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
81
Simplify: x^3 * x^-5
Answer:
1/x^2
First, add the exponents: 3 + (-5) = -2, giving x^-2. Then, convert the negative exponent to a positive one by rewriting it as 1/x^2.
82
Evaluate: (2/3)^-1
Answer:
3/2
Raising a fraction to the power of -1 simply means finding its reciprocal. Flipping the numerator and denominator of 2/3 gives the result 3/2.
83
Calculate: (1/2)^-2
Answer:
4
A negative exponent on a fraction flips the fraction (takes the reciprocal) and makes the exponent positive. So, (1/2)^-2 becomes (2/1)^2, which equals 4.
84
Evaluate: 10^-3
Answer:
1/1000
The expression 10^-3 translates to 1/(10^3). Since 10^3 equals 1000, the final simplified value is 1/1000 (or 0.001).
85
Simplify the expression: a^-5
Answer:
1/a^5
By the rules of negative exponents, moving the base to the denominator makes the exponent positive. Thus, a^-5 is rewritten as 1/a^5.
86
What is the value of 5^-1?
Answer:
1/5
An exponent of -1 indicates the reciprocal of the base number. Therefore, 5^-1 is the reciprocal of 5, which is 1/5.
87
Simplify: y^-4
Answer:
1/y^4
A negative exponent flips the position of the term in a fraction. Changing y^-4 to a positive exponent moves it to the denominator, becoming 1/y^4.
88
Calculate: 3^-2
Answer:
1/9
The negative exponent rule dictates that 3^-2 flips the base to the denominator, giving 1/(3^2). Since 3^2 is 9, the final answer is 1/9.
89
Simplify the expression: x^-2
Answer:
1/x^2
To rewrite a term with a negative exponent, place it in the denominator with a positive exponent. Therefore, x^-2 is equivalent to 1/x^2.
90
Evaluate: 2^-3
Answer:
1/8
A negative exponent means taking the reciprocal of the base and making the exponent positive. So, 2^-3 becomes 1/(2^3), which evaluates to 1/8.