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QJEEM24Maed3f: JEE Main 2024 Mathematics - Class 11 JEEM24Maed3f Solution: In a survey of 220 students of a higher secondary school, it…

In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied both Physics and Chemistry; 50 studied both Chemistry and Mathematics; 40 studied both Mathematics and Physics and 10 studied none of these subjects. Let m and n respectively be the least and the most number of students who studied all the three subjects. Then m+n is equal to ___________.

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JEE Main 2024 (Online) 4th April Morning Shift Mathematics - Sets and Relations Question 17 English Explanation

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padding-right: 0px; padding-top: 0.15em; padding-bottom: 0.15em;"><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd extra="true"></mjx-mtd></mjx-mtr><mjx-mtr><mjx-mtd style="text-align: right; padding-right: 0px; padding-top: 0.15em; padding-bottom: 0.15em;"><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; padding-left: 0px; padding-top: 0.15em; padding-bottom: 0.15em;"><mjx-mi class="mjx-n"></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c21D2"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c35"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-texatom space="4" texclass="ORD"><mjx-mi class="mjx-n"><mjx-c class="mjx-c78"></mjx-c></mjx-mi></mjx-texatom><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c34"></mjx-c><mjx-c class="mjx-c35"></mjx-c></mjx-mn><mjx-mi class="mjx-n"><mjx-c class="mjx-c26"></mjx-c></mjx-mi><mjx-mn class="mjx-n"><mjx-c class="mjx-c33"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="3"><mjx-c class="mjx-c2212"></mjx-c></mjx-mo><mjx-texatom space="3" texclass="ORD"><mjx-mi class="mjx-n"><mjx-c class="mjx-c78"></mjx-c></mjx-mi></mjx-texatom><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2265"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr><mjx-mtr><mjx-mtd style="text-align: right; padding-right: 0px; padding-top: 0.15em; padding-bottom: 0.15em;"><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd extra="true"></mjx-mtd></mjx-mtr><mjx-mtr><mjx-mtd style="text-align: right; padding-right: 0px; padding-top: 0.15em; padding-bottom: 0.15em;"><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; padding-left: 0px; padding-top: 0.15em; padding-bottom: 0.15em;"><mjx-mi class="mjx-n"></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c21D2"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c35"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-texatom space="4" texclass="ORD"><mjx-mi class="mjx-n"><mjx-c class="mjx-c78"></mjx-c></mjx-mi></mjx-texatom><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c33"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr><mjx-mtr><mjx-mtd style="text-align: right; padding-right: 0px; padding-top: 0.15em; padding-bottom: 0.15em;"><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd extra="true"></mjx-mtd></mjx-mtr><mjx-mtr><mjx-mtd style="text-align: right; padding-right: 0px; padding-top: 0.15em;"><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; padding-left: 0px; padding-top: 0.15em;"><mjx-mn class="mjx-n"><mjx-c class="mjx-c33"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="3"><mjx-c class="mjx-c2B"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="3"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c35"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c34"></mjx-c><mjx-c class="mjx-c35"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr></mjx-itable></mjx-table></mjx-mtable></mjx-math><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left" columnspacing="0em" rowspacing="3pt"><mtr><mtd></mtd><mtd><mn>125</mn><mo>≤</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">m</mi></mrow><mo>+</mo><mn>90</mn><mo>−</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">x</mi></mrow><mo>≤</mo><mn>130</mn></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mn>85</mn><mo>≤</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">P</mi></mrow><mo>+</mo><mn>70</mn><mo>−</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">x</mi></mrow><mo>≤</mo><mn>95</mn></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mn>75</mn><mo>≤</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">C</mi></mrow><mo>+</mo><mn>80</mn><mo>−</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">x</mi></mrow><mo>≤</mo><mn>90</mn></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mtext>&nbsp;</mtext><mi mathvariant="normal">m</mi></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">P</mi></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">C</mi></mrow><mo>+</mo><mn>120</mn><mo>−</mo><mn>2</mn><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">x</mi></mrow><mo>=</mo><mn>210</mn></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo stretchy="false">⇒</mo><mn>15</mn><mo>≤</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">x</mi></mrow><mo>≤</mo><mn>45</mn><mi mathvariant="normal">&amp;</mi><mn>30</mn><mo>−</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">x</mi></mrow><mo>≥</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo stretchy="false">⇒</mo><mn>15</mn><mo>≤</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">x</mi></mrow><mo>≤</mo><mn>30</mn></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mn>30</mn><mo>+</mo><mn>15</mn><mo>=</mo><mn>45</mn></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container>

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