M4maths Previous Puzzles

19 Jul 2012 x

if x^3+3x^2+2x+5=0
then (x+1)^3 will be

OPtion

1) x+3
2) x+5
3) x+8
4) x+1
5) x-1
6) x-3
7) x-5
8) x-6
9) x-4
10) none of these

Solution

(x+1)^3 = x^3+3x^2+3x+1 = (x^3+3x^2+2x+5)+(x-4) = 0 + (x-4)

Correct Option: 9 Best Solution (0)

18 Jul 2012 root

a+5 = a^2-25, a>0
then sum of the roots of the given equation and inequation will be

OPtion

1) 6
2) 1
3) -1
4) 11
5) -5
6) 12
7) 2
8) 9
9) 3
10) none of these

Solution

(a+5) = (a+5)(a-5)
so (a+5)(a-5) - (a+5) = 0
or (a+5)[(a-5)-1] = 0
or a= -5 and a = 6
since a>0 so only root is 6

Correct Option: 1 Best Solution (15)

17 Jul 2012 percentage

40 % of a number x is 60 % of another number y. If sum of the two numbers is 1. Then the number x will be

OPtion

1) 0.1
2) 0.2
3) 0.3
4) 0.4
5) 0.5
6) 0.6
7) 0.7
8) 0.8
9) 0.9
10) none of these

Solution

according to the given condition
0.4x = 0.6(1-x)
so x = 0.6

Correct Option: 6 Best Solution (41)

16 Jul 2012 sequence

next number of the sequence
1, 5, 14, 30, 55, .........
will be

OPtion

1) 61
2) 68
3) 72
4) 76
5) 79
6) 83
7) 89
8) 91
9) 98
10) none of these

Solution

1^2 = 1
1^2 + 2^2 = 5
1^2 + 2^2 + 3^2 = 14
1^2 + 2^2 + 3^2 + 4^2 = 30
similarly

Correct Option: 8 Best Solution (0)

13 Jul 2012 dictionary

18th word of the dictionary formed by letters of the word RAMESH (all words of 6 letters)

OPtion

1) AERSHM
2) HREASM
3) HERASM
4) AHRSME
5) AERHSM
6) AERSMH
7) HRSAEM
8) ERASMH
9) EARHMS
10) NONE OF THESE

Solution

Total words = 720
first 120 will start with A
for the next place first 24 will start with E
so first two letters are AE
in 24 words 6-6 will start with H, M, R, S
so required word will have first 3 letters as AER
next splitting 2-2 with H, M, S
so 18th word will have first 4 letters as AERS
so 17th word is AERSHM
and 18th word is AERSMH

Correct Option: 6 Best Solution (8)

12 Jul 2012 square and rectangle

Sum of the sum and positive difference of areas of a square of side 10 cm. and rectangle of sides 11 cm. and 9 cm. will be

OPtion

1) 1
2) 199
3) 165
4) 200
5) 198
6) 193
7) 99
8) 110
9) 10
10) none of these

Solution

area of the two geometries = 100 and 99
so sum = 199
difference = 1
so grand sum = 200

Correct Option: 4 Best Solution (30)

11 Jul 2012 shortest distance

A man travels 300 m north then 200 m east then 300sqrt(2) m south-west. Shortest distance between initial and final point will be

OPtion

1) 50 m
2) 100sqrt(2) m
3) 50sqrt(2) m
4) 100 m
5) 200 m
6) 500+300sqrt(2) m
7) 100+300sqrt(2) m
8) 400 m
9) 20 m
10) none of these

Solution

300sqrt(2) along west-south means 300 m along west and 300 m along south.
300 m along north is recovered by 300 m along south, and 200 m east and 300 m west means 100 m along west.
you can understand it by taking a diagram.
[shortest distance means direct distance (displacement) between initial and final point.]

Correct Option: 4 Best Solution (2)

10 Jul 2012 solve

if [(x+1)/(x-3)]^1/2 = [(x-3)/(x+2)]^1/2
then x will be

OPtion

1) 7/9
2) 3/5
3) 4/7
4) 1/7
5) 9/7
6) 3/7
7) 1/8
8) 2/7
9) no solution
10) none of these

Solution

[(x+1)/(x-3)]^1/2 = [(x-3)/(x+2)]^1/2
squaring both the side, we get
[(x+1)/(x-3)] = [(x-3)/(x+2)]
or (x+1)(x+2) = (x-3)^2
or x = 7/9
but this value makes (x-3) negative inside square root
so this value is unacceptable.

Correct Option: 9 Best Solution (0)

09 Jul 2012 sequence

6, ?, 37, 7, 48, ?, 8, ?, 65
sum of all the 3 question marks will be

OPtion

1) 148
2) 127
3) 117
4) 112
5) 108
6) 99
7) 165
8) 178
9) 198
10) none of these

Solution

this sequence is
6, 6^2-1, 6^2+1, 7, 7^2-1, 7^2+1, 8, 8^2-1, 8^2+1

Correct Option: 1 Best Solution (0)

06 Jul 2012 word

How many words can be formed by using the letters of the word LETTER, if all the words will be started from L.

OPtion

1) 120
2) 720
3) 24
4) 12
5) 360
6) 30
7) 48
8) 60
9) 6
10) none of these

Solution

First letter is L
so methods for arranging the other letters = 5*4*3*2*1/(2*1)*(2*1)
denominator is here for the repetition of E and T

Correct Option: 6 Best Solution (22)