Q23. Find the unit digit in product (684 x 759 x 413 x 676)?
A. 9
B. 8
C. 10
D. 13
Answer- Option B
Explanation-
Unit digit in the given product
= Unit digit in the product (4 x 9 x 3 x 6) = 8.
Q24. What is the unit digit in the product (3547)153 x (251)72?
A. 7
B. 8
C. 10
D. 9
Answer- Option A
Explanation-
Required digit = unit digit in (7153 x 172)
Now, 74 gives unit digit 1 and 172 = 1.
(7153 x 172) = [(74)38 x 7 x 1] Required unit digit = (1 x 7 x 1) = 7.
Q25. Find the total number of prime factors in the product {(4)11 x 75 x (11)2}.
A. 30
B. 25
C. 28
D. 29
Answer- Option D
Explanation-
{(4)11 x 75 x (11)2} = (2 x 2)11 x 75 x (11)2
= (22)11 x 75 x (11)2
= (222 x 75 x (11)2)
Required number of factors = (22 + 5 + 2) = 29.
Q26. What is the unit digit in {(264)102 + (264)103}?
A. 8
B. 3
C. 0
D. 4
Answer- Option C
Explanation-
(264)102 + (264)103 = (264)102 {1 + 264} = (264)102 x 265. Required unit digit = unit digit in [(4)102 x 5] = unit digit in [(44)25 x 42 x 5] = unit digit in (6 x 6 x 5) = 0.
Q27. Find the remainder when 231 is divided by 5
A. 3
B. 4
C. 5
D. 2
Answer- Option A
Explanation-
231 = (210 x 210 x 210) x 2 = (210)3 x 2 = (1024)3 x 2
Unit digit in 231 = Unit digit in {(1024)3 x 2} = (4 x 2) = 8
Now, 8 when divied by 5 gives 3 as remainder 231 when divied by 5 gives remainder = 3
Q28. The difference between the place value and the face value of 6 in numeral 856973 is
A. 6973
B. 973
C. 5994
D. None of these
Answer- Option C
Explanation-
(Place value of 6) - (Face Value of 6) = (6000 - 6) = 5994.
= ?
Required unit digit = (1 x 7 x 1) = 7.
