12th Class Mathematics MCQS Differentiation Online Test 2

3-cp-3-e-3-cspan-style-3-d-22-font-size-3-a-13-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-tahoma-22-2-c-22-sans-serif-22-27-3-e-if-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-g-28-x-29-3-d-5-c-5-cfrac-7-b-1-7-d-7-bx-5-e-7-b-2-7-d-7-d-28-x-5-c-5-cneq-0-29-5-c-5-c-29-3-c-2-fspan-3-e-c-2-a-0-then-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-gog-28-x-29-5-c-5-c-29-3-c-2-fspan-3-e-c-2-a-0-is-equal-to-3-a-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fp-3-e_-_3-cp-3-e-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-x-5-e-7-b-2-7-d-5-c-5-c-29-3-c-2-fspan-3-e-3-c-2-fp-3-e,3-cp-3-e-3-cspan-style-3-d-22-font-size-3-a-13-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-tahoma-22-2-c-22-sans-serif-22-27-3-e-if-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-y-3-de-5-e-7-b-2-x-7-d-5-c-5-c-29-3-c-2-fspan-3-e-2-c-then-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-y-7-b-2-7-d-5-c-5-c-29-3-c-2-fspan-3-e-c-2-a-0-is-equal-to-3-a-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fp-3-e_-_3-cp-3-e-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-284-e-5-e-7-b-2-x-7-d-5-c-5-c-29-3-c-2-fspan-3-e-3-c-2-fp-3-e,3-cp-3-e-3-cspan-style-3-d-22-font-size-3-a-13-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-tahoma-22-2-c-22-sans-serif-22-27-3-e-the-function-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-f-28-x-29-3-d-5-c-5-cfrac-7-b-2-2-b-3-x-7-d-7-b-2-x-7-d-5-c-5-c-29-3-c-2-fspan-3-e-c-2-a-0-is-not-continuous-at-3-a-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fp-3-e_-_3-cp-3-e-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-x-3-d-0-5-c-5-c-29-3-c-2-fspan-3-e-3-c-2-fp-3-e,3-cp-3-e-3-cstrong-3-e-3-cspan-style-3-d-22-font-size-3-a-10-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-times-new-roman-22-2-c-22-serif-22-27-3-e-3-cspan-style-3-d-22-color-3-ablack-22-3-e-if-f-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-cspan-style-3-d-22-font-size-3-a-12-0-pt-22-3-e-3-cspan-style-3-d-22-font-family-3-a-symbol-22-3-e-3-cspan-style-3-d-22-color-3-ablack-22-3-e-c-2-a-2-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-cspan-style-3-d-22-font-size-3-a-10-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-times-new-roman-22-2-c-22-serif-22-27-3-e-3-cspan-style-3-d-22-color-3-ablack-22-3-e-28-c-29-3-d-0-2-c-then-the-number-c-is-called-a-value-of-f-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fstrong-3-e-3-c-2-fp-3-e_-_3-cp-3-e-3-cspan-style-3-d-22-font-size-3-a-10-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-times-new-roman-22-2-c-22-serif-22-27-3-e-3-cspan-style-3-d-22-color-3-ablack-22-3-e-critical-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fp-3-e,3-cp-3-e-3-cstrong-3-e-3-cspan-style-3-d-22-font-size-3-a-10-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-times-new-roman-22-2-c-22-serif-22-27-3-e-3-cspan-style-3-d-22-color-3-ablack-22-3-e-if-s-is-the-distance-traveled-by-a-body-at-time-t-2-c-the-velocity-is-given-by-the-expression-3-a-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fstrong-3-e-3-c-2-fp-3-e_-_3-cp-3-e-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-5-c-5-cfrac-7-bds-7-d-7-bdt-7-d-5-c-5-c-29-3-c-2-fspan-3-e-3-c-2-fp-3-e,3-cp-3-e-3-cstrong-3-e-3-cspan-style-3-d-22-font-size-3-a-10-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-times-new-roman-22-2-c-22-serif-22-27-3-e-3-cspan-style-3-d-22-color-3-ablack-22-3-e-the-technique-or-method-to-find-such-a-function-whose-derivative-is-given-involves-the-inverse-process-of-differentiation-called-3-a-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fstrong-3-e-3-c-2-fp-3-e_-_3-cp-3-e-3-cspan-style-3-d-22-font-size-3-a-10-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-times-new-roman-22-2-c-22-serif-22