If the product of four consecutive natural numbers increased by a natural number p, is a perfect square, then the value of p is = ?
A. 1
B. 2
C. 4
D. 8
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {\text{We have,}} \cr & 1 \times 2 \times 3 \times 4 = 24 \cr & {\text{And }}24 + 1 = 25\left[ {25 = {5^2}} \right] \cr & 2 \times 3 \times 4 \times 5 = 120{\text{ }} \cr & {\text{And 1}}20 + 1 = 121\left[ {121 = {{11}^2}} \right] \cr & 3 \times 4 \times 5 \times 6 = 360{\text{ }} \cr & {\text{And }}360 + 1 = 361\left[ {361 = {{19}^2}} \right] \cr & 4 \times 5 \times 6 \times 7 = 840{\text{ }} \cr & {\text{And }}840 + 1 = 841\left[ {841 = {{29}^2}} \right] \cr & \therefore p = 1 \cr} $$Related Questions on Square Root and Cube Root
The least perfect square, which is divisible by each of 21, 36 and 66 is:
A. 213444
B. 214344
C. 214434
D. 231444
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