Explore topic-wise InterviewSolutions in .

i) 96,08,54,039 = 9 × 10,00,00,000 + 6 × 1,00,00,000 + 8 × 10,00,000 + 5 × 10,000 + 4 × 1000 + 3 × 10 + 9 × 1 

Ninety six crores eight lakhs fifty four thousand and thirty nine.

ii) 857,90,00,756 = 8 × 100,00,00,000 + 5 × 10,00,00,000 + 7 × 1,00,00,000 + 9 × 10,00,000 + 7 × 100 + 5 × 10 + 6 × 1 

Eight hundred fifty seven crores ninety lakhs seven hundred and fifty six.

(i) Three hundred three and nine hundredths = 303 + \(\frac{9}{100}\)

= 303 + 0 x \(\frac{1}{10}\) + 9 x \(\frac{1}{100}\)

= 303.09

(ii) Six and fifty five thousands 6 + \(\frac{55}{100}\) = 6 + \(\frac{5}{100}\) + \(\frac{5}{1000}\)

= 6 + \(\frac{0}{10}\) + \(\frac{5}{100}\) + \(\frac{5}{1000}\)

= 6.055

Let the numbers be 14x and 14y

14x × 14y = 14 × 210

⇒ xy = 210/14 = 30/2 = 15

x = 1, y = 15; x = 3, y = 5

(14, 210), (42, 70) Two pairs

\(0.\overline{23}\) = 0.232323….

\(0.\overline{22}\) = 0.222222….

Now, \(0.\overline{23}\) + \(0.\overline{22}\) = 0.23232323…. + 0.22222222…. 

= 0.45454545….

= \(0.\overline{45}\)

(iv) 0.6

\(\frac{3}{5}\) = \(\frac{3\times2}{5\times2}\)

= \(\frac{6}{10}\)

= 0.06

Largest number = 9, 65, 320.

(i) The given digits are 3, 7, 2 and 5

(a) The greatest 4-digit number = 7532

(b) and the smallest 4-digit number = 2357

(ii) The digits are given : 6, 1, 4 and 9

(a) The greatest 4-digit number = 9641

(b) and the smallest 4-digit number = 1469

(iii) The digits are given 7, 0, 4 and 2

(a) The greatest 4-digit number = 7420

(b) The smallest 4-digit number = 2047

(iv) the digits are given 1, 8, 5 and 3

(a) The greatest 4-digit number = 8531

(b) and the smallest 4-digit number =1358

(v) The digits are given 9, 6, 0 and 7

(a) The greatest 4-digit number = 9760

(b) and the smallest 4-digit number = 6079

Smallest 4 digits number = 1023

Greatest number of 4 digits = 9876

Greatest 5-digit number = 97865 and smallest 5-digit number = 10823

(i) 7 is at unit’s place

The smallest 4-digit number using the digits 5, 4, 7 and 9, and keeping 7 at unit’s place = 4597

The greatest 4-digit number using the digits 5, 4, 7 and 9 and keeping 7 at unit’s place = 9547

(ii) 9 is at ten’s place

The smallest 4-digit number using the digits 5, 4, 7 and 9 and keeping 9 at ten’s place = 4597

The greatest 4-digit number using the digits 5, 4, 7 and 9 and keeping 9 at ten’s place = 7594

(iii) 4 is at hundred’s place

The smallest 4-digit number using the digits 5, 4, 7 and 9 and keeping 4 at hundred’s place = 5479

The greatest 4-digit number using the digits 5, 4, 7 and 9 and keeping 4 at hundred’s place = 9475

The condition for 4-digit number of four different digits is that 5 is always at its tens place

The greatest 4-digit number will be 9857 and the smallest 4-digit number will be 1052

By using the digit 5 at ten’s place, the greatest 5-digit number is 98756, and the smallest 5-digit number is 10253.

The correct option is (C) LC.

(D) LLX

As we know that, the symbol L can never be repeated.

Therefore, LLX is incorrect.

i) 717,858: Seven hundred seventeen thousand eight hundred and fifty eight. 

ii) 3,250,672: Three million two hundred fifty thousand six hundred and seventy two. 

iii) 75,623,562: Seventy five million six hundred twenty three thousand five hundred and sixty two. 

iv) 956,237,676: Nine hundred fifty six million two hundred thirty seven thousand six hundred and seventy six.

False.

A number with three or more digits is divisible by 6, if the number formed by its last two digits (i.e., ones and tens) is divisible by 6.

The number 66 in Roman numerals is LXVI.

In roman numerals 66 can be written as LXVI. 

(L= 50, X = 10, V= 5, I = 1) 

66 = 60 + 6 = 50 + 10 + 5 + 1 = LXVI

The distance between Sringar and Leh is 422km. The same distance in metres is 422000.

1 km = 1000 m

422 km =1000 x 422= 422000 m

False.

Among kilo, milli and centi, the smallest is milli.

