Answer: a. 112225
Explanation:
Tip:
To find square of number ending in 5
Example - 3352
335 ends with 5.
So 3352 will have 52 = 25 at end
Now leave last digit i.e. 5.
We have 33. Add 1 to it.
We get 33 + 1 = 34
33 x 34 = 1122
3352 = 112225
| 7. Find value of M + | 1 | , if M = | 7 - 5 |
| M | 7 + 5 |
Answer: d. 12
Explanation:
| M = | 7 - 5 |
| 7 + 5 |
| ∴ | 1 | = | 7 + 5 |
| M | 7 - 5 |
| M + | 1 | = | 7 - 5 | + | 7 + 5 | = | (7 - 5)2 + (7 + 5)2 |
| M | 7 + 5 | 7 - 5 | (7 + 5)(7 - 5) |
Tip:
(a+b)2 = a2 + 2ab + b2
(a-b)2 = a2 - 2ab + b2
(a+b)(a - b) = a2 - b2
| ∴ M + | 1 | = | 2(7)2 + 2(5)2 |
| M | (7)2 - (5)2 |
| ∴ M + | 1 | = 12 |
| M |
Answer: c. 7
Explanation:
In such cases, first we need to find various factors of 42.
42 = 2 x 21
42 = 3 x 14
42 = 6 x 7
Select the factors which have a difference of 1 between them.
7 - 6 = 1 ∴ Select 7 and 6
Select the larger factor among the two
∴ Answer = 7
Tip:
Going Further, if we have
then use the same above trick just select the smaller factor instead of bigger one.
if value of 15 = 3.872Answer: d. 1.290
Explanation:
Answer: b. 0.4
Explanation:
The solution might look lengthy but is very easy.
(0.004096)1/6 = (0.004096)1/3 x 1/2
Here we need to find cube root first and then square root.
4096 ends with 6. So cube root will have 6 in the end.
Neglect last 3 digits. We are left with 4
Nearest cube to 4 which is less than 4 is 13 = 1.
So cube root of 4096 = 16
Also there are 6 decimal places.
We want cube root. Hence decimals in cube root will be 6/3 = 2
So (0.004096)1/3 = 0.16
Now, square root of 16 = 4
There are 2 decimal places and we want square root.
So decimals in square root will be 2/2 = 1
So 0.16 = 0.4
∴ 0.0040961/6 = 0.4