Mutually Exclusive Events

Q. What is the probability of getting at least one six in a single throw of three unbiased dice?

1. 
2. 
3. 
4. 

Q.

Write the place value of the underlined digit in the following numbers: $\underline{3},26,70,804$

Q.

In a horse race, the odds in favor of three horses are $1:2,1:3,\mathrm{and}1:4$. The probability that one of the horses will win the race is.

1. $\frac{7}{60}$

2. $\frac{47}{60}$

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

4. $\frac{3}{4}$

Q.

There are $\mathrm{m}$ persons sitting in a row. Two of these are selected at random. The probability that the two selected persons are not together is

1. $\frac{1}{\left(\mathrm{m}+1\right)}$

2. $1-\left(\frac{2}{\mathrm{m}}\right)$

3. $1-\left(\frac{2}{\mathrm{m}+1}\right)$

4. $\frac{\mathrm{m}(\mathrm{m}+1)}{(\mathrm{m}-1)(\mathrm{m}-2)}$

Q. Total runs scored by India and Australia in Match 4 together is approximately what percentage of the total runs scored by England in all the five matches together?

1. 42
2. 18
3. 36
4. 24
5. 28

Q.

An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered 2, 3, 4, .., 12 is picked and the number on the card is noted. The probability that the noted number is either 7 or 8, is

1. $0.24$

2. $0.244$

3. $0.024$

4. None of these.

Q. Study the following table carefully to answer the questions that follow:

Number (N) of candidates (in lakhs) appearing for an entrance examination from six different states and the percentage (P) of candidates clearing the same over the years
$\begin{array}{ccccccc}State\to & A& B& C& D& E& F\\ Year\downarrow & & & & & & \\ & N\mid P& N\mid P& N\mid P& N\mid P& N\mid P& N\mid P\\ 2004& 1.23\mid 42& 1.04\mid 51& 1.11\mid 32& 1.32\mid 24& 1.23\mid 36& 1.33\mid 31\\ 2005& 1.05\mid 43& 1.12\mid 62& 1.07\mid 47& 1.15\mid 49& 1.18\mid 55& 1.24\mid 24\\ 2006& 2.04\mid 38& 1.48\mid 32& 1.08\mid 28& 1.96\mid 35& 1.42\mid 49& 1.58\mid 26\\ 2007& 1.98\mid 41& 2.07\mid 43& 1.19\mid 30& 1.88\mid 46& 1.36\mid 47& 1.79\mid 29\\ 2008& 1.66\mid 53& 1.81\mid 50& 1.56\mid 42& 1.82\mid 60& 1.73\mid 57& 1.86\mid 34\\ 2009& 1.57\mid 39& 1.73\mid 36& 1.64\mid 52& 2.01\mid 56& 1.69\mid 55& 1.95\mid 37\end{array}$
What is the number of candidates not clearing the entrance exam from State A in the year 2007?

1. 11682
2. 1868200
3. 1166820
4. None of these
5. 186820

Q.

Study the following table carefully to answer the questions that follow:

Number (N) of candidates (in lakhs) appearing for an entrance examination from six different states and the percentage (P) of candidates clearing the same over the years
$\begin{array}{ccccccc}State\to & A& B& C& D& E& F\\ Year\downarrow & & & & & & \\ & N\mid P& N\mid P& N\mid P& N\mid P& N\mid P& N\mid P\\ 2004& 1.23\mid 42& 1.04\mid 51& 1.11\mid 32& 1.32\mid 24& 1.23\mid 36& 1.33\mid 31\\ 2005& 1.05\mid 43& 1.12\mid 62& 1.07\mid 47& 1.15\mid 49& 1.18\mid 55& 1.24\mid 24\\ 2006& 2.04\mid 38& 1.48\mid 32& 1.08\mid 28& 1.96\mid 35& 1.42\mid 49& 1.58\mid 26\\ 2007& 1.98\mid 41& 2.07\mid 43& 1.19\mid 30& 1.88\mid 46& 1.36\mid 47& 1.79\mid 29\\ 2008& 1.66\mid 53& 1.81\mid 50& 1.56\mid 42& 1.82\mid 60& 1.73\mid 57& 1.86\mid 34\\ 2009& 1.57\mid 39& 1.73\mid 36& 1.64\mid 52& 2.01\mid 56& 1.69\mid 55& 1.95\mid 37\end{array}$
In which year did the highest number of candidates clear the entrance exam from state D?

1. 2008

2. 2006

3. 2009

4. 2007

5. None of these

Q. If 3 balls are picked at random, what is the probability that all are pink?

1. $\frac{3}{680}$
2. $\frac{2}{650}$
3. $\frac{1}{680}$
4. $\frac{4}{630}$
5. $\frac{4}{680}$

Q. In an examination a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 75 questions and secures 125 marks, the number of questions he attempted correctly is

1. 42
2. 35
3. 40
4. 46

Q. The total number of candidates who qualified the test in the year 2009 and 2010 together is the second highest in which zone?

1. Q
2. R
3. S
4. T
5. P

Q. A bag contains $3$ red and $3$ white balls. Two balls are drawn one by one. The probability that they are of different colours is

1. None of these
2. $\frac{3}{5}$
3. $\frac{2}{5}$
4. $\frac{3}{10}$

Q. How many students have opted for cricket and painting together?

Q. Study the following table carefully and answer the questions below:

Number of Candidates found Eligible and the Number of candidates Short listed for Interview for a recent Recruitment Process for Six Posts from Different States
E - Eligible S - Short listed
$\begin{array}{ccccccc}Post& I& II& III& IV& V& VI\\ State& E\mid S& E\mid S& E\mid S& E\mid S& E\mid S& E\mid S\\ A& 2500\mid 65& 7200\mid 240& 5200\mid 76& 3600\mid 200& 4600\mid 110& 5400\mid 380\\ B& 3200\mid 220& 8500\mid 420& 8400\mid 190& 6200\mid 320& 5800\mid 180& 6200\mid 430\\ C& 2800\mid 280& 4500\mid 350& 7600\mid 160& 8200\mid 440& 7300\mid 310& 3700\mid 250\\ D& 2400\mid 85& 4800\mid 200& 2600\mid 55& 7500\mid 350& 3900\mid 160& 4800\mid 360\\ E& 3000\mid 120& 5600\mid 280& 3800\mid 75& 6800\mid 280& 6100\mid 260& 7800\mid 520\\ F& 4800\mid 325& 6400\mid 320& 4400\mid 220& 4700\mid 180& 4900\mid 220& 8800\mid 640\\ G& 6500\mid 550& 7000\mid 140& 6000\mid 325& 5500\mid 220& 8100\mid 410& 2700\mid 200\end{array}$

What is the ratio of the total number of candidates shortlisted for all the posts together from State E to that from state G?

1. 9 : 7
2. 307 : 369
3. 73 : 79
4. 6 : 5
5. None of these

Q. The probability that at least a person will hit a target in shooting practice is $0.3$. If he shoots $10$ times, the probability that he hits the target is

1. $1$
2. ${\left(0.3\right)}^{10}$
3. ${\left(0.7\right)}^{10}$
4. $1-{\left(0.7\right)}^{10}$

Q. The population of a variety of tiny bush in an experimental field increased by 10% in the first year, increased by 8% in the second year but decreased by 10% in the third year. If the present number of bushes in the experimental field is 26730 then find the sum of digits of number of bushes in the beginning.

Q.

Write in figure: Seventy-three crore five lakh eighty-five thousand three hundred five.

Q.

$634\times 0=..............$