Q. 44

# If N ÷ 5 leaves remainder 3 and N ÷ 2 leaves remainder 0, then N ÷ 10 leaves remainder 4.

Answer :

False(F)

Here it’s given N ÷ 5 leaves remainder 3

⇒ N = 5n + 3,where n = 0,1,2,3,..

and N ÷ 2 leaves remainder 0

⇒ N is an even number

But N = 5n + 3,it’s sum of two terms whose second term is odd.

Therefore,5n should be an odd number.

5n can be odd when n = 1,3,5,…

So, in this case when N = 5n + 3

⇒ N = 5(1) + 3 = 8 when(n = 1)

Hence when we substitute n = 1,3,5,.. in N = 5n + 3,we get 8,18,28 etc

Now, when we divide N by 10 ,N can be written as

N = 10×n + 8,when n = 0,1,2,3,..

Therefore, when N ÷ 10 ,always leaves remainder 8.

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If x + y + z = 6 and z is an odd digit, then the three-digit number xyz is

NCERT - Mathematics ExemplarTest the divisibility of each of the following numbers by 11:

(i) 22222

(ii) 444444

(iii) 379654

(iv) 1057982

(v) 6543207

(vi) 818532

(vii) 900163

(viii) 7531622

RS Aggarwal - MathematicsTest the divisibility of each of the following numbers by 4:

(i) 134

(ii) 618

(iii) 3928

(iv) 50176

(v) 39392

(vi) 56794

(vii) 86102

(viii) 66666

(ix) 99918

(x) 77736

RS Aggarwal - MathematicsTest the divisibility of each of the following numbers by 8:

(i) 6132

(ii) 7304

(iii) 59312

(iv) 66664

(v) 44444

(vi) 154360

(vii) 998818

(viii) 265472

(ix) 7350162

RS Aggarwal - MathematicsTest the divisibility of each of the following numbers by 9:

(i) 327

(ii) 7524

(iii) 32022

(iv) 64302

(v) 89361

(vi) 14799

(vii) 66888

(viii) 30006

(ix) 33333

RS Aggarwal - MathematicsTest the divisibility of each of the following numbers by 5:

(i) 95

(ii) 470

(iii) 1056

(iv) 2735

(v) 55053

(vi) 35790

(vii) 98765

(viii) 42658

(ix) 77990

RS Aggarwal - MathematicsTest the divisibility of each of the following numbers by 3:

(i) 83

(ii) 378

(iii) 474

(iv) 1693

(v) 60005

(vi) 67035

(vii) 591282

(viii) 903164

(ix) 100002

RS Aggarwal - MathematicsTest the divisibility of each of the following numbers by 10:

(i) 205

(ii) 90

(iii) 1174

(iv) 57930

(v) 60005

RS Aggarwal - MathematicsWhich of the following numbers are divisible by 9?

(i) 524618

(ii) 7345845

(iii) 8987148

RS Aggarwal - Mathematics