-2,-1,0,1,2,-2,-1,0,1,2,-2,-1,0,1,2,-2,-1,0,1,2
| sum of 473rd,474th and 475th term | 0 |
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Solution
The cycle repeats after every five nos. Thus 473rd, 474th and 475th terms are 3rd, 4th and 5th numbers in the list i.e. 0, 1,2 ∴ The sum is 3
| No. of pairs of natural numbers with LCM as 72. | 12 |
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Solution
1,72 2,72 3,72 4,72 6,72 8,72 9,72 12,72 18,72 24,72 36, 72 8,9 8,18 9,24 etc.
| Smallest value of x + Y such that 2x + 5y is divisible by 17 | 8 |
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Solution
2x + 5y = 17k where k can take all natural values. For k = 1, 2x + 5y = 17
∴ x = 1,Y= 3 ∴ x + y = 4 is least value.
| Smallest possible value of xv | 12 |
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Solution
Col. A-
2x ≥ 10 x ≥ 5
8-y ≤ 5 3 ≤ y
∴ Smallest value of xy = 15
| smallest possible value of w | -10 |
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Solution
Col. A-
= \(\frac{2-19}{1}=-17\)
| HCF of 7-11,77,7-13, and 7-29 | 77 |
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Solution
All the 4 nos. have 7-29 in common. So it is HCF
A square oven tray 4 inches on a side is filled with 16 circular cherry pies.
| Total area of pie crusts on top of pies | 2π |
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Solution
Col. A
Diameter of pie circuit = 1 inch
Area = 1⁄4πd2 = 1⁄4π12 = π⁄4
∴ Total area of 16 pies = 16 × π⁄4 = 4π
| Percent increase in the volume of a cube when its edge is increased by 50% | 300% |
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Solution
Let initial edge be 1. Volume = 13 = 1
New edge = 1.5 Volume = (1.5)3 = 3.375
∴ Change in volume 3.375 - 1 = 2.375
= 2.375 × 100 = 237.5%
| Total number of prime factors of (77)19 × (29)4 × (6)11 × (37)8 | 42 |
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Solution
Col. A-
719 × 1119 × 294 × 211 × 311 × 378
7, 1,29,2,3,37 are prime nos.
| Number of (1⁄8)th in 17.25 | 140 |
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Solution
Col. A-
17.25 =\(\frac{69}{4}=\frac{138}{8}\div \frac{1}{8}=\frac{138}{8}\times 8=138\)