Question

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Answer 1

Question : 1

1) HCF of 2 numbers is 16 and their product is 3072. Find their LCM

Formula Used :

Product of LCM And HCF = Product of the 2 numbers

Solution :

• Given HCF of 2 numbers = 16

• Let the numbers be x, y

• Product of x and y = 3072

Product of LCM And HCF = Product of the 2 numbers

$HCF \times LCM = x \times y \\\\\\16\times LCM = 3072\\\\\\LCM = \dfrac{3072}{16}\\\\\\=192$

Answer :

LCM of x and y = 192

Question : 2

Write down the decimal expansion of the rational number $\dfrac{7}{80}$ by writing the denominator in the form $2^m\times5^n$

Solution :

The given number is  $\frac{7}{80}$ , where clearly 80 = 2⁴ × 5 is in the form $2^m\times5^n$

So,

$\dfrac{7}{80}\\\\\\=\dfrac{7\times5^3}{2^4\times5\times5^3}\\\\\\=\dfrac{7\times125}{(2\times5)^4}\\\\\\=\dfrac{875}{10^4}\\\\\\=\dfrac{875}{10000}\\\\\\=0.0875$

Answer :

Hence the answer is 0.0875  

Question : 3

If $\dfrac{2}{3}$ is a solution of the equation $7x^2+kx-3=0$. Find the value of k

Solution :

Given , the equation is  $7x^2+kx-3=0$

Substitute the value of k in equation

$7[\dfrac{2}{3}]+k[\dfrac{2}{3}]-3=0\\\\\\7[\frac{4}{9}]+[\dfrac{2k}{3}]-3=0\\\\\\\dfrac{28+6k-27}{9}=0\\\\\\6k+1=0\times9\\\\\\6k+1=0\\\\\\6k=-1\\\\\\k=\dfrac{-1}{6}$

Answer :

Therefore the value of  $k=\dfrac{-1}{6}$

Question : 4

Check whether x =2 is a solution of the equation $3x^2+10=11x$

Solution :

Given , the equation is  $3x^2+10=11x$

Substitute the value of x in equation

$3(2)^2+10=11(2)\\\\\\=3(4)+10=22\\\\\\=12+10=22\\\\\\=22=22\\\\\\\boxed{L.H.S=R.H.S}$

Answer :

Therefore x = 2 is a solution of   $3x^2+10=11x$

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