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Phrases Previous Year Questions (PYQs)

Phrases Probability Critical Thinking PYQ

Phrases PYQ
In a class of 100 students, 55 passed in Mathematics and 67 passed in Physics.The number of students who passed in Physics only is:





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Phrases Previous Year PYQ Phrases NIMCET 2012 PYQ

Solution

Use the formula: 
$\text{Physics only} = n(P) - n(M \cap P)$ 
First find $n(M \cap P$) using: 
$n(M) + n(P) - n(M \cap P) = 100$ 
So: $55 + 67 - n(M \cap P) = 100$ 
$122 - n(M \cap P) = 100$ 
$n(M \cap P) = 22$ 
Now: $\text{Physics only} = 67 - 22 = 45$
Phrases PYQ
Survey: $63%$ like cheese, $76%$ like apples. If $x%$ like both?





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Phrases Previous Year PYQ Phrases NIMCET 2010 PYQ

Solution

Using inclusion–exclusion: 
$63 + 76 - x \le 100$ 
$139 - x \le 100$ 
$x \ge 39$ 
 Max value of $x$ cannot exceed minimum of both percentages 
→ $x \le 63$ 
 Thus $39 \le x \le 63$.
Phrases PYQ
A six-faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is





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Phrases Previous Year PYQ Phrases NIMCET 2008 PYQ

Solution

Let $P(\text{even})=p$ and $P(\text{odd})=3p$ $p+3p=1 \Rightarrow p=\dfrac14$ So $P(\text{even})=\dfrac14,\quad P(\text{odd})=\dfrac34$ Sum is even when both outcomes are even or both are odd. $P=\left(\dfrac14\right)^2+\left(\dfrac34\right)^2=\dfrac1{16}+\dfrac9{16}=\dfrac{10}{16}=\dfrac58$ Answer: $\boxed{\dfrac58}$
Phrases PYQ
A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, are visible. The probability that the letter has come from CALCUTTA is





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Phrases Previous Year PYQ Phrases NIMCET 2008 PYQ

Solution

TATANAGAR has $2$ occurrences of TA CALCUTTA has $3$ occurrences of TA Total occurrences $=5$ Required probability $=\dfrac{3}{5}$ This is not listed. Answer: $\boxed{\text{None of these}}$

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