Permutation: n Different Things Taken r at a Time

Q. The number of four digit even numbers that can be formed with 0, 1, 2, 3, 7, 8, is

1. 180
2. 175
3. 156
4. 160

Q. The number of permutations that can be made out of the letters of the word “EQUATION” which start with a consonant and end with a consonant is

1. 
2. 
3. 
4. 

Q.

What is the decimal equivalent of the octal number $217$?

1. $140$

2. $143$

3. $150$

4. $155$

Q. Anagrams are made by using the letters of the word ${}^{\prime }HINDUSTA{N}^{\prime }$ How many anagrams can be made?

Q. On one page of a telephone directory there were $200$ telephone numbers. The frequency distribution of their unit place digit is given in the following table:

Digit	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$
Frequency	$22$	$26$	$22$	$22$	$20$	$10$	$14$	$28$	$16$	$20$

1. 
   $0.15$
2. 
   $0.17$
3. 
   $0.18$
4. None of these
   

Q. The number of ways in which spensasne number $1,2,3,......8$ can be seated in a ring so that $1$ always sits between $2$ and $3$ is

1. $72$
2. $120$
3. $240$
4. $360$

Q. Find the value of-
$5^2\times (-1{)}^{19}\times (-2{)}^3\times 3^2\times (-10{)}^3$

Q. Consider $a^x$. For $x=10$, when $x$ divides $a$, the remainder is 4. Find the units digit of $a^x$.

1. 6
2. 5
3. 3
4. 4

Q. Seven friends P, Q, R, S, T, U, and V (boys and girls) are sitting on three benches I, II, and III. Such that at least one of them is on each bench and at least one girl is on each bench.

• R, who is a girl, does not sit with P, T, and S.
• U, who is a boy, sits with only Q.
• P sits on the Bench I.
• V sits on the Bench III.
• S and T are the brothers of R.

Who among the following must be a girl?

1. P
2. U
3. V
4. S

Q. Who sits between Rohit and Tarun assuming that there is only one person between them ?

1. Abhishek
2. Pramod
3. Sameer
4. Cannot be determined
5. None of these

Q. Construct an equation using $x=\frac{2}{3}$, such that the numerical factor of $x$ is $\frac{4}{5}$ in the equation.

Q. In a certain sporting goods manufacturing company, a quality control expert tests a randomly selected group of $1,000$ tennis balls in order to determine how many contain defects. If this quality control expert discovered that $13$ of the randomly selected tennis balls were defective, select the most appropriate inference from the following.

1. $98.7\%$ of the company's tennis balls are defective
2. $98.7\%$ of the company's tennis balls are not defective
3. $9.87\%$ of the comany's tennis balls are defective
4. $9.87\%$ of the company's tennis balls are not defective

Q. Six friends A, B, C, D, E, and F are sitting around a circular table, such that:

• A is sitting opposite C.
• An equal number of friends are sitting between B and F.
• C is sitting adjacent to E.
• B is sitting adjacent to A and E.

Who is sitting opposite D?

1. E
2. A
3. B
4. C