Olympiad Mathematics - Cubes and Cube Roots
Exam Duration: 45 Mins Total Questions : 25
The value of 453 - 653 - 203 is ______
- (a)
175500
- (b)
-191500
- (c)
170000
- (d)
-170000
\(\sqrt [ 3 ]{ -2744 } \div \sqrt [ 3 ]{ 0.008 } \) = x, then the value of x is ______
- (a)
70
- (b)
-70
- (c)
14
- (d)
-14
\(\sqrt [ 3 ]{ 3\left( \sqrt [ 3 ]{ x } -\frac { 1 }{ \sqrt [ 3 ]{ x } } \right) } \)=2 then \(\sqrt [ 3 ]{ x } +\frac { 1 }{ \sqrt [ 3 ]{ x } } \) = ______
- (a)
\(\frac{10}{3}\)
- (b)
-\(\frac{10}{3}\)
- (c)
\(\frac{3}{15}\)
- (d)
Both (A) and (B)
How many cubes of side 2 cm can be packed in a cubical box with inner side equal to 4 cm?
- (a)
6
- (b)
4
- (c)
8
- (d)
2
Find the smallest natural number by which 1458 must be divided so that the quotient is a perfect cube.
- (a)
4
- (b)
2
- (c)
6
- (d)
8
In the five digit number 1b6a3, a is the greatest single digit perfect cube and twice of it exceeds b by 7. Then the sum of the number and its cube root is ______
- (a)
18700
- (b)
11862
- (c)
19710
- (d)
25320
The value of \(\sqrt [ 3 ]{ \frac { -{ a }^{ 6 }\times { b }^{ 3 }\times { c }^{ 21 } }{ { c }^{ 9 }\times { a }^{ 12 } } } \) is _________
- (a)
\(\frac { { -bc }^{ 3 } }{ { a }^{ 2 } } \)
- (b)
\(\frac { { -bc }^{ 4 } }{ { a }^{ 2 } } \)
- (c)
\(\frac { { -ab }^{ 4 } }{ { c }^{ 2 } } \)
- (d)
\(\frac { { -bc }^{ 4 } }{ { a }^{ 2 } } \)
Three numbers are in the ratio 2:3:5 to one another. The sum of their cubes is 54880. The numbers are ______
- (a)
14,21,35
- (b)
12, 15, 17
- (c)
14, 18, 21
- (d)
21, 28, 32
The cubes of a 2-digit number will contain _______
- (a)
4 digits
- (b)
5 digits
- (c)
6 digits
- (d)
4, 5 or 6 digits
The cube of an odd natural number is always ________
- (a)
Even
- (b)
Odd
- (c)
Even or odd
- (d)
Can't say
The length of each side of a cubical box is 2.4 m. Its volume is _______
- (a)
1.3824 x 107 cu. cm
- (b)
13.824 cu. cm
- (c)
1.3824 x 106 cu. cm
- (d)
13.824 x 104 cu. cm
The units digit of the cube of a number is 9. The unit'd digit of its cube root is _______
- (a)
9
- (b)
7
- (c)
3
- (d)
1
The cube of a number x is nine times of x, then find x, where x≠0 and x≠-3.
- (a)
8
- (b)
2
- (c)
4
- (d)
3
Two cubes have volumes in the ratio 1:27. The ratio of the area of the face of one to that of the other is ________
- (a)
1:3
- (b)
1:6
- (c)
1:9
- (d)
1:18
The smallest number by which 392 must be multiplied so that the product is a perfect cube is ________
- (a)
3
- (b)
5
- (c)
7
- (d)
9
Mohit gave a problem to Samrath. Help Samrath to answer the question.
- (a)
4
- (b)
6
- (c)
8
- (d)
10
A tank is in the form of a cube whose volume is 9261000 m3. Find the length of side of the tank.
- (a)
230 m
- (b)
250 m
- (c)
210 m
- (d)
180 m
Atul made a cuboid of plastincine. Length breadth and height of the cuboid are cm and 50 cm. How many minimum such cuboids he needs to make a perfect cube?
- (a)
4
- (b)
20
- (c)
12
- (d)
25
A rectangular cubical piece of metal of dimensions 2 cm x 3 cm x 4 cm is melted. Some more of the metal is added and it is made into a cube. The cube has integral measures for its sides. What is the minimum amount of metal that is added and what is the side of this cube?
- (a)
10cm3,4cm
- (b)
3 cm3, 3 cm
- (c)
11 cm3, 3 cm
- (d)
4 cm3, 3 cm
To collect rain water, Mini made a cubical tank which can hold 91125 m3 water. She uses this water for watering the plants of her garden. What is the height of the tank?
- (a)
50 m
- (b)
25 m
- (c)
45 m
- (d)
40 m
Which of the following options is INCORRECT?
- (a)
Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500. The numbers will be 5, 10, 15
- (b)
The digit in the units place for the cube of a four digit number of the form xyz8 is 2
- (c)
The smallest number by which 3600 be divided to make it a perfect cube is 450
- (d)
None of these
Find the cube root of
(i) 0.003375 = P
(ii) 1.331 = Q
(iii) 4.913 = R
(iv) 15.625 = S
- (a)
P Q R S 0.215 1.31 2.7 2.55 - (b)
P Q R S 0.115 1.11 1.1 3.25 - (c)
P Q R S 0.15 1.1 1.7 2.5 - (d)
P Q R S 0.25 1.21 2.17 4.15
Match the following.
Column-I | Column-II |
P. The smallest number that should be subtracted from 130 to make it perfect cube is |
4 |
Q. The smallest number that should be subtracted from 9268 to make it perfect cube is |
3 |
R. The smallest number that should be added to 2194 to make it perfect cube is. |
5 |
S. The smallest number that should be added to 6855 make it perfect cube is |
7 |
- (a)
P ⟶ (iii); Q ⟶ (i); R ⟶ (iv); S ⟶ (ii)
- (b)
p ⟶ (ii); Q ⟶ (iv); R ⟶ (i); S ⟶ (iii)
- (c)
p ⟶ (iii); Q ⟶ (i); R ⟶ (ii); S ⟶ (iv)
- (d)
p ⟶ (iii); Q ⟶ (iv); R ⟶ (ii); S ⟶ (i)
Evaluate the following.
(i) \(\sqrt [ 3 ]{ \frac { 0.027 }{ 0.008 } } \div \sqrt [ 3 ]{ \frac { 0.729 }{ 0.512 } } -\frac { 1 }{ 3 } \)
(ii) \(\sqrt [ 3 ]{ 343 } +\sqrt [ 3 ]{ 0.064 } -\sqrt [ 3 ]{ 0.125 } \)
(iii) \(\left[ \left( \sqrt [ 3 ]{ \frac { -216 }{ 42875 } +\sqrt [ 3 ]{ \frac { 64 }{ 125 } } } \right) \right] \times \sqrt [ 3 ]{ \frac { 343 }{ 1331 } } \).
- (a)
(i) (ii) (iii) 1 6.9 \(\frac{2}{5}\) - (b)
(i) (ii) (iii) 3 7.1 \(\frac{1}{5}\) - (c)
(i) (ii) (iii) 4 7.9 \(\frac{2}{5}\) - (d)
(i) (ii) (iii) 1 6.5 \(\frac{1}{5}\)
Which of the following statements is CORRECT?
Statement - 1: Cube root of 117.649 is a rational number.
Statement - 2: Cube of an odd number may or may not be odd.
- (a)
Only Statement - 1
- (b)
Only Statement - 2
- (c)
Both Statement - 1 and Statement - 2
- (d)
Neither Statement - 1 nor Statement - 2