Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
31
Solve the equation: 10^x = 10000
Answer:
4
Count the number of zeroes in 10000 to find its power of 10. There are four zeroes, so 10000 is 10^4. Therefore, from 10^x = 10^4, x must be 4.
32
Solve for x: 5^x = 125
Answer:
3
Write 125 with a base of 5. Because 5 * 5 * 5 = 125, we know 125 is 5^3. Equating the exponents from 5^x = 5^3 gives x = 3.
33
Find the value of x in the equation: 3^x = 27
Answer:
3
Express 27 as a power of 3, which is 3^3. Setting the exponents equal from the equation 3^x = 3^3 tells us that x equals 3.
34
Solve the exponential equation for x: 2^x = 16
Answer:
4
To solve, express both sides with the same base. Since 16 is equal to 2^4, the equation becomes 2^x = 2^4. Thus, the exponents must be equal, making x = 4.
35
Rationalize the denominator: 2 / sqrt(7)
Answer:
2*sqrt(7) / 7
Multiply numerator and denominator by sqrt(7) to rationalize. The numerator becomes 2*sqrt(7) and the denominator becomes 7, creating the fraction 2*sqrt(7) / 7.
36
Rationalize the denominator: 5 / sqrt(5)
Answer:
sqrt(5)
Multiply both the top and the bottom by sqrt(5). This produces (5*sqrt(5)) / 5. Dividing by 5 leaves only the term sqrt(5).
37
Rationalize the denominator: 3 / sqrt(3)
Answer:
sqrt(3)
Multiply numerator and denominator by sqrt(3) to rationalize. This gives (3*sqrt(3)) / 3. The 3s cancel out, leaving just sqrt(3).
38
Rationalize the denominator: 1 / sqrt(2)
Answer:
sqrt(2) / 2
To remove the radical from the denominator, multiply both numerator and denominator by sqrt(2). This results in (1 * sqrt(2)) / (sqrt(2) * sqrt(2)), which simplifies to sqrt(2) / 2.
39
Calculate: sqrt(50) / sqrt(2)
Answer:
5
Using the quotient property, merge the terms into one square root: sqrt(50 / 2). This simplifies to sqrt(25), which has a value of 5.
40
Divide the radicals: sqrt(24) / sqrt(6)
Answer:
2
For division of radicals, divide the radicands (the numbers inside) under a single root. This makes it sqrt(24 / 6) = sqrt(4). The square root of 4 is exactly 2.