सरलीकरण के इन 30 सवालों मेंं से 1 सवाल हमेशा परीक्षा में आता है !!

Simplification Questions in Hindi

व्यंजक =1+2/{1+2*(1+1/3)} का मान बराबर है –

हल –

$1+2\div \{ 1+2\div (1+\frac {1} {3})\}$

$=\, 1+2\div \{ 1+2\div \frac {4} {3}\}$

$=\, 1+2\div \{ 1+2\times \frac {3} {4}\}$

$=\, 1+2\div \frac {5} {2}=1+\frac {4} {5}\to \frac {9} {5}\to 1\frac {4} {5}$

2. $\frac {0.07\times 0.07-0.0021+0.03\times 0.03} {0.000343+0.000027}$ को सरल करने पर प्राप्त होता है –

हल –

माना a=0.07 तथा b-0.03

$\therefore \frac {{a}^{2}\, -ab+{b}^{2}} {{a}^{3}+{b}^{3}}$

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

$=\, \frac {1} {a+b}$

(a और b का मान रखने पर)

$=\, \frac {1} {0.07+0.03}=\frac {1} {0.10\, }=10$

3. 7,77,77,777 ÷ 77 बराबर है –

हल – 7,77,77,777 ÷ 77=1010101

4. $\frac {0.0203\times 2.92} {0.0073\times 14.5\times 0.7}\,$ बराबर है –

हल – $\frac {0.0203\times 2.92} {0.0073\times 14.5\times 0.7}=\frac {203\times 292} {73\times 145\times 7}$

$=\, \frac {29\times 4} {145}=\frac {4} {5}=0.8$

5. व्यंजक $\frac {1} {1\times 2\times 3}+\frac {1} {2\times 3\times 4}+\frac {1} {3\times 4\times 5}+\frac {1} {4\times 5\times 6}$ का मान बराबर है –

हल – $\frac {1} {1\times 2\times 3}+\frac {1} {2\times 3\times 4}+\frac {1} {3\times 4\times 5}+\frac {1} {4\times 5\times 6}$

$=\, \frac {1} {6}+\frac {1} {24}+\frac {1} {60}+\frac {1} {120}$

$=\, \frac {20+5+2+1} {120}$

$=\, \frac {28} {120}=\frac {7} {30}$

6. यदि x=b+c-2a, y=c+a-2b, z=a+b-2c हो, तो ${x}^{2}+{y}^{2}-{z}^{2}+2xy$ का मान होगा –

हल – x+y=b+c-2a+c+a-2b= -a-b+2c

$\therefore \, {x}^{2}+{y}^{2}-{z}^{2}+2xy$

$=\, {(x+y)}^{2\, }-{z}^{2}$

$=\, {(-a-b+2c)}^{2}-{(a+b-2c)}^{2}$

$=\, (-a-b+2c-a-b+2c)\times (-a-b+2c+a+b-2c)=0$

7. यदि ${(a-1)}^{2}+{(b+2)}^{2}+{(c+1)}^{2}=0$ हो, तो 2a -3b+7c का मान होगा –

हल – $\therefore \, {(a-1)}^{2}+{(b+2)}^{2}+{(c+1)}^{2}=0$

${(a-1)}^{2}=0$

${(b+2)}^{2}\, =0$

${(c+1)}^{2\, }=0$

$\therefore \, a=1$

$b=-2$

$c=-1$

$\therefore \, 2a-3b+7c$

$=2\times 1-3\times (-2)+7\times (-1)$

$=2+6-7=1$

8. यदि $X=\frac {4ab} {a+b}$ और (a ≠ b)

हो तो $\frac {X+2a} {X-2a}+\frac {X+2b} {X-2b}$ का मान क्या होगा –

हल – व्यंजक

$=\frac {X+2a} {X-2a}+\frac {X+2b} {X-2b}$

$=\, \frac {\frac {4ab} {a+b}+\frac {2a} {1}} {\frac {4ab} {a+b}-\frac {2a} {1}}+\frac {\frac {4ab} {a+b}+\frac {2b} {1}} {\frac {4ab} {a+b}-\frac {2b} {1}}$

$=\, \frac {4ab+{2a}^{2\, \, }+2ab} {4ab-{2a}^{2}\, -2ab}+\frac {4ab+2ab+{2b}^{2}} {4ab-2ab-{2b}^{2}}$

$=\, \frac {{2a}^{2}+6ab} {{-2a}^{2}+2ab}+\frac {{2b}^{2}+6ab} {{-2b}^{2}+2ab}$

$=\, \frac {a+3b} {b-a}-\frac {b+3a} {(b-a)}$

$=\, \frac {a+3b-b-3a} {(b-a)}=2$

9. यदि $\frac {a} {3}=\, \frac {b} {2}$ हो तो $\frac {2a+3b} {3a-2b}$ का मन क्या होगा –

