M4maths Previous Puzzles

27 Dec 2021 Cone

Two right circular cones of equal heights have their radii in the ratio of 1:3. Find out the ratio of their volumes

OPtion

1. 1:6
2. 1:44
3. 1:9
4. 2:9
5. 2:6
6. 2:3
7. 1:3
8. 3:9
9. 3:6
10. None of the above

Solution

Ratio of volumes = (Ratio of radii)^2 = (1:3)^2 = 1:9.

Correct Option: 3 Best Solution (1)

24 Dec 2021 Tiles

A hall of length 24 cm and breadth 20 m is to be paved with equal square tiles. What will be the size of the largest tile so that the tiles exactly fi t and also find the number of tiles required.

OPtion

1. 115
2. 116
3. 128
4. 134
5. 130
6. 120
7. 126
8. 110
9. 105
10. None of the above

Solution

Size of the largest possible square tile
= H.C.F. (l, b)
= H.C.F. (24, 20) = 4 m
Number of tiles required
= l x b / H.C.F. (24, 20)
= 24 x 20 / 4 = 120 tiles.

Correct Option: 6 Best Solution (1)

23 Dec 2021 Bamboo

Find out the length of the longest bamboo that can be placed in a room which is 12 m long, 12 m broad and 6 m high.

OPtion

1. 18
2. 17
3. 21
4. 23
5. 26
6. 27
7. 20
8. 15
9. 13
10. None of the above

Solution

Length of the bamboo
= length of the diagonal of the room
= √(12^2 + 12^2 + 6^2)
= √324 = 18 m.

Correct Option: 1 Best Solution (3)

22 Dec 2021 Work & Time

Ahmed is thrice as good a workman as Balkar and takes 22 days less to complete a piece of work than Balkar takes. Find out time in which Balkar alone can complete the work.

OPtion

1. 15
2. 23
3. 26
4. 22
5. 20
6. 33
7. 31
8. 29
9. 38
10. None of the above

Solution

Here, k = 3 and l = 22.
∴ Time taken by Balkar, working alone, to complete the work
= kl / (k – 1) days
= 3 x 22 / (3- 1)days,
i.e., 33 days.

Correct Option: 6 Best Solution (0)

21 Dec 2021 Permutation

In how many different ways can the letters of the word ‘NANAKMATTA’ be permuted?

OPtion

1. 37600
2. 35650
3. 37800
4. 35800
5. 34600
6. 30000
7. 29800
8. 38600
9. 36600
10. None of these

Solution

The word NANAKMATTA has 10 letters in all. The letter ‘A’ occurs 4 times, the letter ‘N’ occurs 2, letter ‘T’ occurs 2 times and the remaining two letters K & M each occur once.
∴ The require number of permutations
= 10! /4!2!2!1!1!
= 10! /4!2!2!
= (10*9*8*7*6*5*4!)/4!2*2
= (10*9*4*7*3*5)
= 37800

Correct Option: 3 Best Solution (3)

20 Dec 2021 Distance

What will be the distance between the pair of points A(2, 5) and B(–3, 7)?

OPtion

1. √29
2. √31
3. √37
4. √27
5. 5
6. √21
7. √30
8. 6
9. 7
10. None of the above

Solution

AB = √(-3-2)^2 + (7-5)^2
= √(25+4)
=√29

Correct Option: 1 Best Solution (4)

17 Dec 2021 Number

The total marks obtained by Ramesh in Hindi, English and Mathematics together is 90 more than the marks obtained by him in English. What are the average marks obtained by him in Hindi and Mathematics together?

OPtion

1. 60
2. 65
3. 45
4. 48
5. 50
6. 55
7. 42
8. 46
9. 62
10. None of the above

Solution

Let, marks got in physics, chemistry and mathematics are H, E and M.
H + E + M = E + 90
∴ H + M = 90
H + M/2 = 45.

Correct Option: 3 Best Solution (1)

16 Dec 2021 value of k

For what value of k, the system of equations 3x + 6y = 8 and 6x + 12y = k represents, coincident lines?

OPtion

1. 12
2. 26
3. 22
4. 24
5. 18
6. 16
7. 20
8. 21
9. 23
10. None of the above

Solution

If the given system of equations represents coincident lines
a1/a2 = b1/b2 = c1/c2
3/6 = 6/12 = 10/k
K = 10 x 12 / 6 = 20

Correct Option: 6 Best Solution (3)

15 Dec 2021 straight line

How many straight lines can be drawn with 26 points on a plane of which no points are collinear?

OPtion

1. 125
2. 153
3. 255
4. 225
5. 325
6. 275
7. 230
8. 330
9. 335
10. None of the above

Solution

The required number of straight lines
= n (n – 1)/2 =
= 26 (26 – 1)/2
= 26 * 25 / 2
= 650/2
= 325

Correct Option: 5 Best Solution (3)

14 Dec 2021 Rice Price

The cost (per Kg) of 3 qualities of rice are 45, 42 and 35 respectively. The cost (per Kg) of a mixture of 10 Kg of first, 8 Kg of second and 7 Kg of third will be

OPtion

1) 39.86
2) 39.64
3) 40.46
4) 41.24
5) 42.34
6) 42.38
7) 43.46
8) 43.12
9) 44.42
10) none of these

Solution

Total cost of the mixture:
(10*45)+(8*42)+(7*35)=Rs.1031
Total Qty of the mixture:(10+8+7)=25kg.
Cost per Kg. of mixture=1031/25=Rs.41.24

Correct Option: 4 Best Solution (0)