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A rectangular paper sheet of dimensions \( 54 \, \text{cm} \times 4 \, \text{cm} \) is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken. Then, the ratio of the volume of the cylindrical tube to the volume of the cube is:
  • GATE NM - 2024
  • GATE NM
  • General Aptitude
  • mathematical reasoning
For positive non-zero real variables \( p \) and \( q \), if \[ \log \left( p^2 + q^2 \right) = \log p + \log q + 2 \log 3, \] then the value of \( \frac{p^4 + q^4}{p^2 q^2} \) is:
  • GATE NM - 2024
  • GATE NM
  • General Aptitude
  • mathematical reasoning
Consider the following sample of numbers: \[ 9, 18, 11, 14, 15, 17, 10, 69, 11, 13 \] The median of the sample is:
  • GATE NM - 2024
  • GATE NM
  • General Aptitude
  • mathematical reasoning
If \( \rightarrow \) denotes increasing order of intensity, then the meaning of the words [dry \( \rightarrow \) arid \( \rightarrow \) parched] is analogous to [diet \( \rightarrow \) fast \( \rightarrow \) \(\_\_\_\_\_\_\_\_\)]. Which one of the given options is appropriate to fill the blank?
  • GATE NM - 2024
  • GATE NM
  • General Aptitude
  • mathematical reasoning
The number of coins of ₹1, ₹5, and ₹10 denominations that a person has are in the ratio 5:3:13. Of the total amount, the percentage of money in ₹5 coins is:
  • GATE NM - 2024
  • GATE NM
  • General Aptitude
  • mathematical reasoning
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