Unit digit of
58904289053 + 3490224 - 50489
-2
2
4
8
Unit digit of
7895543 × 35802679
3
6
7
9
Unit digit of (12502)¹⁴⁹
2
4
6
8
Unit digit of 152⁵⁷ × 143⁸²
3
6
7
8
If x = 37¹⁴⁶ + 6443³ + 243⁶⁷,
then the unit digit of x is
0
4
7
More than one of the above
Find the unit place of
3674 × 8596 + 5699 × 1589
3
4
5
What is the unit place digit in the expansion of 7⁷³?
1
3
7
What is the unit digit of
178 × 593 + 157?
1
2
3
The digit in the unit’s place of the product
3⁹⁹⁹ × 7¹⁰⁰⁰⁰ is _______.
7
1
3
Find the unit digit of
(432)⁴¹² × (499)⁴³¹.
2
4
6
8
If x=(164)¹⁶⁹ + (333)³³⁷ – (727)⁷²⁶
,then what is the units digit of x?
5
9
7
8
The digit in the unit’s place of the number represented by (7⁹⁵ – 3⁵⁸) is:
6
7
0
4
If N = 7⁹⁴ - 3⁵⁸, then the digit at the unit place of N is
3
4
6
7
The unit digit of
(25⁵³ × 56⁴²) + 456²⁵ + 23⁴² + 76²³ is -
1
2
3
4
The digit in the unit’s place in the number obtained after calculating 3⁵³ - 6³⁸ + 27⁵⁶ is:
4
2
8
6
What is the unit digit of the sum of first 150 natural numbers?
9
5
0
1
Find the unit digit of
83 × 87 × 93 × 59 × 61.
9
4
7
3
Find the digit at unit place in the product
742 × 437 × 543 × 679
2
4
6
8
The unit digit in the product 122¹⁷³ is
a) 2
b) 4
c) 6
d) 8...
The unit digit in the sum of
124³⁷² + 124³⁷³ is
a) 5
b) 4
c) 20
d) 0...
The digit in the unit place in the square root of 66049 is .....
a) 3
b) 7
c) 8
d) 2
Find the unit digit in the product of
4387²⁴⁵ × 621⁷² .
a) 1
b) 2
c) 5
d) 7
If in a two digit number, the digit at unit place is z and the digit at tens place is 8, then the number is
a) 80z + z
b) 80 + z
c) 8z + 8
d) 80z + 1
Find the unit place digit in
71 × 72 × 73 × 74 × 76 × 77 × 78 × 79.
a) 2
b) 0
c) 4
d) 6
Find the unit place digit in
81 × 82 × 83 × 84 × 85 × 86 × 87 × 88 × 89.
a) 5
b) 0
c) 4
d) 6
What is the unit digit of the sum of first 111 whole numbers?
a) 4
b) 6
c) 5
d) 0
What is the unit digit of
217⁴⁸³ × 819⁵⁴⁷ × 414⁶²⁴ × 342⁸¹² ?
a) 2
b) 4
c) 6
d) 8
If the unit digit of
433 × 456 × 43N is (N+2),
then what is the value of N ?
a) 1
b) 8
c) 3
d) 6
Answer (D)
If we multiply 433 and 456 then we will get 8 as unit digit .
But when 433 and 456 multiply together with 43N then the unit digit appears as 8N .
So,Unit digit of 8N= N+2
It is possible only when N=6 .
So, D is correct choice.
Unit digit of
1! + 2! + 3! + 4! + ........... + 50!
a) 1
b) 3
c) 5
d) 8
Unit digit of
(₅₄₈₆₂₁₅)⁴³²⁴⁵²⁴!
a) 1
b) 2
c) 5
d) 7
Unit digit of
(₅₄₈₆₂)⁴³²⁴⁵²⁴!
a) 2
b) 4
c) 6
d) 8
Unit digit of
( ₁₇₄₈₀₄₃₇₄₃₇₂₅₆₇ )⁽ ¹ ⁺ ² ⁺ ³ ⁺ ⁴ ⁺ ••••• ⁺ ¹⁰⁰ ⁾
a) 3
b) 5
c) 7
d) 9
Unit digit of
( ₁₇₄₈₀₄₃₇₄₃₇₂₅₆₇ )⁽ ¹ ⁺ ² ⁺ ³ ⁺ ⁴ ⁺ ••••• ⁺ ¹⁰⁰ ⁾ !
a) 2
b) 4
c) 6
d) 8
Unit digit of
1.1! + 2.2! + 3.3! + 4.4! + ........... + 50.50!
a) 1
b) 2
c) 5
d) 7
Unit digit of
₁¹! ₊ ₂²! ₊ ₃³! ₊ ₄⁴! ₊ ₅⁵! ₊ ₆⁶! ₊ ....... ₊ ₅₀⁵⁰! ?
a) 1
b) 2
c) 3
d) 4
Unit digit of
₁ᴉ ¹! ₊ ₂ᴉ ²! ₊ ₃ᴉ ³! ₊ ₄ᴉ ⁴! ₊ ₅ᴉ ⁵! ₊ ...... ₊ ₅₀ᴉ ⁵⁰!
