NIMCET 2021 Previous Year Questions (PYQs) – Page 8 of 12
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If a number x is selected at random from natural numbers 1,2,…,100, then the probability for $x+\frac{100}{x}{\gt}29$ is
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If X and Y are two sets, then X∩Y ' ∩ (X∪Y) ' is
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Expression: \(X \cap Y' \cap (X \cup Y)'\)
Use De Morgan’s law: \((X \cup Y)' = X' \cap Y'\).
\[ X \cap Y' \cap (X \cup Y)' \;=\; X \cap Y' \cap (X' \cap Y') \;=\; (X \cap X') \cap Y' \cap Y' \;=\; \varnothing. \]
Answer: \(\boxed{\varnothing}\).
If $\vec{e_1}=(1,1,1)$ and $\vec{e_2}=(1,1,-1)$ and $\vec{a}$ and $\vec{b}$ and two vectors such that $\vec{e_2}=\vec{a}+2\vec{b}$ , then angle between $\vec{a}$ and $\vec{b}$
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If P(1,2), Q(4,6), R(5,7) and S(a,b) are the vertices of a parallelogram PQRS, then
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If $a\, \cos \theta+b\, \sin \, \theta=2$ and $a\, \sin \, \theta-b\, \cos \, \theta=3$ , then ${a}^{2^{}}+{b}^2=$
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If three thrown of three dice, the probability of throwing triplets not more than twice is
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There are 50 questions in a paper. Find the number of ways in which a student can attempt one or more questions :
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Consider the following frequency distribution table.
| Class Interval | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| Frequency | 180 | $f_1$ | 34 | 180 | 136 | $f_2$ | 50 |
If the total frequency is 686 and the median is 42.6, then the value of $f_1$;and $f_2$ are
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