Overview Exercise "Act well your part; there all honor lies."
- Alexander Pope
81.
The difference of the squares of two consecutive even integers is divisible by which of the following integers ?
Answer: A
Explanation:
Let the two consecutive even integers be 2n and (2n + 2). Then,
(2n + 2)2 = (2n + 2 + 2n )(2n + 2 - 2n )
= 2(4n + 2)
= 4(2n + 1), which is divisible by 4.
82.
Which one of the following is a prime number ?
Answer: B
Explanation:
551 > 22
All prime numbers less than 24 are : 2, 3, 5, 7, 11, 13, 17, 19, 23.
119 is divisible by 7; 187 is divisible by 11; 247 is divisible by 13 and 551 is divisible by 19.
So, none of the given numbers is prime.
83.
The sum all even natural numbers between 1 and 31 is:
Answer: E
Explanation:
Required sum = (2 + 4 + 6 + ... + 30)
This is an A.P. in which a = 2, d = (4 - 2) = 2 and l = 30.
Let the number of terms be n . Then,
tn = 30 a + (n - 1)d = 30
n - 1) x 2 = 30
n - 1 = 14
n = 15
n =n (a + l )
=
15
x (2 + 30) = 240.
2
2
84.
The difference between the place value and the face value of 6 in the numeral 856973 is
Answer: A
Explanation:
(Place value of 6) - (Face value of 6) = (6000 - 6) = 5994
85.
If a and b are odd numbers, then which of the following is even ?
A. a + b B. a + b + 1C. a b D. a b + 2E. None of these
Answer: B
Explanation:
The sum of two odd number is even. So, a + b is even.
86.
Which one of the following numbers is completely divisible by 99?
A. 3572404 B. 135792 C. 913464 D. 114345 E. None of these
Answer: B
Explanation:
99 = 11 x 9, where 11 and 9 are co-prime.
By hit and trial, we find that 114345 is divisibleby 11 as well as 9. So, it is divisible by 99.
87.
The sum of how may tersm of the series 6 + 12 + 18 + 24 + ... is 1800 ?
Answer: C
Explanation:
This is an A.P. in which a = 6, d = 6 and Sn = 1800
Then,
n [2a + (n - 1)d ] = 1800
2
n [2 x 6 + (n - 1) x 6] = 1800
2
n (n + 1) = 1800
n (n + 1) = 600
n 2 + n - 600 = 0
n 2 + 25n - 24n - 600 = 0
n (n + 25) - 24(n + 25) = 0
n + 25)(n - 24) = 0
n = 24
Number of terms = 24.
88.
(51+ 52 + 53 + ... + 100) = ?
Answer: D
Explanation:
This is an A.P. in which a = 51, l = 100 and n = 50.
n (a + l )
=
50
x (51 + 100) = (25 x 151) = 3775.
2
2
89.
1904 x 1904 = ?
A. 3654316 B. 3632646 C. 3625216 D. 3623436 E. None of these
Answer: C
Explanation:
1904 x 1904
= (1904)2
= (1900 + 4)2
= (1900)2 + (4)2 + (2 x 1900 x 4)
= 3610000 + 16 + 15200.
= 3625216.
90.
What is the unit digit in(795 - 358 )?
Answer: E
Explanation:
Unit digit in 795 = Unit digit in [(74 )23 x 73 ]
23 x (343)]
23 x 343)
Unit digit in 358 = Unit digit in [(34 )14 x 32 ]
14 x 32 ]
14 x 32 ]
Unit digit in (795 - 358 ) = Unit digit in (343 - 9) = Unit digit in (334) = 4.
So, Option B is the answer.
a + (n - 1)d = 30
Sn =