M4maths Previous Puzzles

23 May 2013 cuboid

The area of three adjacent faces of a cuboid are x,y and z. If the volumes is V, then value of V^2 is.....

OPtion

1) xyz
2) xy
3) yz
4) zx
5) x^2*yz
6) xy*z^2
7) x^2*y^2*z*2
8) 1/xyz
9) x*y^2*z
10) None of these

Solution

let l,b,h (lenght, breath and height)
x=lb
y=bh
z=hl
xyz=lb*bh*hl
xyz=(lbh)^2
xyz=V^2
option 1

Correct Option: 1 Best Solution (0)

22 May 2013 equations

If the equation x^2-3x=a snd x^2-4x=5 have a common root, then value of a^2-14a+41=

OPtion

1) 0
2) 1
3) 2
4) 3
5) 4
6) 5
7) 6
8) 7
9) 8
10) None of these

Solution

Let k be the coommon root
therefore k^2-3k=a & k^2-4k=5
k=a-5
therefore
(a-5)^2-3(a-5)=a
a^2-14a+40=0
so a^2-14a+41=1
option 2

Correct Option: 2 Best Solution (0)

21 May 2013 Probability

One card is drawn from a well shuffled pack of 52 cards. Probability of getting a heart or a queen....

OPtion

1) 1/52
2) 1/4
3) 1/13
4) 2/13
5) 1/12
6) 5/52
7) 4/13
8) 3/13
9) 3/52
10) None of these

Solution

There are 13 cards of heart and those 13 cards contains 1 queen. So, 3 queens are more.
Total no. of favourable case 13+3=16
Probability 16/52=4/13
option 7

Correct Option: 7 Best Solution (0)

20 May 2013 Sequence

What is the next number of the following sequence
5,11,19,29,....

OPtion

1) 36
2) 38
3) 41
4) 45
5) 48
6) 51
7) 54
8) 59
9) 68
10) None of these

Solution

1+2^2=5
2+3^2=11
3+4^2=19
4+5^2=29
5+6^2=41
option 3

Correct Option: 3 Best Solution (0)

17 May 2013 Age problem

A father's age is four times the sum of ages of his two children. After 10 year his age will be twice the sum of ages of two children. Age of father's will be.....

OPtion

1) 40
2) 42
3) 45
4) 50
5) 55
6) 60
7) 65
8) 68
9) 70
10) None of these

Solution

According to the given condition
x=4y (let father's age x and sum of two children's age y)
(x+10)=2(y+20)
By solving
we get father's age 60 year
option 6

Correct Option: 6 Best Solution (0)

16 May 2013 cone

The semicircle with the maximum possible radius is cut from a 14cm*7cm rectangular sheet of paper and cone is made out of it. Volume of the cone is

OPtion

1) 287/(32*sqrt3) cm^3
2) 395/(4*sqrt3) cm^3
3) 539/(32*sqrt3) cm^3
4) 539/(4*sqrt3) cm^3
5) 545/sqrt3 cm^3
6) 559/sqrt3 cm^3
7) 445/(2*sqrt3) cm^3
8) 565/sqrt2 cm^3
9) 565/(3*sqrt2)
10) None of these

Solution

Maximum possible radium = 7
Arc length of the semicircle = 22/7*7=22cm
let radius of cone = r
therefore 2*pi*r=22
r=7/2
height of the cone = h = sqrt(l^2-r^2) (where l=slant height)
using cone volume formula 1/3*pi*r^2*h=539/(4*sqrt3) cm^3
option 4

Correct Option: 4 Best Solution (0)

15 May 2013 Solve

If (1/(x+2))+(1/(x+6))=(1/(x+3))+(1/(x+5))
Value of x is

OPtion

1) -8
2) -7
3) -6
4) -5
5) -4
6) -3
7) -2
8) -1
9) No Soluction
10) None of these

Solution

Solve
(2x+8)/(x^2+8x+12)=(2x+8)/(x^2+8x+15)
(2x+8)(x^2+8x+15)=(2x+8)(x^2+8x+12)
(2x+8)(x^2+8x+15)-(2x+8)(x^2+8x+12)=0
common (2x+8)
then solve
x=-4
option 5

Correct Option: 5 Best Solution (0)

14 May 2013 line

How many points on the line 2x-3y+7=0 are at a distance of 3 unit form the point P(2,-1).

OPtion

1) 0
2) 1
3) 2
4) 3
5) 4
6) 5
7) 6
8) 7
9) Infinite
10) None of these

Solution

At first, find the distance of a point from the line
using ax1+by1+c/Sqrt(a^2+b^2) (Where P(2,-1) is x1,y1 and get a,b,c by comparing given equation with ax+by+c=0
distance is 14/sqrt13, which is greater then 3, so there is no point on the line..
option 1

Correct Option: 1 Best Solution (0)

13 May 2013 Sequence

What is the missing number of the following sequence
3, 7, 13, ...., 31

OPtion

1) 10
2) 14
3) 16
4) 21
5) 24
6) 28
7) 25
8) 27
9) 12
10) None of these

Solution

1^2+2=3
2^2+3=7
3^3+4=13
4^2+5=21.....
5^2+6=31

option 4

Correct Option: 4 Best Solution (0)

10 May 2013 new number

average of 5 numbers is 35 and average of 7 numbers (2 new numbers are added) is 25. Sum of the 2 newly added numbers will be

OPtion

1) 45
2) 54
3) 55
4) 35
5) 65
6) 75
7) 25
8) 50
9) 0
10) none of these

Solution

35*5 = 175
and 25*7 = 175 so sum of two newly added number will be 0

Correct Option: 9 Best Solution (25)