5,23,78,401

The number five crore twenty three lakh seventy eight thousand four hundreds can be written using commas in the Indian system of numeration as 5,23,78,401.

(a) 874 rounded off to the nearest hundreds = 900

478 rounded off to the nearest hundreds = 500

Estimated sum = 900 + 500 = 1400

(b) 793 rounded off to the nearest hundreds = 800

397 rounded off to the nearest hundreds = 400

Estimated sum = 800 + 400 = 1200

(c) 11244 rounded off to the nearest hundreds =11200

3507 rounded off to the nearest hundreds = 3500

Estimated sum = 11200 + 3500 = 14700

(d) 17677 rounded off to the nearest hundreds =17700

13589 rounded off to the nearest hundreds =13600

Estimated sum = 17700 + 13600 = 31300

(i) 5981 rounded off to nearest tens = 5980 

4428 rounded off to nearest tens = 4430

The estimated product = 5980 × 4430 = 26491400 

(ii) 5981 rounded off to nearest hundreds = 6000 

4428 rounded off to nearest hundreds = 4400 

The estimated product = 6000 × 4400 = 26400000

(i) 5981 rounded off to nearest tens = 5980 4428 rounded off to nearest tens = 4430

The estimated product = 5980 × 4430 = 26491400 

(ii) 5981 rounded off to nearest hundreds = 6000

4428 rounded off to nearest hundreds = 4400 

The estimated product = 6000 × 4400 = 26400000

(B) 99999

The number which comes immediately before a particular number is called its predecessor.

The predecessor of 1 lakh is = 1,00,000 – 1

= 99,999

Weight of cake made using 23.4 kg sugar = 50 kg 

Weight of cake made using 1 kg sugar = \(\frac{50}{23.4}\)

= \(\frac{50}{23.4}\) x \(\frac{10}{10}\)

= \(\frac{500}{234}\)

= 2.1367 Kg

= 2.14 Kg

Weight of cake made using 1 kg sugar = 2.14 Kg

1 is a factor of every number.

The given numbers in descending order are as :

4, 999 < 43, 877 < 78, 396 < 5, 43, 287 < 27, 32, 940 < 54, 82, 900

A number is a multiple of each of its factor.

32 × (27 × 19) = (32 × 27) × 19

According to BODMAS rule, first we should multiply and then add the products therefore ,

786 x 3 = 2358

786 x 7= 5502

2358 + 5502 = 7860

24 x 25 = 24 x 25

19 × 12 + 19 = 19 × (12 + 19)

24 x 35 = 24 x 18 + 24 x 17

8925 x 1 = 8925

The population of Tripura = 3,199,203 i.e., Three million one hundred ninety-nine thousand two hundred three.

And the population of Meghalaya = 2,318,822, i.e., Two million three hundred eighteen thousand eight hundred twenty two.

Radius of the Earth = 6400 km = 6400 × 1000 m = 6400000 m

And radius of the Mars = 4300000 m

∴ Radius of the Earth is greater than the radius of the Mars by (6400000 – 4300000) m = 2100000 m.

(D) sometimes rational, sometimes irrational

Explanation:

The product of any two irrational numbers is sometimes rational and sometimes irrational.

Hence, (D) is the correct option

(D) non-terminating non-recurring

Explanation:

The decimal expansion of the number √2 = 1.41421356237…

Hence, (D) is the correct option

There is no contradiction. When we measure a length with a scale or any other device we get quotient. 

Therefore we cannot judge whether c is a rational number of d is an irrational number. 

∴ Value of \(\frac{c}{d}\) is irratrional number. 

∴ Value of π is also irrational number.

Answer is (ii) 0

(iii) 16 ÷ (-4)

The water in the well is at 20^th step. 

For each jump the dog goes low 4 steps. 5 

∴ Number of jumps the dog to reach the water = \(\frac{20}{4}\) = 5 jumps

Answer is (ii) 20

Water level fall per week = -3 inches

∴ Water level decrease for 6 weeks = 6 Rs (-3) = 18 inches 

∴ Decrease of 18 inches of water level.

1 dozen = 12 bananas 

For 1 banana loss = Rs 2 

For 12 bananas loss = Rs 2 x 12 = Rs 24

Total pencils Kabilan had = 10 

No. of pencils given to Senthil = 2 

No. of pencils given to Karthick = 3. 

Now number of pencils left with Kabilan 

= 10 – 2 – 3 = 8 – 3 = 5 

Number of pencils got from his father = 6 

No. total pencils Kabilan had = 5 + 6 = 11 

Number of pencils given to his sister = 8 

Number of pencils left with Kabilan = 11 – 8 = 3

Water used for one day = 100 litres. 

Water used for 10 days = 100 x 10 = 1000 litres. 

After 10 days water left in the tank = 2000 litres.

Initially amount of water will be = 2000 + 1000 = 3000 litres.

According to the problem = -17 + A number 

= -19 

The number = -19 + 17 = -2 

∴ -2 should be added to -17 to get -19