16, 25, 36, 72, 144, 196, 225
Question:
16, 25, 36, 72, 144, 196, 225
[A].
36
72
196
225
16, 25, 36, 72, 144, 196, 225
[A].
[B].
[C].
[D].
Answer: Option B
Explanation:
Each of the numbers except 72 is a perfect square.
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In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been
Question:
In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been
[A].24 [B].
144 [C].
292 [D].
584 Answer: Option D
Explanation:
5 | x z = 13 x 1 + 12 = 25
————–
9 | y – 4 y = 9 x z + 8 = 9 x 25 + 8 = 233
————–
13| z – 8 x = 5 x y + 4 = 5 x 233 + 4 = 1169
————–
| 1 -12585) 1169 (1
585
—
584
—Therefore, on dividing the number by 585, remainder = 584.
In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?
Question:
In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?
[A].10080 [B].
4989600 [C].
120960 [D].
None of these Answer: Option C
Explanation:
In the word ‘MATHEMATICS’, we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Number of ways of arranging these letters = 8! = 10080. (2!)(2!) Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters = 4! = 12. 2! Required number of words = (10080 x 12) = 120960.
The correct expression of 6.46 in the fractional form is:
Question:
The correct expression of 6.46 in the fractional form is:
[A].646 99 [B].
64640 1000 [C].
640 100 [D].
640 99 Answer: Option D
Explanation:
6.46 = 6 + 0.46 = 6 + 46 = 594 + 46 = 640 . 99 99 99 What is the difference between the compound interest on Rs.12000 at 20% p.a. for one year when compounded yearly and half yearly?
What is the difference between the compound interest on Rs.12000 at 20% p.a. for one year when compounded yearly and half yearly?A. Rs.140
B. Rs.120
C. Rs.130
D. Rs.110
E. None of these.Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
Question:
Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
[A].16 hours [B].
18 hours [C].
20 hours [D].
24 hours Answer: Option D
Explanation:
Speed upstream = 7.5 kmph.
Speed downstream = 10.5 kmph.
Total time taken = 105 + 105 hours = 24 hours. 7.5 10.5 (22 + 42 + 62 + … + 202) = ?
Question:
(22 + 42 + 62 + … + 202) = ?
[A].770 [B].
1155 [C].
1540 [D].
385 x 385 Answer: Option C
Explanation:
(22 + 42 + 62 + … + 202) = (1 x 2)2 + (2 x 2)2 + (2 x 3)2 + … + (2 x 10)2
= (22 x 12) + (22 x 22) + (22 x 32) + … + (22 x 102)
= 22 x [12 + 22 + 32 + … + 102]
Ref: (12 + 22 + 32 + … + n2) = 1 n(n + 1)(2n + 1) 6 = 4 x 1 x 10 x 11 x 21 6 = (4 x 5 x 77)
= 1540.