Cube Numbers

Q. What is Hardy-Ramanujan number?

Q.

Three numbers are in the ratio 3:4:5. If the sum of the largest and that smallest equals the sum of the second and 52, find the numbers.

Q.

If $u=\log (x^3+y^3+z^3-3xyz)$, then $\left(\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}+\frac{\partial u}{\partial z}\right)(x+y+z)=$

1. $0$

2. $1$

3. $2$

4. $3$

Q.

A vendor supplies $32liters$ of milk to a hotel in the morning and$68liters$of milk in the evening. If the milk costs $Rs.15perliter,$ how much money is due to the vendor per day?

Q. $a^3$ – $b^3$ = $(a-b{)}^3$ + 3ab(a - b)​

1. True
2. False

Q.

You are told that $1331$ is a perfect cube. Can you guess without factorisation what is its cube root? Similarly guess the cube roots of $4913,12167,32768$

Q.

A person spends 1/3 of the money with him on clothes, 1/5 of the remaining on food and 1/4 of the remaining on travel. Now he is left 400 rupees.How much did he nave with him in the beginning?

Q.

Question 7

Write the correct answer from the given four options.

The one's digit of the cube of 23 is

a) 6
b) 7
c) 3
d) 9

Q. Divide Rs 1380 among Aehmad , Johan and Babita, so that the amount Aehmad received is 5 times as much as Babita share and 3 times as much as Johan 's share

Q.

The length of the total boundary of a closed figure is called its area.

1. True

2. False

Q. The volume of a cubical box is 32.768 cubic meters. Find the length of a side of the box.

1. 32m
2. 3.2m
3. 0.32m
4. 0.032m

Q.

Cube of any odd number is even.

1. True
2. False

Q. Cube of an even number is always ______ .

1. odd
2. even
3. prime
4. coprime to the given number

Q.

Which of the following numbers are not perfect cubes?

1. $216$

2. $128$

3. $1000$

4. $100$

5. $46656$

Q. 39. if x=3-2 root 2, find the value of- 1) 1 upon x 2) x+1 upon x 3) x-1 upon x 4) x cube + 1upon x cube 5) x cube - 1 uponx

Q.

The cube of an odd number is always an _________ number.

Q.

Evaluate the product $104\times 96$ without multiplying directly

Q. Evaluate $106\times 94$, using an appropriate algebraic identity.

1. 9904
2. 9562
3. 9964
4. 8552

Q.

100 is the smallest perfect square number that is the sum of cubes of 4 consecutive natural numbers.

1. True

2. False

Q. If $\frac{-4}{3}y=-\frac{3}{4},$ then y is equal to _____.

1. $-{\left(\frac{3}{4}\right)}^2$
2. $-{\left(\frac{4}{3}\right)}^2$
3. ${\left(\frac{3}{4}\right)}^2$
4. ${\left(\frac{4}{3}\right)}^2$

Q.

Find the volume of a cube whose surface area is $384m^2.$

Q.

There is no perfect cube that ends with $8$ (True or False)

1. True
2. False

Q.

Is 3087 a perfect cube.

Q. A bag contains ₹600 in the form of ₹1, 50 paise and 25 paise coins in the ratio 3:4:12.Find the number of 25paise coins.

Q. The value of {83^3 + 17^3} / (83 x 66 + 17^2)

Q.

Question 85 (g)

Evaluate
$\frac{6^4\times 9^2\times {25}^3}{3^2\times 4^2\times {15}^6}$

Q.

Find two numbers such that one of them exceeds the other by 9 and their sum is 81.

Q. Two numbers are in the ratio 7 is to 8 on adding 3 to the first and 8 to the second their ratio become 3 is to 4 find the number

Q.

$a^3$ - $b^3$ is always divisible by:

1. a - b

2. a × b

3. 2a + b

4. a + b

Q. 7. If x=cube root of 3, y=fourth root of 4, z=sixth root of 6, then 1) x