सरलीकरण के महत्वपूर्ण सवाल भाग

सरलीकरण के महत्वपूर्ण सवाल भाग – 3

- June 07, 2019

$frac {frac {1} {3}div frac {1} {3}times frac {1} {3}} {frac {1} {3}div frac {1} {3}kafrac {1} {3}}-, frac {1} {9}$ सरलीकृत मान है –

हल – $frac {frac {1} {3}div frac {1} {3}times frac {1} {3}} {frac {1} {3}div frac {1} {3}kafrac {1} {3}}$

$=, frac {frac {1} {3}times frac {1} {3}times frac {1} {3}} {frac {1} {3}div (frac {1} {3}times frac {1} {3})}-frac {1} {9}$

$=, frac {frac {1} {3}} {frac {1} {3}div frac {1} {9}}-frac {1} {9}=frac {frac {1} {3}} {frac {1} {3}times frac {9} {1}}-frac {1} {9}$

$=, frac {1} {3}times frac {1} {3}-frac {1} {9}=frac {1} {9}-frac {1} {9}=0$

2. $[{(0.111)}^{3}+{(0.222)}^{3}-{(0.333)}^{3}+{(0.333)}^{2}{(0.222)]}^{2}$ का सरलीकृत मान है –

हल – यदि a+b+c=0

तो ${a}^{3}+{b}^{3}+{c}^{3}=3abc$

$because 0.111+0.222-0.333=0$

$therefore , {(0.111)}^{3}+{(0.222)}^{3}+{(-0.333)}^{3}$

$=3(0.111)(0.222)(-0.333)$

$therefore [{(0.111)}^{3}+{(0.222)}^{3}-{(0.333)}^{3}+{(0.333)}^{2}times {(0.222)]}^{2}$

$=, [3(0.111)(0.222)(-0.333)+{(0.333)}^{2}{(0.222)]}^{2}$

$=, {[(0.222)(0.333)times { -3(0.111)+0.333} ]}^{2}$

$={[(0.222)(0.333)(0)]}^{3}=0$

3. $frac {{(2.697-0.498)}^{2}+{(2.697+0.498)}^{2}} {2.697times 2.697+0.498times 0.498}$ का मान है –

हल -माना a=2.697 तथा b= 0.498 $frac {{(a-b)}^{2}+{(a+b)}^{2}} {{a}^{2}+{b}^{2}}$

$=, frac {{a}^{2}+{b}^{2}-2ab+{a}^{2}+{b}^{2}+2ab} {{a}^{2}+{b}^{2}}$

$=, frac {{2a}^{2}+{2b}^{2}} {{a}^{2}+{b}^{2}}$

$=, frac {2({a}^{2}+{b}^{2})} {({a}^{2}+{b}^{2})}=2$

4. $frac {4.41times 0.16} {2.1times 1.6times 0.21}$ का सरलीकृत रूप है –

हल – $frac {4.41times 0.16} {2.1times 1.6times 0.21}=frac {2.1times 2.1times 0.16} {2.1times 1.6times 0.21}$

$=, frac {21times 16} {16times 21}=1$

5. $frac {5.42times 6+5.42times 24} {32.71times 32.71-27.29times 27.29}div frac {6.54times 6.54-3.46times 3.46} {3.08times 5+3.08times 45}$ के बराबर है –

हल -माना a=32.71, b=27.29,c=6.54, d= 3.46

$frac {5.42times 6+5.42times 24} {32.71times 32.71-27.29times 27.29}+, frac {6.54times 6.54-3.46times 3.46} {3.08times 5+3.08times 45}$

$=, frac {5.42times (6+24)} {{a}^{2}+{b}^{2}}+frac {{c}^{2}-{d}^{2}} {3.08(5+45)}$

$=, frac {5.42times 30} {(a+b)(a-b)}+frac {(c+d)(c-d)} {3.08times 50}$

$=, frac {5.42times 30} {60times 5.42}+frac {10times 3.08} {3.08times 50}$

(a,b,c तथा d का मान रखने पर) $=, frac {5.42times 30times 3.08times 50} {60times 5.42times 10times 3.08}$

$=, frac {5} {2}=2.5$

6. $frac {0.1times 0.1times 0.1+0.02times 0.02times 0.02} {0.2times 0.2times 0.2+0.04times 0.04times 0.04}$ का मान है –

हल – $frac {0.1times 0.1times 0.1+0.02times 0.02times 0.02} {0.2times 0.2times 0.2+0.04times 0.04times 0.04}$

$=, frac {.001+.000008} {.008+.0000064}$

$=, frac {.001008} {.008064}=, frac {1008} {8064}$

$=, frac {1} {8}=0.125$

7. $frac {{(998)}^{2}-{(997)}^{2}-45} {{(98)}^{2}-{(97)}^{2}}$ बराबर है –

हल – $frac {{(998)}^{2}-{(997)}^{2}-45} {{(98)}^{2}-{(97)}^{2}}$

$=, frac {(998+997)(998-997)-45} {(98+97)(98-97)}$

$=, frac {1995times 1-45} {195times 1}=, frac {1950} {195}=10$

8. $(0., 05times 5-0., 005times 5)$ बराबर है –

हल – $0.05times 5-0.005times 5$

$=, 0.25-0.025=0.225$

9. $frac {256times 256-144times 144} {112}$ बराबर है –

हल – माना a=256 तथा b= 144

$therefore , frac {{a}^{2}-{b}^{2}} {a-b}=frac {(a+b)(a-b)} {(a-b)}$

=256 + 144

(a और b का मान रखने पर)

=400

10. $frac {3.25times 3.20-3.20times 3.05} {0.064}$ बराबर है –

हल – $frac {3.25times 3.20-3.20times 3.05} {0.064}$

$=, frac {3.20(3.25-3.05)} {0.064}$

$=, frac {3.20times 0.2} {0.064}$

$=, frac {0.640} {0.064}=10$

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सरलीकरण के महत्वपूर्ण सवाल भाग – 3

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