a) 1
b) 2
c) 3
d) 4
Unit digit of (₃₇39)⁴¹ ?
a) 1
b) 2
c) 3
d) 4
Unit digit of ₃₂32³² ?
a) 1
b) 2
c) 3
d) 4
Unit digit of ₃₇39⁴¹ ?
a) 1
b) 2
c) 3
d) 4
Unit digit of ₉23³² ?
a) 1
b) 2
c) 3
d) 9
Unit digit of ₂₂33⁴⁴ ?
a) 2
b) 4
c) 6
d) 8
Find unit digit in \( \sum_{n=1}^{90} n \cdot n! \)
ㅤㅤₓˣ = ₃ˣ⁺⁹ ⠀⠀
............................................................⠀
𝗔𝗻𝘄𝗲𝗿 = 𝟵⠀⠀
............................................................⠀
⠀
⠀
⠀
𝗠𝗲𝘁𝗵𝗼𝗱 𝟭𝘀𝘁 ⠀⠀
⠀⠀
ㅤㅤₓˣ = ₃ˣ⁺⁹ ⠀⠀
⠀⠀
ㅤㅤₓˣ = ₃ˣ × ₃⁹ ⠀⠀
⠀⠀
ㅤㅤ(ˣ/₃)ˣ = ₃⁹ ⠀⠀
⠀⠀
ㅤㅤPower x can be written as ˣ/₃ × 3 ⠀⠀
⠀⠀
ㅤㅤ(ˣ/₃)^[ ˣ/₃ × 3] = ₃⁹ ⠀⠀
⠀⠀
ㅤㅤNow this can be written as ⠀⠀
⠀⠀
ㅤㅤ[ (ˣ/₃)^ˣ/₃ ]³ ==> ₃⁹ ⠀⠀
⠀⠀
ㅤㅤCube root both side , ⠀⠀
⠀⠀
ㅤㅤ(ˣ/₃)^ ˣ/₃ ==> ₃³ ⠀⠀
⠀⠀
ㅤㅤNow, ˣ/₃ = 3 ⠀⠀
⠀⠀
ㅤㅤx = 9⠀
⠀
⠀
𝗠𝗲𝘁𝗵𝗼𝗱 𝟮𝗻𝗱 ⠀⠀
⠀⠀
ㅤㅤₓˣ = ₃ˣ⁺⁹ ⠀⠀
⠀⠀
ㅤㅤₓˣ = ₃ˣ × ₃⁹ ⠀⠀
⠀⠀
ㅤㅤ(ˣ/₃) ˣ = ₃⁹ ⠀⠀
⠀⠀
ㅤㅤHere by observation we can say x = 9 ⠀⠀
⠀
⠀
⠀
𝗠𝗲𝘁𝗵𝗼𝗱 𝟯𝗿𝗱 ⠀⠀
⠀⠀
ㅤㅤₓˣ = ₃ˣ⁺⁹ ⠀⠀
⠀⠀
ㅤㅤtaking log both side ⠀⠀
⠀⠀
ㅤㅤLog(ₓˣ )=log (₃ˣ⁺⁹) ⠀⠀
⠀⠀
ㅤㅤx log x ==> (x+9)log3 ⠀⠀
⠀⠀
ㅤㅤx logx ===> x log3 + 9 log3 ⠀⠀
⠀⠀
ㅤㅤx logx - x log3 ===> 9 log3 ⠀⠀
⠀⠀
ㅤㅤx [ log (ˣ/₃) ] ===> 9 log3 ⠀⠀
⠀⠀
ㅤㅤBy comparing x = 9⠀⠀
⠀⠀
⠀
⠀
𝗠𝗲𝘁𝗵𝗼𝗱 𝟰𝘁𝗵⠀
⠀
ㅤㅤₓˣ = ₃ˣ⁺⁹ ⠀⠀
⠀⠀
ㅤㅤₓˣ = ₃ˣ × ₃⁹ ⠀⠀
⠀⠀
ㅤㅤ(ˣ/₃)ˣ = ₃⁹⠀
⠀
ㅤㅤIn ₃⁹ we can write 3 as ⁹/₃⠀
⠀
ㅤㅤ(ˣ/₃)ˣ = (⁹/₃)⁹⠀
⠀
ㅤㅤx = 9⠀
⠀
⠀
𝗠𝗲𝘁𝗵𝗼𝗱 𝟱𝘁𝗵
ㅤㅤₓˣ = ₃ˣ⁺⁹
ㅤㅤtake ¹/ₓ power both side
ㅤㅤx = ( ₃ˣ⁺⁹ )^(¹/ₓ)
ㅤㅤx = 3^(¹ ⁺ ⁹/ₓ)
ㅤㅤx = 3 × 3^(⁹/ₓ)
ㅤㅤˣ/₃ == 3^(⁹/ₓ)
ㅤㅤˣ/₃ == (₃³)^(³/ₓ)
ㅤㅤtaking power ˣ/₃ both side
ㅤㅤ(ˣ/₃)^(ˣ/₃) = ₃³
ㅤㅤˣ/₃ = 3
ㅤㅤx = 9
⠀⠀
⠀
..............................................................................................................................................................................................................................................................................