हल – $\frac {a} {3}=\, \frac {b} {2}\to \frac {a} {b}=\frac {3} {2}$

व्यंजक $=\, \frac {2a+3b} {3a-2b}$

$=\, \frac {2\frac {a} {b\, }+3} {3\frac {a} {b}-2}=\frac {2\times \frac {3} {2}+3} {3\times \frac {3} {2}-2}$

$=\, \frac {6} {\frac {5} {2}}=\frac {12} {5}$

10. यदि $X+\frac {1} {X}=5$ हो तो $\frac {2X} {3{X}^{2}-5X+3}$ कितना होगा –

हल – व्यंजक $=\, \frac {2X} {3{X}^{2}-5X+3}$

$=\, \frac {2} {3X-5+\frac {3} {X}}$

$=\, \frac {2} {3(X+\frac {1} {X})-5}$

Simplification Questions in Hindi, Simplification Tricks in Hindi

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

हल – $\frac {\frac {1} {3}\div \frac {1} {3}\times \frac {1} {3}} {\frac {1} {3}\div \frac {1} {3}ka\frac {1} {3}}$

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

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

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

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. $\frac {{(2.697-0.498)}^{2}+{(2.697+0.498)}^{2}} {2.697\times 2.697+0.498\times 0.498}$ 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. $\frac {4.41\times 0.16} {2.1\times 1.6\times 0.21}$ का सरलीकृत रूप है –

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

हल – $0.05\times 5-0.005\times 5$

$=\, 0.25-0.025=0.225$

9. $\frac {256\times 256-144\times 144} {112}$ 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. $\frac {3.25\times 3.20-3.20\times 3.05} {0.064}$ बराबर है –

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

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

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

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

$\frac {0.3555\times 0.5555\times 2.055} {0.255\times 1.7775\times 0.2222}$ का मान है –

हल – व्यंजक $=\, \frac {0.3555\times 0.5555\times 2.025} {0.225\times 1.7775\times 0.2222}$

$=\, \frac {3555\times 5555\times 2025} {225\times 17775\times 2222}=4.5$

2. यदि a+b=1 तथा ${a}^{3}+\, {b}^{3}+3ab=k$ तो k का मान है –

हल – a+b=1

दोनों पक्षों का हल करने पर, ${(a+b)}^{3}=1$

$=\, {a}^{3}+{b}^{3}+3ab(a+b)=1$

$=\, {a}^{3}+{b}^{3}+3ab=1=k$

3. यदि $X+\frac {1} {X}=3$ हो, तो ${X}^{5}+\frac {1} {{X}^{5}}$ का मान कितना होगा –

हल – $X+\frac {1} {X}=3$

दोनों पक्षों का वर्ग करने पर, (i) ${X}^{2}+\, \frac {1} {{X}^{2}}+2=9$

$=\, {X}^{2}+\frac {1} {{X}^{2}}=9-2=7$

पुन: $X+\frac {1} {X}=3$

दोनों पक्षों का घन करने पर, (ii) ${X}^{3}+\frac {1} {{X}^{3}}+3(X+\frac {1} {X})=27$ $=\, {X}^{3}+\frac {1} {{X}^{3}}=27-9=18$ $\therefore \, ({X}^{2}+\frac {1} {{X}^{2}})({X}^{3}+\frac {1} {{X}^{3}})=7\times 18=126$ $\therefore \, {X}^{5}+\frac {1} {X}+X+\frac {1} {{X}^{5}}=126$ $=\, {X}^{5}+\frac {1} {{X}^{5}}+3=126$ $=\, {X}^{5}+\frac {1} {{X}^{5}}=126-3=123$ 4. यदि x-y=2, xy=24 हो, तो $({x}^{2}+{y}^{2})$ का मान कितना होगा –

हल – x-y=2 (i)

xy=24 (ii)

