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
171
The number $93248x6$ is divisible by 11. Then the digit x is equal to. (a) 5 (b) 2 (c) 8 (d) 7
Answer:
7
According to the divisibility rule of 11, the difference between the sum of digits at odd places and the sum of digits at even places must be 0 or a multiple of 11.
172
How many digits are there to the right of the decimal point in the product of 95.75 and 0.02554? (a) 5 (b) 3 (c) 4 (d) 6
Answer:
6
**Step 1:** The number of decimal places in a product is typically the sum of the decimal places of the numbers being multiplied.
173
How many times does the digit 2 appear in the tens place in the counting from 1 to 100? (a) 20 (b) 11 (c) 10 (d) 19
Answer:
10
We need to find all the numbers between 1 and 100 that have a '2' in the tens digit position. These are the numbers in the twenties.
174
When a number n is divided by 5, the remainder is 2. When $n^2$ is divided by 5, the remainder will be: (a) 3 (b) 1 (c) 4 (d) 0
Answer:
4
**Method 1: Using Algebra**
175
$3^{71}+3^{72}+3^{73}+3^{74}+3^{75}$ is divisible by: (a) 8 (b) 5 (c) 11 (d) 7
Answer:
11
To solve this, we can factor out the smallest term, which is $3^{71}$, from the expression.
176
$(41^{43} + 43^{43})$ is divisible by: (a) 86 (b) 74 (c) 12 (d) 84
Answer:
84
We use the algebraic identity: for an odd integer $n$, the expression $(a^n + b^n)$ is always divisible by $(a+b)$.
177
Find the least number to be added to 1739 so that it is exactly divisible by 11. (a) 11 (b) 2 (c) 1 (d) 10
Answer:
10
**Step 1:** Divide 1739 by 11 to find the remainder.
178
$(47)^{25} – 1$ is exactly divisible by: (a) 21 (b) 24 (c) 23 (d) 19
Answer:
23
We use the algebraic identity: $(a^n - b^n)$ is always divisible by $(a-b)$ for any positive integer $n$.
179
How many numbers from 3 to 60 are odd numbers that are exactly divisible by 5? (a) 7 (b) 5 (c) 8 (d) 6
Answer:
6
We are looking for numbers that satisfy three conditions:
180
The least number consisting of five digits which is divisible by 97 is x. What is the sum of the digits of x? (a) 13 (b) 15 (c) 17 (d) 16
Answer:
17
**Step 1:** The smallest five-digit number is 10000.