} \; $ and$\; b=\frac{1}{b}$
⇒ $a^2=1 \;$ and $\; b^2 = 1$
$\therefore a^{4}+b^{4}=2$
Hence, the correct answer

7 Views

Question : Which of the following is one of the Trustees of the PM CARES Fund?

Option 1: Shri Azim Premji

Option 2: Shri Gautam Adani

Option 3: Shri Mukesh Ambani

Option 4: Shri Ratan N. Tata

Team Careers360 24th Jan, 2024

Correct Answer: Shri Ratan N. Tata


Solution : The correct answer is Shri Ratan N. Tata.

The PM CARES Fund has appointed veteran entrepreneur Ratan Tata, former deputy speaker of the Lok Sabha Kariya Munda, and former Supreme Court judge K. T. Thomas as trustees. On March 27, 2020,

24 Views

Question : Till which year did the High Court of Delhi continue to exercise jurisdiction over Himachal Pradesh?

Option 1: 1969

Option 2: 1967

Option 3: 1971

Option 4: 1968

Team Careers360 23rd Jan, 2024

Correct Answer: 1971


Solution : The correct option is 1971.

Until 1971, the High Court of Delhi had jurisdiction over Himachal Pradesh. Himachal Pradesh was granted its own High Court, known as the Himachal Pradesh High Court, in 1971, and it began operating autonomously. Before that, the Delhi High Court

138 Views

Question : The given sentence is divided into three segments. Select the option that has the segment with a grammatical error. If there is no error, select "No error" as your answer.

She won't be / watch the news / on the BBC channel.

Option 1: on the BBC channel

Option 2: watch the news

Option 3: She won't be

Option 4: No error

Team Careers360 24th Jan, 2024

Correct Answer: watch the news


Solution : The correct choice is the second option.

The given sentence contains a grammatical error in the segment "watch the news". This segment has an error because it should use the continuous form "watching" after "be". Grammatically, when we use "be" followed by a

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