Change set

Pick exam & year, then Go.

Question map
Not attempted Correct Incorrect ★ Bookmarked
Loading…
Q148 (IAS/1994) Science & Technology › Basic Science (Physics, Chemistry, Biology)

The square root of the cube of this number is the cube of its square root. It is not 1 and it is less than 6. What is it ?

Result
Your answer: —  Â·  Correct: C

Explanation

The question describes a mathematical identity. Let the number be x. The two conditions given are:

  • Square root of the cube: √(x³) = (x³)^{1/2} = x^{3/2}
  • Cube of the square root: (√x)³ = (x^{1/2})³ = x^{3/2}

Mathematically, x^{3/2} = x^{3/2} is an identity that holds true for all non-negative numbers. However, the problem provides specific constraints: the number is not 1 and is less than 6. Among the options (2, 3, 4, 5), all satisfy the mathematical condition. In competitive exams, 4 is the intended answer because it is the only perfect square, allowing the square root to result in a rational integer (√4 = 2), making the calculation clean (8 = 8).

How others answered
Each bar shows the % of students who chose that option. Green bar = correct answer, blue outline = your choice.
Community Performance
Out of everyone who attempted this question.
40%
got it right
✓ Thank you! We'll review this.

SIMILAR QUESTIONS

IAS · 2006 · Q103 Relevance score: -1.28

Each of the six faces of a cube is numbered by one of the six digits from 1 to 6. This cube is shown in its four different positions in the figures I, II, III and IV: Consider the following statements: I. Figures II and III are sufficient to know as to which face is opposite to the face numbered 6. II. Figure II and III are sufficient to know as to which face is opposite to the face numbered 4. III. Figures I and IV are sufficient to know as to which face is opposite to the face numbered 3. Which of the statements given are correct?

IAS · 2007 · Q41 Relevance score: -1.67

Six faces of a cube are numbered from 1 to 6, each face carrying one different number. Further, 1. The face 2 is opposite to the face 6. 2. The face 1 is opposite to the face 5. 3. The face 3 is between the face 1 and the face 5. 4. The face 4 is adjacent to the face 2. Which one of the following is correct?

CAPF · 2019 · Q40 Relevance score: -3.91

What is the natural number n for which (3^9 + 3^{12} + 3^{15} + 3^n) is a perfect cube of an integer?

IAS · 1997 · Q140 Relevance score: -4.72

If the number representing volume and surface area of a cube are equal, then the length of the edge of the cube in terms of the unit of measurement will be

CAPF · 2022 · Q1 Relevance score: -4.98

Which one of the following is the difference of the sum of cubes of first ten natural numbers and the sum of squares of first ten natural numbers?