-27-3-e-3-cspan-style-3-d-22-color-3-ablack-22-3-eintegration-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fp-3-e,3-cp-3-e-3-cstrong-3-e-3-cspan-style-3-d-22-font-size-3-a-10-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-times-new-roman-22-2-c-22-serif-22-27-3-e-if-a-function-f-28-x-2-c-y-29-have-same-maximum-value-at-any-two-points-2-c-then-it-is-at-all-the-points-of-the-line-segment-between-these-points-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fstrong-3-e-3-c-2-fp-3-e_-_3-cp-3-e-3-cspan-style-3-d-22-font-size-3-a-10-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-times-new-roman-22-2-c-22-serif-22-27-3-emaximum-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fp-3-e,3-cp-3-e-3-cstrong-3-e-3-cspan-style-3-d-22-font-size-3-a-10-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-times-new-roman-22-2-c-22-serif-22-27-3-ea-point-does-not-lie-in-the-feasible-region-is-corner-point-of-the-feasible-region-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fstrong-3-e-3-c-2-fp-3-e_-_3-cp-3-e-3-cspan-style-3-d-22-font-size-3-a-10-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-times-new-roman-22-2-c-22-serif-22-27-3-enot-a-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fp-3-e,30spkGfIbKdsBn34VgQ7,4lcNyBpmEcp5TW4xp0TI,5-c-28-0-crac-7-bd-7-d-7-b-7-bdx-7-d-7-d-28-5-csin-5-csqrt-x-29-5-c-29-equals-3-a_-_5-c-28-0-crac-7-b-7-b-5-ccos-5-csqrt-x-7-d-7-d-7-b-7-b-2-5-csqrt-x-7-d-7-d-5-c-29,5-c-28-0-crac-7-bd-7-d-7-b-7-bdx-7-d-7-d-28-7-b-5-ccos-5-e-7-b-1-7-d-7-d-3-x-29-3-d-3-a-5-c-29_-_5-c-28-0-crac-7-b-7-b-3-7-d-7-d-7-b-7-b-5-csqrt-7-b-1-9-7-bx-5-e-2-7-d-7-d-7-d-7-d-5-c-29,5-c-28-0-crac-7-bd-7-d-7-b-7-bdx-7-d-7-d-28-7-b-5-csinh-5-e-7-b-1-7-d-7-dx-29-5-c-29-is-equal-to-3-a_-_5-c-28-0-crac-7-b-1-7-d-7-b-7-b-5-csqrt-7-b-1-2-b-7-bx-5-e-2-7-d-7-d-7-d-7-d-5-c-29,5-c-28-0-crac-7-bd-7-d-7-b-7-bdx-7-d-7-d-5-cleft-28-7-b-0-crac-7-b-1-7-d-7-b-7-bax-2-b-b-7-d-7-d-7-d-0-dight-29-5-c-29-equals-3-a_-_5-c-28-0-crac-7-b-7-b-a-7-d-7-d-7-b-7-b-7-b-7-b-28-ax-2-b-b-29-7-d-5-e-2-7-d-7-d-7-d-5-c-29,5-c-28-0-crac-7-bd-7-d-7-b-7-bdx-7-d-7-d-5-cleft-28-7-b-0-crac-7-b-7-b-7-bx-5-e-2-7-d-4-7-d-7-d-7-b-7-bx-2-7-d-7-d-7-d-0-dight-29-5-c-29-equals-3-a_-_1,5-c-28-0-crac-7-bd-7-d-7-b-7-bdx-7-d-7-d-7-b-28-7-bx-5-e-3-7-d-2-b-1-29-5-e-9-7-d-3-d-5-c-29_-_5-c-289-7-b-28-7-bx-5-e-3-7-d-2-b-1-29-5-e-8-7-d-283-7-bx-5-e-2-7-d-29-5-c-29,5-c-28-0-crac-7-bd-7-d-7-b-7-bdx-7-d-7-d-7-b-28-ax-2-b-b-29-5-en-7-d-3-d-na-7-b-28-ax-2-b-b-29-5-e-7-bn-1-7-d-7-d-5-c-29-2-c-where-n-is-any-rational-number-is-called-rule_-_power-rule,5-c-28-0-crac-7-bd-7-d-7-b-7-bdx-7-d-7-d-7-be-5-e-7-bx-2-b-h-7-d-7-d-5-c-29-3-d-3-a_-_5-c-28-7-be-5-e-7-bx-2-b-h-7-d-7-d-5-c-29,5-c-28-7-b-5-cleft-7-c-7-bfog-28-x-29-7-d-0-dight-7-c-5-e-27-7-d-3-d-3-f-5-c-29_-_5-c-28-7-bf-5-e-27-7-d-5-c-7-b-g-28-x-29-09-imes-7-bg-5-e-27-7-d-28-x-29-5-c-7-d-5-c-29,5-c-28-7-ba-0-7-d-2-b-7-ba-1-7-dx-2-b-7-ba-2-7-d-7-bx-5-e-2-7-d-2-b-2-b-7-ba-n-7-d-7-bx-5-en-7-d-2-b-5-c-29-is-3-a_-_power-series,if-5-c-28-f-28-x-2-b-h-29-3-d-5-ccos-28-x-2-b-h-29-5-c-29then-5-c-28-7-bf-5-e-27-7-d-28-x-29-5-c-29-equals-3-a_-_sin-x,if-5-c-28-y-3-d-0-crac-7-b-1-7-d-7-b-7-b-7-bx-5-e-2-7-d-7-d-7-d-5-c-29-2-c-then-5-c-28-0-crac-7-b-7-bdy-7-d-7-d-7-b-7-bdx-7-d-7-d-5-c-29-at-5-c-28-x-3-d-1-5-c-29-is-3-a_-_2,if-s-is-the-distance-travled-by-a-body-at-time-t-2-c-the-velocity-is-given-by-the-expression-3-a_-_5-c-28-0-crac-7-b-7-bds-7-d-7-d-7-b-7-bdt-7-d-7-d-5-c-29,if-y-3-d-e-3-csup-3-e-2-x-3-c-2-fsup-3-e-2-c-then-y-3-csub-3-ex-3-c-2-fsub-3-e-is-equal-to_-_4-e-3-csup-3-e-2-x-3-c-2-fsup-3-e,the-derivation-of-5-c-28-5-csqrt-x-5-c-29-at-5-c-28-x-3-d-a-5-c-29-is-3-a_-_5-c-28-0-crac-7-b-1-7-d-7-b-7-b-2-5-csqrt-4-7-d-7-d-5-c-29,the-symbol-5-c-28-0-crac-7-b-7-bdy-7-d-7-d-7-b-7-bdx-7-d-7-d-5-c-29-is-used-for-the-derivation-of-3-a_-_x-with-respect-to-x