Combination

Q.

Statement I The number of ways distributing $10$, identical balls in $4$ distinct boxes such that no box is empty, is ${}^9{C}_3$ .

Statement II The number of ways of choosing any $3$ places from $9$ different places, is ${}^9{C}_3$ .

Which is correct?

1. Statement I is correct, Statement II is correct; Statement II is not a correct explanation for Statement I

2. Statement I is correct, Statement II is incorrect

3. Statement I is incorrect, Statement II is correct

4. Statement I is correct, Statement II is correct; Statement II is a correct explanation for Statement I

Q. A room has 8 doors. In how many ways can a man enter the room by a door and exit by a different door?

1. 64
2. 56
3. 49
4. 15

Q. The number of 4-digit numbers that can be formed by using the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 such that the At least digit used is 4, when repetition of digits is allowed, is

1. 617
2. 761
3. 671
4. 716

Q. The map given below shows five different villages. Village M lies exactly halfway between the two pairs of villages A and B as well as and P and Q. What is the distance between village A and village P?

1. 4 km
   
2. 3 km
   
3. 5 km
   

4. 6 km

Q. If m parallel lines in plane are intersected by n parallel lines, then number of parallelograms formed is

1. 
   
2. 
   
3. 
   
4. 

Q.

Which one is greater?
$8^2$ or $2^8$

Q. Number of four different digits are formed from the digits $1,2,3,4,5,6,7,8,9$. How many of them are greater than $4000$?

1. ${{}^{9}P}_4$
2. $2016$
3. none of these
4. $2010$

Q. The perimeter of a triangle is $6p^2-4p+9$ and two of its sides are $p^2-2p+1$ and $3p^2-5p+3$. Find the third side of the triangle.

1. $8p^2+11p-7$
2. $2p^2+3p+5$
3. $5p^2-5p+9$
4. $3p^2+5p-4$

Q. John and Alex play in the same soccer team. Alex scored 3 more goals than John, but together they scored less than 9 goals. What is the possible number of goals Alex scored?

1. 4, 5, 6
2. 5, 6, 7
3. 4, 5, 6, 7
4. 3, 4, 5

Q. The number of ways of distriuting 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

1. 5
2. 21
3. $3^8$
4. ${}^8{C}_3$

Q. The base of a triangle lies along the line $x=a$ and is of length $a$. If the area of the triangle is $a^2$, the vertex lies of the line.

1. $x=-a$
2. $x=0$
3. $x=\frac{a}{2}$
4. $x=3a$

Q. In an examination hall, there are four rows of chairs. Each row has $8$ chairs one behind the other. There are two classes sitting for the examination with $16$ students in each class. It is desired that in each row all students belong to the same class and that no two adjacent rows are allotted to the same class. If the $32$ students can be seated in $m$ ways, the value of $\frac{m}{(16!{)}^2}$ is:

Q. What is the output after for loop executes for (i =0; i<10;++i)
Printf("%d", i &1);

1. 01 01 01 01 01
2. 00 00 00 00 00
3. 01 11 11 11 11
4. 11 11 11 11 11

Q. The digit in the units' place in the cube root of 21952 is

1. 8
2. None of these
3. 4
4. 6

Q.

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is

1. 6210

2. 5040

3. 1110

4. 385

Q. Find the number of ways in which a committee of 2 teachers and 3 students can be formed out of 10 teachers and 20 students. In how many of these committees a particular teacher is included?

Q. How many sides does the given closed shape has?

1. 5 sides
2. 6 sides
3. 7 sides
4. 4 sides

Q. A restaurant has two favourite dishes. What is the probability that both the dishes will be liked by people?

1. $\frac{1}{648}$
2. $\frac{25}{650}$
3. $\frac{25}{648}$
4. $\frac{5}{648}$

Q. Vij is developing a weight loss regimen, which includes both a workout plan and a calorie-restriction plan. Vij wants to work out for no less than $30$ minutes and no more than $60$ minutes a day and consume no less than $2,000$ and no more than $2,500$ calories. If each minute, m, of his workout time burns $50$ calories, which of the following inequalities represents the number of minutes, $m$, that Vij can work out each day to burn off as many calories as he consumes?

1. $30\le m\le 60$
2. $30\le m\le 50$
3. $40\le m<50$
4. $40\le m\le 50$

Q. Statement-1; The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is $9C_3$.
Statement-2: The number of ways of choosing any 3 places from 9 different places is $9C_3$.

1. Statement-1 is true, Statement-2is false.
2. Statement-1 is true, Statement -2 is true: Statement-2 is not a correct explanation for Statement-1.
3. Statement-1 is false, Statement-2 is true.
4. Statement-1 is true, Statement-2 true; Statement-2 is a correct explanation for Statement-1.

Q. If 7 points out of 12 are in the same straight line, then the number of traingles formed is

1. 19
2. 158
3. 201
4. 185

Q. The probability of India winning a test match against West Indies is $\frac{1}{2}$. Assuming independence from match to match, the probability that in a 5 match series. India's second win occurs at third test is

1. $\frac{1}{8}$
2. $\frac{1}{4}$
3. $\frac{1}{2}$
4. $\frac{2}{3}$