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Quantitative Aptitude

SQUARE ROOT AND CUBE ROOT MCQs

Square Roots, Cube Roots, Squares And Square Roots

Total Questions : 547 | Page 10 of 55 pages
Question 91.

Determine the rth term of an A.P. whose 6th term is 12 and 8th term is 22

  1.    3r-7
  2.    5r-18
  3.    2r-6
  4.    5r-9
  5.    None of these
 Discuss Question
Answer: Option B. -> 5r-18
Question 92.

If pth term of an A.P is q the qth term is p, Find its term

  1.    p+q-r
  2.    -p+q+r
  3.    -r+p+q
  4.    pq+r
  5.    None of these
 Discuss Question
Answer: Option A. -> p+q-r
Question 93.

If 7 times the 7th term of an A.P is equal to 11 times its eleventh term, find the 18th term of the A.P

  1.    0
  2.    3
  3.    5
  4.    6
  5.    None of these
 Discuss Question
Answer: Option A. -> 0
Question 94.

Determine k so that k+2,4k-6 and 4k-2 are the three consecutive terms of an A.P

  1.    2
  2.    4
  3.    8
  4.    -4
  5.    None of these
 Discuss Question
Answer: Option C. -> 8
Question 95. Just by looking at the numbers, identify which of the following can not be a perfect square.
  1.    382
  2.    484
  3.    576
  4.    529
 Discuss Question
Answer: Option A. -> 382
:
A
Numbers ending with 2, 3, 7, or 8 at unit's place are never perfect squares.
Estimation without actually finding roots:
484 can be the perfect square of a number ending with 2 or 8.
576 can be the perfect square of a number ending with 4 or 6.
529 can be the perfect square of a number ending with 3 or 7.
Question 96. Aman has 729 coins. He gives only a part of these coins to his cousin as his birthday gift. This part is the square root of 729. How many coins did his cousin get?
  1.    27
  2.    9
  3.    12
  4.    81
 Discuss Question
Answer: Option A. -> 27
:
A
The square root of 729 should have 3 or 7 in its unit place. Because square of 3 and 7 has 9 in it's units place.Only 27 satisfies this.
Thus, Aman's cousin gets 27 coins as a birthday gift.
Also, we can find the square root using prime factorization as
729=3×3×3×3×3×3
729=36
Square root of 729 is equal to
729=36=33=27
Question 97. What will be the number of zeroes in the square of 60?
  1.    2
  2.    1
  3.    3
  4.    4
 Discuss Question
Answer: Option A. -> 2
:
A
If a number ends with n zeroes,its square will end with 2n zeroes.
Here, 60 ends with one zero, so its square will endwith 2 zeroes.
It is important to note thatthis stands true only for natural numbers (not decimals).
Question 98. If A, B, C, ..., X, Y, Z represents digits, which of the following could be a perfect square?
  1.    XX1
  2.    ABC2
  3.    PQR7
  4.    Can't be said without actual calculation
 Discuss Question
Answer: Option A. -> XX1
:
A
The numbers 7, 2 and 3 do not appear in the unit place ofany perfect square. So, ABC2 and PQR7 can not be perfect squares and XX1 is the only number which could be a perfect square.
Question 99. Square root of 1024 is 32.
  1.    True
  2.    False
  3.    9
  4.    Can't be determined
 Discuss Question
Answer: Option A. -> True
:
A
By division method,
323¯¯¯¯¯¯10¯¯¯¯¯¯249621241240
The square root of 1024 is 32.
Question 100. Which of the following could be a perfect square?
  1.    1681
  2.    23453
  3.    222222
  4.    1057
 Discuss Question
Answer: Option A. -> 1681
:
A
Perfect squares cannot have 2, 3, 7 or 8in their unit's place.
In the given options only 1681 does not endwith a number other than these.
The perfect squares of numbers ending in 1 and 9 have 1 at their unit's place.
Thus, 1681 could be a perfect square of an integer ending with either 1 or 9.

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