Simplification and Approximation

  • Last Updated : 27 Sep, 2023

Question 1
(1015)2 = ?
Cross
1040125
Tick
1030225
Cross
1050125
Cross
1025125


Question 1-Explanation: 

10152 = (1000+15)2

= 10002 + 152 +2 x 1000 x 15

=1000000 + 225 + 30000

=1030225

Question 2
103 x 103 + 97 x 97 = ?
Cross
21348
Tick
20018
Cross
19648
Cross
21428


Question 2-Explanation: 
103 x 103 + 97 x 97
= (100+3)2 + (100-3)2
= 2 (1002 + 32 )  
[ (X +Y)2 + ( X – Y)2 = 2 ( X2 + Y2 ) ]
= 2 (10000 + 9 )
= 2 x 10009
= 20018
Question 3
9848 x 125 = ?
Cross
1232000
Cross
1242000
Tick
1231000
Cross
1233000


Question 3-Explanation: 
9848 x 125 = 9848 x (250 / 2)
           = 4924 x (500 / 2)
           = 2462 x (1000 / 2)
           = 1231 x (1000)
           = 1231000
Question 4
512 x 512 + 488 x 488 = ?
Cross
512438
Cross
502568
Tick
500288
Cross
514318


Question 4-Explanation: 
Let X=500 & Y=12
Now, (X + Y)2 + (X – Y)2 = 2 ( X2 + Y2 )
		        = 2 ( 5002 + 122 )
 			= 2 ( 250000 + 144 )
 			= 2 * 250144
 			= 500288
Question 5
What should be the value of x in equation (x / √216) = (√96 / x)
Tick
12
Cross
13
Cross
9
Cross
11


Question 5-Explanation: 
Let (x / √216) = (√96 / x)

Then x2 = √(216 x 96)
       = √(36 x 2 x 3 x 16 x 2 x 3)
       = √(62 x 42 x 22 x 32)
       = 6 x 4 x 2 x 3
       = 144
Or x = 12
Question 6
7 + 72 + 73...........76 =?
Cross
140136
Cross
142156
Cross
133256
Tick
137256


Question 6-Explanation: 
Given series is a G. P. with a = 7, r = 7 and n = 6

∴ Sn = a(rn-1) / (r-1)

∴ Sn = 7(76-1) / 6

  Sn = = 137256
Question 7
What could be the maximum value of Y in the following equation given that neither of X, Y, Z is zero? 5X8 + 3Y4 + 2Z1 = 1103
Cross
0
Tick
7
Cross
8
Cross
9


Question 7-Explanation: 
  1 1    <- CARRY

  5 X 8
+ 3 Y 4
+ 2 Z 1
--------
 11 0 3
--------
Clearly, X + Y + Z + 1 = 10 => X + Y + Z = 9 Now, since neither of X, Y, Z can be zero, the value of Y will be maximum when X = Z = 1. => Max Y = 7
Question 8
What is the unit's digit in the product (267)153 x (66666)72 ?
Cross
7
Cross
6
Cross
1
Tick
2


Question 8-Explanation: 
We have to find the unit digit only.
In 267 unit digit is 7 and cyclicity of 7 is 4.
So, (267)153 can be written as (267)Rem(153)/4 = (267)1 
Unit digit of (267)1 = 7.
similarly for 66666 unit digit is 6 and cyclicity for 6 is 1.
Unit digit for (66666)72 = 6.

Therefore , Unit digit of the resultant is 7 * 6 = 2
Question 9
√7321 x 35.999 = ?
Tick
3060
Cross
3204
Cross
3410
Cross
2930


Question 9-Explanation: 
85*9*100/25=765*4=3060
Question 10
5432.91 ÷ 2324.65 × 210.05 =?
Cross
471
Cross
431
Tick
491
Cross
501


Question 10-Explanation: 
Approx: 2.3*210 = 483
There are 23 questions to complete.