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Mathematics Test - 14
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  • Question 1/10
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    The value of \(\underset{{{x \rightarrow 0}}}{\lim} \frac{\tan ^{2} 3 x}{x^{2}}\) is:

  • Question 2/10
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    The value of \(\omega^{6}+\omega^{7}+\omega^{5}\) is

  • Question 3/10
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    Let \(\mathrm{L}\) denote the set of all straight lines in a plane. Let a relation \(\mathrm{R}\) be \(\mathrm{l R m}\) if \(\mathrm{l}\) is perpendicular to \(\mathrm{m \forall l, m \in L}\). Then \(\mathrm{R}\) is:

  • Question 4/10
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    Let S={1,2,3,...,2022}. Then the probability, that a randomly chosen number n from the set S such that HCF(n,2022)=1, is :

  • Question 5/10
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    If \(\mathrm{f}(\mathrm{x})=\frac{\log (1+\mathrm{ax})-\log (1-\mathrm{bx})}{\mathrm{x}}\) for \(\mathrm{x} \neq 0\) and \(\mathrm{f}(0)=\mathrm{k}\) and \(\mathrm{f}(\mathrm{x})\) is continuous at \(\mathrm{x}=0\), then \(\mathrm{k}\) is equal to:
  • Question 6/10
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    What is the area of the parabola \(x^2=y\) bounded by the line \(y=1\)?

  • Question 7/10
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    If \(\mathrm{y}=\mathrm{x}^{3}-\mathrm{ax}^{2}+48 \mathrm{x}+7\) is an increasing function for all real values of \(x\), then a lies in:
  • Question 8/10
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    Which one of the following is wrong statement?

  • Question 9/10
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    Find the principal value of \(\sin ^{-1}\left(\frac{-1}{\sqrt{2}}\right)\).

  • Question 10/10
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    The value of \(\lim _{x \rightarrow 0} \frac{\cos 4 x-1}{1-\cos x}\) is:

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