Question 51
Which of the following statements about number properties is/are CORRECT?
Detailed Solution
All four statements are correct.
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GATE CSE Quantitative Aptitude – Number Systems, Percentages, Ratio & Work | Set 1
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Question 52
Which of the following numbers is/are divisible by 11?
Detailed Solution
121=11², 1331=11³, and 14641=11⁴ are divisible by 11; 12321 is not.
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Question 53
Find the remainder when $7^84$ is divided by 342.
Detailed Solution
Since $7^3$ = 343 = 342+1, $7^84$=($7^3$)^28 ≡1 (mod 342).
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Question 54
How many trailing zeros are in the product $1^1 * 2^2 * 3^3$ * ... * 10^10?
Detailed Solution
Trailing zeros are determined by power of 5: factors with 5 are $5^5$ (gives 5 factors of 5) and 10^10 (gives 10 factors of 5). Total 5s = 5 + 10 = 15.
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Question 55
If $x = 1 / (2 + sqrt(3))$, find the value of $x^3 - 2x^2 - 7x + 5$.
Detailed Solution
$1/(2+√3)=2-√3. Using x²-4x+1=0, substitution gives x³-2x²-7x+5=3.$
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