CAT 2023 Question Paper (Available): Download CAT Question Paper with Solutions PDF

CAT 2023 Questions

• 1.

  If \(x\) and \(y\) are real numbers such that \(4x^2 + 4y^2 - 4xy - 6y + 3 = 0\), then the value of \((4x + 5y)\) is

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• 2.

  Two points A and B are 45 km apart. Anil started from A. Sunil started from B. They met each other after 1 hour 30 mins. and after meeting, they continued towards their destinations. Time taken by Anil to reach Point B was 1 hr 15 mins more than the time taken by Sunil to reach point A. Find speed of Anil

  • 12
  • 16
  • 18
  • 24
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• 3.

  The sum of all four-digit numbers that can be formed with the distinct non-zero digits $a$, $b$, $c$, and $d$, with each digit appearing exactly once in every number, is $153310 + n$, where $n$ is a single digit natural number. Then, the value of $(a + b + c + d)$ is ?

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• 4.

  Let $x$, $y$, and $z$ be real numbers satisfying
  \(4(x^2 + y^2 + z^2) = a,\)
  \(4(x - y - z) = 3 + a.\)
  Then $a$ equals ?

  • 3
  • 4
  • 1
  • $1\frac{1}{3}$
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• 5.

  The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is

  • \(\frac{4}{3}\)
  • -\(\frac{4}{3}\)
  • \(\frac{2}{3}\)
  • -\(\frac{2}{3}\)
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