मान ज्ञात करना है $({x}^{2}+{y}^{2})=?$

हम जानते है ${(x-y)}^{2}={x}^{2}+{y}^{2}-2xy$

${(2)}^{2}={x}^{2}+{y}^{2}-2\times 24$

${x}^{2}+{y}^{2}=4+48=52$

5. यदि ${a}^{3}-{b}^{3}=56$ तथा a-b=2 हो तो ${a}^{2}+{b}^{2}$ का मान क्या होगा –

हल – हम जानते है कि ${a}^{3}-{b}^{3}=(a-b)({a}^{2}+ab+{b}^{2})$

$56=2({a}^{2}+ab+{b}^{2})$

${a}^{2}+ab+{b}^{2}=28$

${a}^{2}+{b}^{2}=28-ab$

${(a-b)}^{2}={a}^{2}+{b}^{2}-2ab$

${(2)}^{2}=28-ab-2ab$

$({a}^{2}+{b}^{2}=28-ab)$

$4=28-3ab$

$3ab=24$ $=\, ab=8$

समीकरण (i) से ${a}^{2}+{b}^{2}=28-ab$

$=\, 28-8=20$

6. $1\div [1+1\div \{ 1+1\div (1+1\div 2)\} ]$ का मान है –

हल – $1\div [1+1\div \{ 1+1\div (1+1\div 2)\} ]$

$=\, 1\div [1+1\div \{ 1+1\div (1+\frac {1} {2})\} ]$

$=\, 1\div [1+1\div \{ 1+1\div (\frac {3} {2})\} ]$

$=\, 1\div [1+1\div \{ 1+1\times (\frac {2} {3})\} ]$

$=\, 1\div [1+1\div \{ 1+\frac {2} {3}\} ]$

$=1\div [1+\frac {3} {5}]-1\div [\frac {8} {5}]$

$=1\times \frac {5} {8}=\frac {5} {8}$

7. सरल कीजिए – $8\frac {1} {2}-[3\frac {1} {4}\div \{ 1\frac {1} {4}-\frac {1} {2}(1\frac {1} {2}-\frac {1} {3}-\frac {1} {6})\} ]$

हल – $8\frac {1} {2}-[3\frac {1} {4}\div \{ 1\frac {1} {4}-\frac {1} {2}(1\frac {1} {2}-\frac {1} {3}-\frac {1} {6})\} ]$

$=\, \frac {17} {2}-[\frac {13} {4}\div \{ \frac {5} {4}-\frac {1} {2}(\frac {3} {2}-\frac {1} {3}-\frac {1} {6})\} ]$

$=\, \frac {17} {2}-[\frac {13} {4}\div \{ \frac {5} {4}-\frac {1} {2}(1)\} ]$

$=\, \frac {17} {2}-[\frac {13} {4}\div \{ \frac {5} {3}-\frac {1} {2}\} ]$

$=\, \frac {17} {2}-[\frac {13} {4}\div \{ \frac {3} {4}\} ]$

$=\, \frac {17} {2}-[\frac {13} {4}\times \frac {4} {3}]=\frac {17} {2}-\frac {13} {3}=4\frac {1} {6}$

8. $\frac {{(0.03)}^{2}-{(0.01)}^{2}} {0.03-0.01}$ का मान ज्ञात कीजिए –

हल – $\frac {{(0.03)}^{2}-\, {(0.01)}^{2}} {(0.03-0.01)}$

$=\, \frac {(0.03+0.01)(0.03-0.01)} {(0.03-0.01)}$

$=\, 0.03+0.01=0.04$

9. सरल कीजिए –

$1+\frac {4} {2+\frac {3} {5-\frac {1} {2}}}-\frac {1} {2}(10\div 2)$

हल – $1+\frac {4} {2+\frac {3} {5-\frac {1} {2}}}-\frac {1} {2}(10\div 2)$

$=\, 1+\frac {4} {2+\frac {2} {3}}-\frac {5} {2}$

$=\, 1+\frac {2} {3}-\frac {5} {2}$

$=\frac {2+3-5} {2}=0$

10. $\frac {2} {2+\frac {2} {3+\frac {2} {3+\frac {2} {3}}}\times 0.39}$ का सरलीकृत रूप है –

हल – $=\, \frac {2} {2+\frac {2} {3+\frac {2\times 3} {11}}\times 0.39}$

$=\, \frac {2} {2+\frac {2\times 11} {39}\times 0.39}$

$=\, \frac {2} {2+\frac {22} {100}}$

$=\, \frac {2\times 100} {222}=\frac {200} {222}=\frac {100} {111}$

Categorized in:

Math

Tagged in:

math

मुख्य विषय
ज्ञानकोश	इतिहास	भूगोल
गणित	अँग्रेजी	रीजनिंग
डाउनलोड	एसएससी	रणनीति
अर्थव्यवस्था	विज्ञान	राज्यव्यवस्था
राज्यवार	हिन्दी	टेस्ट सीरीज़ (Unlimited)
कृषि	क्विज़	जीवनी

सरलीकरण के इन 30 सवालों मेंं से 1 सवाल हमेशा परीक्षा में आता है !!

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