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Graduate Aptitude Test in Engineering

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Question : If the radius of a right circular cylinder open at both ends is decreased by 25% and the height of the cylinder is increased by 25%, the curved surface area of the cylinder thus formed:

Option 1: remains unaltered

Option 2: is increased by $25\%$

Option 3: is increased by $6.25\%$

Option 4: is decreased by $6.25\%$

Team Careers360 19th Jan, 2024

Correct Answer: is decreased by $6.25\%$


Solution : The curved surface area of a right circular cylinder before the change, where $r$ is the radius and $h$ is the height $ = 2\pi rh$
The radius is decreased by $25\%$,
$r' = 0.75r$
The height is increased by $25\%$,
$h'

12 Views

Question : The oath of office is administered to the Governor by the:

Option 1: Chief Justice of India

Option 2: Speaker of Legislative Assembly

Option 3: Chairman of Legislative Council

Option 4: Chief Justice of the High Court

Team Careers360 21st Jan, 2024

Correct Answer: Chief Justice of the High Court


Solution : The correct answer is Chief Justice of the High Court.

A state's governor is chosen by the president and serves at his pleasure for five years. The governor's oath is administered by the Chief Justice of the relevant State

13 Views

Question : Total revenue from operations Rs. 9,00,000, Cash revenue from operations Rs. 3,00,000, Debtors Rs. 1,00,000, B/R Rs. 20,000. Trade Receivables Turnover Ratio will be :

Option 1: 5:1

Option 2: 10:1

Option 3: 7.5:1

Option 4: 9:1

Team Careers360 12th Jan, 2024

Correct Answer: 10:1


Solution : The formula for trade receivables turnover ratio is equal to

Credit revenue from operations / average trade receivable

Credit revenue from operations= Total revenue for operations- cash revenue from operations.= 9,00,000-3,00,000= 6,00,000

Average trade receivables= 1,00,000+20,000/2 = 1,20,000/2= 60,000

trade receivables turnover ratio = 6,00,000/60,000=

10 Views

Question : If $x-\frac{1}{x}=1$, then what is the value of $\left (\frac{1}{x-1}-\frac{1}{x+1}+\frac{1}{x^{2}+1}-\frac{1}{x^{2}-1} \right)\;$?

Option 1: $\pm \sqrt{5}$

Option 2: $\frac{2}{5}$

Option 3: $\pm\frac{2}{\sqrt{5}}$

Option 4: $\pm\frac{\sqrt{5}}{2}$

Team Careers360 24th Jan, 2024

Correct Answer: $\pm\frac{2}{\sqrt{5}}$


Solution : Given: $x-\frac{1}{x}=1$
$⇒x^{2}-1=x$
$⇒x^{2}+1=x+2$
$\left (\frac{1}{x-1}-\frac{1}{x+1}+\frac{1}{x^{2}+1}-\frac{1}{x^{2}-1} \right)$
$=(\frac{2}{x^{2}-1}+\frac{1}{x^{2}+1}-\frac{1}{x^{2}-1})$
$=(\frac{1}{x^{2}-1}+\frac{1}{x^{2}+1})$
$=(\frac{2x^{2}}{(x^{2}-1)(x^{2}+1)})$
Using $x^{2}-1=x$ and $x^{2}+1=x+2$, we get,
$=(\frac{2x^{2}}{(x)(x+2)})$
$=\frac{2x}{x+2}$
Solving $x^{2}-x-1=0$, we get $x=\frac{1\pm\sqrt{5}}{2}$
So, $x+2=\frac{5\pm\sqrt{5}}{2}$
When $x=\frac{1+\sqrt{5}}{2}$, $\frac{2x}{x+2}=\frac{2}{\sqrt{5}}$
When $x=\frac{1-\sqrt{5}}{2}$, $\frac{2x}{x+2}=-\frac{2}{\sqrt{5}}$
Hence, the correct answer is $\pm\frac{2}{\sqrt{5}}$.

13 Views

what is the Syllabus for Gate 2024( CSE)??

Sajal Trivedi 10th Jan, 2024

Hello aspirant,

The 30 topic areas on the GATE 2024 syllabus have been made available by IISc Bangalore. Candidates can visit the official website, gate2024.iisc.ac.in, to download the GATE 2024 admission card. The CSE, Civil, Electrical, Mechanical, and other paper GATE test syllabus 2024 pdf is available here. Key subjects

79 Views

Can Btech Biotechnology students apply through GATE (BT/XL) score in BARC.

Tanya Gupta 23rd Jan, 2024

Hello,

Yes, B.Tech Biotechnology students can apply through GATE (BT/XL) scores for BARC. GATE scores are accepted for admission to the BARC Training School programs. It's a great opportunity for B.Tech Biotechnology students to pursue research and training in the field of nuclear science and technology.

You will have to

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