M4maths Previous Puzzles

14 Mar 2013 polynomial

If x^2=p=4
then the value of x^p

OPtion

1) 4
2) 8
3) 16
4) 32
5) 64
6) 72
7) 96
8) 128
9) 256
10) None of these

Solution

x^2=p=4
x^2=4
x=2
and p=4
x^p=16

Correct Option: 3 Best Solution (8)

13 Mar 2013 sphere

Surface area of a solid sphere of radius 5 cm is equal to the difference of outer and inner surface area of a hollow sphere of thickness 1 cm, Product of the inner and outer radius will be

OPtion

1) 156
2) 1
3) 78
4) 72
5) 1.6
6) .9
7) 60
8) 65
9) 100
10) None of these

Solution

By the given condition
4(pi)*5^2 = 4(pi)*r^2 - 4(pi)*(r-1)^2 (let the radius of hollow sphere be r)
By solving equation
find r and (r-1)
r*(r-1) = 12*13 = 156

Correct Option: 1 Best Solution (0)

12 Mar 2013 probability

Find the probability of getting 53 saturdays in leap year.

OPtion

1) 7/52
2) 7/53
3) 53/365
4) 2/7
5) 7/365
6) 2/9
7) 2/53
8) 4/7
9) 1/7
10) None of these

Solution

In a leap year, there are 366 days. Out of these 364 days make 52 weeks and hence 52 saturday. Remaining 2 days can be: Sun-Mon, Tue-Wed, Wed-Thu, Fri-Sat, Sat-Sun.
Total number of possible outcomes = 7
No of saturday outcomes = 2 (Fri-Sat, Sat-Sun)
Then probability of 53 saturdays = 2/7

Correct Option: 4 Best Solution (18)

11 Mar 2013 sequence

Find the next number of the following sequence
log4(base2),log8(base2),log16(base2),.........

OPtion

1) 1
2) 2
3) 3
4) 4
5) 5
6) 6
7) 7
8) 8
9) 9
10) None of these

Solution

let log4(base2)=p
therefore 2^p=4
so p = 2,
Again log8(base2)=p
therefore 2^p=8
so p = 3,
Last Again log16(base2)=p
therefore 2^p=16
so p=4,
By the possibility
let last value be logx(base2)=p
but by the condition, p should be 5
therefore 5=logx(base2)
represent in square form 2^5=x
so x = 32
p=log32(base2)

Correct Option: 5 Best Solution (36)

08 Mar 2013 rectangle

The diagonal of a rectangle is thrice its smaller side. The ratio of its sides is

OPtion

1) sqrt2 : 1
2) 2 sqrt2 : 1
3) 1 : 2
4) 3 : 2
5) sqrt3 : 1
6) 3 : 2
7) 2 : 3
8) sqrt3 : 2
9) 1 : 3 sqrt2
10) None of these

Solution

let the smaller side be x
then diagonal is 3x
by using pythagoras theorem
largest side is 2(sqrt2)x
then the ratio of side
2(sqrt2)x : x
therefore 2 sqrt2 : 1
option no 2

Correct Option: 2 Best Solution (17)

07 Mar 2013 equaion

If x be a natural number, then the number, then the number of possible solutions of the equation ax=x+6 for various values of a is

OPtion

1) 1
2) 2
3) 3
4) 4
5) 5
6) 6
7) 7
8) 8
9) 9
10) None of these

Solution

Given that ax=x+6
therefore x = 6/(a-1)
put a = 2,3,4 and 7
then we have find only 4 solution for value of x is always natural
so answer is 4
option 4

Correct Option: 4 Best Solution (10)

06 Mar 2013 equation

If 4^x-(4^(x-1))=24, then (2x)^x equal to

OPtion

1) 8*sqrt5
2) 25*sqrt5
3) sqrt5
4) 125
5) 3
6) 3*sqrt5
7) 125*sqrt5
8) 5*sqrt5
9) 25
10) None of these

Solution

solve equation
x = 5/2
then(2x)^x = 25*sqrt5

Correct Option: 2 Best Solution (6)

05 Mar 2013 rank

Rank of the word PUZZLE in the dictionary of words formed by the letters of the word PUZZLE will be

OPtion

1) 144
2) 148
3) 150
4) 152
5) 154
6) 156
7) 158
8) 160
9) 162
10) none of these

Solution

total no of words = 6*5*4*3*2*1/2 = 360
rank = (360/6)*2 + (60/5)*2 + (12/4)*2 + (3*2/3)*2 + (2/2)*1 + 1 = 156

Correct Option: 6 Best Solution (0)

04 Mar 2013 Find the next number

1,9,36,100,?

OPtion

1) 121
2) 144
3) 149
4) 169
5) 196
6) 225
7) 256
8) 289
9) 400
10) none of these

Solution

1^2, 3^2, 6^2, 10^2,
next will be 15^2
225

Correct Option: 6 Best Solution (0)

01 Mar 2013 area

A cooper wire when bent in the form of square enclose an area of 48400 cm^2. If the same wire is bent in the form of circle, then the area enclosed by it will be.

OPtion

1) 48400 cm^2
2) 58400 cm^2
3) 68400 cm^2
4) 49600 cm^2
5) 52400 cm^2
6) 57600 cm^2
7) 59600 cm^2
8) 62400 cm^2
9) 61600 cm^2
10)None of these

Solution

let the side of square be a
then the area of square = 48400 cm^2
therefore a^2 = 48400 cm^2
a = 220 cm
when same copper wire bents in the form of circle then
perimeter of square = perimeter of circle
4a = 2(22/7)r (Where r is the radius of circle)
r = 140
then area of circle = (22/7)140*140 = 61600 cm^2
option no 9

Correct Option: 9 Best Solution (0)