Lakshya Education MCQs

Question: How many non-perfect squares lie in between 752 and 762 ?
Options:
A.75
B.100
C.125
D.150
Answer: Option D
: D

Between the squares of any two consecutive numbers n and (n+1), lie 2n non-perfect squares.
Therefore between squares of 75 and 76 (n = 75 and n + 1 = 76), lie (2 x 75) = 150 non-perfect squares.

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Question 1. Three identical square sheets of paper need to be cut into 4, 5, and 6 stripes of equal size respectively. Find the minimum length of the side of the original square sheet.

  1.    45
  2.    40
  3.    30
  4.    25
Answer: Option C
: C

Since the square sheet needs to be divided equally into 4, 5, and 6 equal parts respectively, its area must be a perfect square divisible by 4, 5, and 6; or the area of the square sheet should be a multiple of 4, 5, and 6.
L. C. M. of 4, 5, and 6 = 60. But 60 is not a perfect square.
60=2×2×3×5=22×3×5.
If we multiply the LCM by 3 and 5 both, it will become a perfect square. Therefore the minimum area of the square sheet =60×3×5=900 sq. units.
Now 900 is a minimum perfect square, which is divisible by 4, 5, and 6. Therefore the side of the square should be the square root of the area of the square (Area of a square = side2 sq. units).
Hence, the minimum length of the side of the square = (900)=(22×32×52) = 30 units.
Question 2. 1,024 trees are planted in a grid fashion such that the number of rows is equal to the number of columns. One row and one column of trees are cut such that the number of rows and columns after cutting remain equal. Find the number of trees that were cut?
  1.    61
  2.    63
  3.    65
  4.    67
Answer: Option B
: B

Number of trees = 1024. Since number of rows = number of columns, this means that the number of trees is a perfect square. Therefore number of rows/columns = square root of 1024 (number of trees).
1024= 2×2×2×2×2×2×2×2×2×2=32
Therefore, the initial number of rows/columns = 32. After cutting 1 row and one column, number of rows/columns = 32-1 = 31.
The remaining number of trees = 312.
Therefore, number of trees that were cut = 322312 = 1024 - 961 = 63.
Question 3. Find the square root of 3364 by Long division Method.
  1.    58
  2.    68
  3.    78
  4.    88
Answer: Option A
: A

Given number: 3364

By grouping the numbers from theleft, we get¯¯¯¯¯¯33¯¯¯¯¯¯64.

Now, perform the long division.

585¯¯¯¯¯¯33¯¯¯¯¯¯64251088648640

Thus, the square root of 3364 is 58.
Question 4. Use Prime Factorization method to find the square root of the following:-  

i. (1024)   =   ______

 ii. (2025)   =  _______
  1.    32, 45
  2.    36, 35
  3.    28, 25
  4.    28, 45
Answer: Option A
: A

1024=2×2×2×2×2×2×2×2×2×2
=22×22×22×22×22(1024)=(22×22×22×22×22)=2×2×2×2×2=32

2025=3×3×3×3×5×5
=32×32×52(2025)=(32×32×52)=3×3×5=45

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