Highest Power of a Number

Q.

H.C.F. of 3240, 3600 and a third number is 36 and their L.C.M. is 2${}^4$ x 3${}^5$ x 5${}^2$ x 7${}^2$. The third number is ____.

1. None

2. 2² x 3⁵ x 7²

3. 2² x 5³ x 7²

4. 2⁵ x 5² x 7²

5. 2³ x 3⁵ x 7²

Q. The greatest number, which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32 and 35 is _____.

1. 4714
2. 5200
3. 5600
4. 2316
5. 1120

Q.

What is the cube of 8?

Q.

What is the value of $\frac{1}{2}$ to the power $-6$?

Q.

The sum of the cubes of first 8 natural numbers is

1. 1269

2. 1298

3. 1296

4. 1297

Q.

What is the largest power of $20$ contained in $100$ factorial?

Q.

By what least number 675 be multiplied to obtain a number which is a perfect cube?

1. 6

2. 7

3. 8

4. 9

5. 5

Q.

In how many ways can the letters of the word MANAGER be rearranged so that the two A's do not appear together?

1. 1600

2. 1700

3. 1750

4. 1800

5. 1900

Q. Seema, Meena and Reena start jogging around a circular stadium and complete one round in 54 seconds, 42 seconds and 63 seconds respectively. Approximately after how many minutes they will meet again at the starting point?

1. 8
2. 10
3. 3
4. 6
5. 32

Q.

What is the value of $1\times 1!+2\times 2!+3\times 3!+............n\times n!$; where n! means n factorial or n(n-1)(n-2)...1

1. (n+1)!

2. n!-1

3. n!

4. None of these

5. (n+1)!-1

Q.

If a metallic cuboid weighs 16 kg, what would be the weight of the new cuboid of metal, if all dimensions are reduced to one – fourth of the original?

1. 0.50 kg

2. 0.75 kg

3. 1 kg

4. 0.95 kg

5. 0.25 kg

Q.

For which battery is the total sales of all the seven years the maximum?

1. 32 AH

2. 35 AH

3. 55 AH

4. 4 AH

5. 7 AH

Q.

How many integers that lie between 0 and 1000 which when divided by 2 or 4 leave a remainder of 1 and by 7 leaves a remainder of 2 ?

1. 38

2. 36

3. 40

4. 39

Q. Find the cube of 34.

1. 44304
2. 39304
3. 50864
4. 38304

Q.

8, 10, 18, 28, (?), 74

1. None of These

2. 48

3. 46

4. 50

5. 44

Q. If a₁ = 1 and a_n+1 – 3a_n + 2 = 4n for every positive integer n, then a₁₀₀ equals

1. 3⁹⁹ – 200
2. 3⁹⁹ + 200
3. 3¹⁰⁰ – 200
4. 3¹⁰⁰ + 200
5. 3⁹⁹-100

Q. f(f(f(k))) = 27. What is the sum of the digits of k ?

1. 3
2. 6
3. 9
4. 8
5. cannot be determined

Q. State True or False.

1. True
2. False

Q.

What is the value of $1\times 1!+2\times 2!+3\times 3!+............n\times n!$; where n! means n factorial or n(n-1)(n-2)...1

1. (n+1)!-1

2. (n+1)!

3. n!-1

4. None of these

Q.

How many integers are there from 500 to 2000 that leave a remainder of 2 on division by 5 and a remainder of 1 on division by 7?

1. 35

2. 36

3. 43

4. 42

Q. When 315! is divided by ${1215}^x$, remainder=0. What is the maximum possible value for x?

1. 31
2. 15
3. 33
4. none of these
5. 32

Q. Determine the number of people who like RNBDJ and Singh is King but not Ghajni.

1. 120
2. 200
3. 240
4. 180
5. 280

Q. Find the minimum value of$a+\frac{1}{a},(a>0)$

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

Q. There is a number which is formed from 6 natural numbered tiles arranged in a row. The value of the first tile (leftmost) is 1. If this tile is moved from the leftmost place to the rightmost place, then the number obtained is three times of the original number. Then the sum of the digits of this special number is?

1. 20
2. 19
3. 26
4. 21

Q. The average age of 30 students in a class is 12 years. The average age of a group of 5 of the students is 10 years and that of another group of 5 of them is 14 years. The average age of the remaining students is

1. 8 years
2. 10 years
3. 14 years
4. 12 years

Q.

The number of 6’s present in the quotient obtained when 111…..111 (99 number of 1’s) is divided by 33……3(33 number of 3’s) is

1. 35

2. 32

3. 33

4. 34

Q. If a²b³c = 256/27 find min value of a + b + c, given a, b, c are positive real nos

1. 6
2. 11
3. 12
4. 4
5. 10

Q. The H.C.F. of $4\times 27\times 3125,8\times 9\times 25\times 7$ and $16\times 81\times 5\times 11\times 49$ is _____.

1. 45
2. 180
3. 360
4. 540
5. 1260

Q.

In how many ways can the letters of the word MANAGER be rearranged so that the two A's do not appear together?

1. 1800

2. 1600

3. 1750

4. 1900

Q.

What will come in place of the question mark (?) in the following question?

$0.0005\times 75\times {10}^3+?=150\%of29.98$

1. 10

2. 7.5

3. 5

4. 12.5

5. None of these