Maths Quiz of the Day – I For IBPS PO Mains 2019 : 21-08-2019

Directions (1-2): Read the following passage and answer the questions that follow:

        A boy has 4 library tickets i.e. he can issue a maximum of four books from the library. There exist 12 books of his interest in the library.

1. In how many ways can he choose the three books if he does not want to issue English part 2 unless English part 1 is issued?

        (1) 105

        (2) 125

        (3) 145                                        

        (4) 175

        (5) 195

2. What is the total number of possible combinations of books that he can issue from the library if he issues at least 1 book from the library?

        (1) 726

        (2) 759

        (3) 799                                        

        (4) 817

        (5) 793

 

Directions (3-7): What should come in place of the question mark ‘?’ in the following numbers series?

3. 18, 20, 44, 138, 560, 2810, ?

        (1) 16818

        (2) 16836

        (3) 16854             

        (4) 16872

        (5) 16890

4. 841, 961, 1089, 1225, 1369, 1521, ?

        (1) 1581

        (2) 1681

        (3) 1781               

        (4) 1881

        (5) 1981

5. 5, 11, 23, 47, 95, ?

        (1) 181

        (2) 185

        (3) 190                                        

        (4) 191

        (5) None of these

6. 8, 21, 60, ?, 528, 1581

        (1) 177

        (2) 214

        (3) 334                                        

        (4) 114

        (5) 224

7. 30, 25, ?, 18, 16, 15

        (1) 20

        (2) 21

        (3) 24                                          

        (4) 15

        (5) 18

8. The diameter of a rod is 2 cm and its length is 32 cm. This rod is drawn into a wire of length 128 cm and uniform thickness. What is the thickness of the new wire?

        (1) 2 cm

        (2) √2 cm

        (3) 1 cm               

        (4) 1.5 cm

        (5) None of these

9. Rajan is trying to make a cube using three old cubes having edges 6 cm, 8 cm and 10 cm. What will be the edge of new cube?

        (1) 3 cm

        (2) 5 √2 cm

        (3) 12 cm             

        (4) 6 cm

        (5) 9 cm

10. If Sheenu, Rohan and Neeta work together on the painting for 2 days, but after 2 days only Rohan and Neeta are left to complete the remaining work on the painting, then total work will be completed in

        (1) 26 days

        (2) 23 days          

        (3) 31 days          

        (4) 29 days

        (5) 33 days

Solutions:

Ans.1(4) The total number of ways to select = 12C3 = 220

           The number of ways in which English part 2 is selected and not English part 1 = 10C2 = 45

           ∴ Necessary ways = 220 – 45 = 175

Ans.2(5) Number of ways to get 1 book released

               = 12C1 = 12

               Number of ways to get 2 books released

               = 12C2 = 66

               Number of ways to get 3 books released

               = 12C3 = 220

               Number of ways to get 4 books released

               = 12C4 = 495

               ∴ Total number of ways = 12 + 66 + 220 + 495

               = 793

Ans.3(4) The given method of the series is as follows:

               ⇒ 18 × 1 + 2 = 20

               ⇒ 20 × 2 + 4 = 44

               ⇒ 44 × 3 + 6 = 138

               ⇒ 138 × 4 + 8 = 560

               ⇒ 560 × 5 + 10 = 2810

               ⇒ 2810 × 6 + 12 = 16872

Ans.4(2) The given method of the series is as follows:

               ⇒ 961 – 841 = 120

               ⇒ 1089 – 961 = 128

               ⇒ 1225 – 1089 = 136

               ⇒ 1369 – 1225 = 144

               ⇒ 1521 – 1369 = 152

               ⇒ 1681 – 1521 = 160

Ans.5(4) The given method of the series is as follows:

               ⇒ 5 × 2 + 1 = 11

               ⇒ 11 × 2 + 1 = 23

               ⇒ 23 × 2 + 1 = 47

               ⇒ 47 × 2 + 1 = 95

               ⇒ 95 × 2 + 1 = 191

Ans.6(1) The given method of the series is as follows:

               ⇒ 8

               ⇒ 8 × 3 – 3 = 21

               ⇒ 21 × 3 – 3 = 60

               ⇒ 60 × 3 – 3 = 177 = ?

               ⇒ 177 × 3 – 3 = 528

               ⇒ 528 × 3 – 3 = 1581

Ans.7(2) The given method of the series is as follows:

               ⇒ 30

               ⇒ 30 – 5 = 25

               ⇒ 25 – 4 = 21 = ?

               ⇒ 21- 3 = 18

               ⇒ 18 – 2 = 16

               ⇒ 16 -1 = 15

Ans.8(3)     πR2H = πr2h

               12 × 32 = r2 × 128

               r2 = ¼

               r = ½

               Diameter = 1 cm    

Ans.9(3) It has been given that the new cube is made of old cubes. Volume of new cubes, 6 cm, 8 cm And 10 cm The sum of the volume of the cube with the sides will be equal to.

               Volume of a cube = (side)3

               Thus, the volume of the new cube

               = (6)3 + (8)3 + (10)3

               ⇒ Volume = 216 + 512 + 1000 = 1728cm3

               ∴ Side of 1728 cubic cm volume = ∛(volume) 

               = √1728=12 cm.

Ans.10(2)  Sheenu and Rohan can complete a painting in 18 days. Rohan and Neeta can do it in 24 days, Sheenu and Neeta can do it in 36 days.

              Work done by Sheenu, Rohan and Neeta in one day = 1/16

              Work done by Sheenu, Rohan and Neeta in 2 days = 1/16×2= 1/8

              The remaining work to be completed by Rohan and Neeta = 1-1/8= 7/8

              Also, we know,

              Rohan and Neeta can complete the entire work in 24 days.

              Rohan and Neeta work 24×7/8day = 21 days

              ∴ The number of days it takes to do the whole work = 2 + 21 = 23 days

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