M4maths Previous Puzzles

02 Sep 2021 x+y

x+y = 9, then number of possible values of x and y are,
given that x and y are non zero positive integers s. t. x>y

OPtion

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

Solution

x+y = 9,
given that x and y are non zero positive integers s. t. x>y
then possible values of x and y are (5,4),(6,3),(7,2),(8,1) .
Hence number of possible values of x and y are 4.

Correct Option: 4 Best Solution (2)

01 Sep 2021

6 boys and 7 girls are available for a counselling. In how many ways, we can arrange them in a row, if middlest one is a boy and girls are sat on both the corners.

OPtion

1) 42*10!
2) 21*10!
3) 6*10!
4) 7*10!
5) 126*10!
6) 252*10!
7) 84*10!
8) 12*10!
9) 420
10) none of these

Solution

6 ways for boys
7c2 = 21 ways for girls
and 10! ways for remaining 10 children
sp 6*21*10!= 126*10!

Correct Option: 5 Best Solution (1)

31 Aug 2021 Bodmas

(1+1(1+1(1+1(1+1(1+1))))) = ?

OPtion

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

Solution

(1+1(1+1(1+1(1+1(1+1)))))
=(1+1(1+1(1+1(1+1(2)))))
=(1+1(1+1(1+1(1+2)))))
=(1+1(1+1(1+1(3)))))
=(1+1(1+1(4)))
=(1+1(5))
=(1+5)=6 opt 6

Correct Option: 6 Best Solution (4)

30 Aug 2021 PROBABILITY

There are 7 pair of shoes. The color of all the pairs are different. There is dark in the room. What will be the probability to get a complete pair. Left and right leg shoes can be differentiated.

OPtion

1) 1/13
2) 1/14
3) 2/13
4) 13/14
5) 2/3
6) 11/7
7) 1/7
8) 1/6
9) 2/7
10) none of these

Solution

Solution1 shoes can be pick randomly
So probability to choosing the 2nd shoes is 1*1/7 because Left and right leg shoes can be differentiated.

Correct Option: 7 Best Solution (2)

27 Aug 2021 Proportion

Find the third proportion to 2.4 kg, 9.6 kg

OPtion

1) 36.6
2) 36.8
3) 36.4
4) 38.9
5) 38.6
6) 38.4
7) 37.5
8) 40.2
9) 41
10) None of the above

Solution

Let the third proportion to 2.4 kg, 9.6 kg be x kg.
Then 2.4 kg, 9.6 kg and x kg are in continued proportion since b2 = ac
So, 2.4/9.6 = 9.6/x or, x = (9.6 × 9.6)/2.4 = 38.4

Correct Option: 6 Best Solution (6)

26 Aug 2021 PROBABILITY

A box contains 12 green and 8 blue bulbs .2 bulbs are drawn at random. Find the probability that they
are of same colour.

OPtion

1) 91/47
2) 47/105
3) 47/95
4) 95/47
5) 96/43
6) 95/43
7) 91/43
8) 93/47
9) 99/47
10) None of the above

Solution

Let S be the sample space
Then n(S) = no of ways of drawing 2 bulbs out of (12+8) = 20c2=20*19/2*1=190
Let E = event of getting both bulbs of same colour
Then, n(E) = no of ways (2 bulbs out of 12) or (2 bulbs out of 8)
=12C2+ 8C2=(132/2)+(56/2) = 66+28 = 94
Therefore, P(E) = n(E)/n(S) = 94/190 = 47/95

Correct Option: 3 Best Solution (4)

24 Aug 2021 Taps

Two taps can fill a tank in 4 hours and 5 hours .If two taps are operate simultaneously, In how much time will the tank be filled ?

OPtion

1) 4hrs 18min
2) 10min 12min
3) 2hrs 13min
4) 12hrs 10min
5) 08hrs 14min
6) 11hrs 10min
7) 18 hrs
8) 07hrs 26min
9) 6hrs 22min
10) None of the above

Solution

1/(A+B) =1/4 + 1/5
= (5+4)/20
= 9/20
=>20/9=2hrs 13min to filled the tank

Correct Option: 3 Best Solution (6)

23 Aug 2021 Combination

A shopkeeper has 15 models of cup and 9 models of saucer. In how many ways can he make a pair of cup and saucer?

OPtion

1) 100
2) 80
3) 110
4) 130
5) 122
6) 88
7) 104
8) 135
9) 116
10) None of the above

Solution

He has 15 patterns of cup and 9 model of saucer
A cup can be selected in 15 ways.
A saucer can be selected in 9 ways.
Hence one cup and one saucer can be selected in 15×9 ways =135 ways

Correct Option: 8 Best Solution (3)

20 Aug 2021 Rectangle

The length of a rectangle pillow is twice its breadth. If its length is decreased by 25cm and breadth is
increased by 25 cm, the area of the rectangle is increased by 375sq. cm. Find the length of the rectangle.

OPtion

1) 100 cm
2) 80cm
3) 75cm
4) 55cm
5) 66cm
6) 85cm
7) 72cm
8) 66cm
9) 61cm
10) None of the above

Solution

Let breadth = x. Then, length = 2x Then,
(2x -25) (x + 25) - 2x * x = 375
50x – 25x- 625= 375
25x = 1000
x = 40
Length of the rectangle = 2x = 80 cm.

Correct Option: 2 Best Solution (0)

19 Aug 2021 Wheel Dia

A jeep has wheels of diameter 140m. How many revolutions can the wheel complete in 40minutes if the jeep is travelling at a speed of 220 m/s?

OPtion

1) 1750
2) 1700
3) 1280
4) 1450
5) 1200
6) 1360
7) 1450
8) 1500
9) 1350
10) None of the above

Solution

Radius of wheel = 140/2 = 70 cm
Distance travelled in one revolution = 2πr = 2 * 22/7 * 70 = 440 cm
Let the number of revolutions made by wheel is x
So total distance travelled = distance travelled in one revolution * number of revolutions
So total distance travelled = 440x cm
40 mins = 40*60 seconds
Speed of jeep = 440x/(40*60)
So 220 = 220x/(20*60)
Solve, x = 1200

Correct Option: 5 Best Solution (4)