71.
397 x 397 + 104 x 104 + 2 x 397 x 104 = ?
A. 250001 B. 251001
C. 260101 D. 261001
Answer & Explanation
Answer: Option B
Explanation:
Given Exp. = (397)2 + (104)2 + 2 x 397 x 104
= (397 + 104)2
= (501)2 = (500 + 1)2
= (5002) + (1)2 + (2 x 500 x 1)
= 250000 + 1 + 1000
= 251001
72.
(35423 + 7164 + 41720) – (317 x 89) = ?
A. 28213 B. 84307
C. 50694 D. 56094
E. None of these
Answer & Explanation
Answer: Option D
Explanation:
35423 317 x 89 = 317 x (90 -1 )
+ 7164 = (317 x 90 – 317)
+ 41720 = (28530 – 317)
—– = 28213
84307
– 28213
—–
56094
—–
73.
(xn – an) is completely divisible by (x – a), when
A. n is any natural number B. n is an even natural number
C. n is and odd natural number D. n is prime
Answer & Explanation
Answer: Option A
Explanation:
For every natural number n, (xn – an) is completely divisible by (x – a).
74.
Which one of the following numbers is completely divisible by 45?
A. 181560 B. 331145
C. 202860 D. 2033555
E. None of these
Answer & Explanation
Answer: Option C
Explanation:
45 = 5 x 9, where 5 and 9 are co-primes.
Unit digit must be 0 or 5 and sum of digits must be divisible by 9.
Among given numbers, such number is 202860.
75.
Which of the following numbers will completely divide (325 + 326 + 327 + 328) ?
A. 11 B. 16
C. 25 D. 30
Answer & Explanation
Answer: Option D
Explanation:
(325 + 326 + 327 + 328) = 325 x (1 + 3 + 32 + 33) = 325 x 40
= 324 x 3 x 4 x 10
= (324 x 4 x 30), which is divisible by30.
76.
A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is:
A. 0 B. 1
C. 2 D. 3
Answer & Explanation
Answer: Option D
Explanation:
Let x = 6q + 3.
Then, x2 = (6q + 3)2
= 36q2 + 36q + 9
= 6(6q2 + 6q + 1) + 3
Thus, when x2 is divided by 6, then remainder = 3.
77.
The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ?
A.
12
35
B.
1
35
C.
35
8
D.
7
32
Answer & Explanation
Answer: Option A
Explanation:
Let the numbers be a and b. Then, a + b = 12 and ab = 35.
a + b = 12 1 + 1 = 12
ab 35 b a 35
Sum of reciprocals of given numbers = 12
35
V
78.
What will be remainder when 17200 is divided by 18 ?
A. 17 B. 16
C. 1 D. 2
Answer & Explanation
Answer: Option C
Explanation:
When n is even. (xn – an) is completely divisibly by (x + a)
(17200 – 1200) is completely divisible by (17 + 1), i.e., 18.
(17200 – 1) is completely divisible by 18.
On dividing 17200 by 18, we get 1 as remainder.
79.
If 1400 x x = 1050. Then, x = ?
A.
1
4
B.
3
5
C.
2
3
D.
3
4
E. None of these
Answer & Explanation
Answer: Option D
Explanation:
1400 x x = 1050 x = 1050 = 3
1400 4
80.
(12 + 22 + 32 + … + 102) = ?
A. 330 B. 345
C. 365 D. 385
Answer & Explanation
Answer: Option D
Explanation:
We know that (12 + 22 + 32 + … + n2) = 1 n(n + 1)(2n + 1)
6
Putting n = 10, required sum = 1 x 10 x 11 x 21 = 385