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251.

The H.C.F. of two numbers is 18. First number is of three digits and Second number is of two digits and their L.C.M. is 936. The sum of the numbers is?1). 2762). 3063). 2784). 310

Answer»

Let the numbers be 18x and 18y where x and y are co-prime

LCM of 18x and 18y = 18xy

According to the question

18xy = 936

⇒ XY = 936/18

⇒ xy = 52

⇒xy = 13 × 4

⇒ x =13 and y = 4

First NUMBER = 18 × 13 = 234

Second number = 18 × 4 = 72

∴ Sum of the number = 234 + 72 = 306
Discussion
252.

If √51 = 7.14 and 3√45 = 3.55, find the value of (√0.1275 + 3√2.88).1). 0.017772). 0.17773). 1.7774). 17.77

Answer»

We can write,

⇒ √0.1275 = √{(51 × 25)/10000} = (7.14 × 5)/100 = 0.357

Similarly,

⇒ 3√2.88 = 3√{(45 × 64)/1000} = (3.55 × 4)/10 = 1.42

∴ (√0.1275 + 3√2.88) = 0.357 + 1.42 = 1.777
Discussion
253.

If (b + c), (c + a), (a + b) are in A.P. then1). b = a + c2). \(a = \frac{{b + c}}{2}\)3). \(c = \frac{{a + b}}{2}\)4). \(b = \frac{{a + c}}{2}\)

Answer»

The GIVEN EXPRESSION,

(b + c), (c + a), (a + b) are in A.P

Then,

⇒ (c + a) = [(b + c) + (a + b)]/2

⇒ 2C + 2a = 2B + c + a

⇒ c + a = 2b

∴ b = (a + c)/2
Discussion