12th Class Mathematics MCQS Differentiation Online Test 1

3-cp-3-e-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-5-c-5-cint-5-c-5-c-2-ccosec-5-e-2-x-28-ax-2-bb-29-5-c-5-c-2-cdx-3-d-5-c-5-c-2-c-2-c-5-c-5-c-2-c-28-a-5-c-5-cneq-0-29-5-c-5-c-29-3-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-28-5-c-5-cfrac-7-b-1-7-d-7-ba-7-d-5-c-5-c-2-ccot-5-c-5-c-2-c-28-ax-2-bb-29-2-bc-5-c-5-c-29-3-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-28-5-c-5-cunderline-j-5-c-5-c-2-c-5-c-5-ctimes-5-c-5-c-2-c-5-c-5-cunderline-j-3-d-5-c-5-c-29-3-c-2-fspan-3-e-3-c-2-fp-3-e_-_3-cp-3-e-0-3-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-dx-1-2-br-5-c-5-c-2-ccos-5-c-5-c-2-c-5-c-5-ctheta-2-cy-3-dy-1-2-br-5-c-5-c-2-csin-5-c-5-c-2-c-5-c-5-ctheta-5-c-5-c-29-3-c-2-fspan-3-e-is-called-the-3-a-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-eparametric-form-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-cspan-style-3-d-22-font-size-3-a-10-0-pt-22-3-e-3-cspan-style-3-d-22-color-3-ablack-22-3-e-if-c-2-a-0-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-5-c-5-cint-5-c-5-climits-7-ba-7-d-5-e-7-bb-7-df-28-x-29-5-c-5-c-2-cdx-5-c-5-c-29-3-c-2-fspan-3-e-2-c-then-the-interval-5-ba-2-c-b-5-d-is-called-the-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-22-color-3-ablack-22-3-eof-integration-3-c-2-fspan-3-e-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-10-0-pt-22-3-e-3-cspan-style-3-d-22-color-3-ablack-22-3-erange-3-c-2-fspan-3-e-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-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-focus-of-the-parabola-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-y-5-e-2-5-c-5-c-29-3-c-2-fspan-3-e-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-3-d-4-ax-is-3-a-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-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-a-2-c-0-29-3-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-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-ea-line-segment-having-both-the-end-points-on-a-circle-and-not-passing-through-the-centre-is-called-a-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-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-ea-chord-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-cspan-style-3-d-22-font-size-3-a-11-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-arial-22-2-c-22-sans-serif-22-27-3-e-equation-of-line-through-origin-with-slope-2-3-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-style-3-d-22-font-size-3-a-11-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-arial-22-2-c-22-sans-serif-22-27-3-e-2-x-y-3-d-0-3-c-2-fspan-3-e-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-11-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-arial-22-2-c-22-sans-serif-22-27-3-e-if-p-3-d-282-2-c-3-29-2-c-q-3-d-286-2-c-2-29-2-c-then-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-5-c-5-cleft-7-c-5-c-5-coverline-7-bpq-7-d-5-c-5-cright-7-c-5-c-5-c-29-3-c-2-fspan-3-e-c-2-a-0-is-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-28-5-c-5-csqrt-7-b-41-7-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-11-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-arial-22-2-c-22-sans-serif-22-27-3-e-it-is-not-unit-vector-3-a-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fp-3-e_-_3-cp-3-e-5-b-1-2-c-1-2-c-1-5-d-3-c-2-fp-3-e,3-cp-3-e-3-cspan-style-3-d-22-font-size-3-a-11-0-pt-22-3-e-3-cspan-style-3-d-27-font-family-3-a-22-arial-22-2-c-22-sans-serif-22-27-3-e-solution-of-3-c-2-fspan-3-e-3-cspan-style-3-d-27-font-family-3-a-calibri-2-c-22-sans-serif-22-27-3-e-3-cspan-style-3-d-27-font-family-3-a-22-arial-22-2-c-22-sans-serif-22-27-3-e-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-7-bdy-5-c-5-cover-dx-7-d-3-d-2-x-5-c-5-c-29-3-c-2-fspan-3-e-c-2-a-0-is-3-a-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-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-y-3-dx-5-e-2-2-bc-5-c-5-c-29-3-c-2-fspan-3-e-3-c-2-fp-3-e,3-cp-3-e-3-cspan-styl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cdelta-x-2-cc-2-b-5-cdelta-x-29-2-c-5-c-29then-the-function-f-is-said-to-have-a-2-fan-at-x-3-dc_-_relative-minima,if-5-c-28-x-3-d-a-5-csin-09-heta-5-c-29-2-c-5-c-28-y-3-d-a-5-ccos-09-heta-5-c-29then-5-c-28-0-crac-7-b-7-bdy-7-d-7-d-7-b-7-bdx-7-d-7-d-5-c-29-3-d_-_tan-5-c-28-09-heta-5-c-29,if-5-c-28-y-3-d-5-ccos-x-2-c-5-c-2-cu-3-d-5-csin-x-5-c-2-cthen-5-c-2-c-0-crac-7-b-7-bdy-7-d-7-d-7-b-7-bdu-7-d-7-d-3-d-1-5-c-29_-_tan-x,if-x-3-d-a-28-t-sint-29-2-c-y-3-da-281-2-bcost-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-is-given-by-3-a_-_5-c-28-5-ccot-0-crac-7-b-1-7-d-7-b-2-7-d-5-c-29,implies-f-is-neither-increasing-nor-decreasing-function-at-the-point-x-3-csub-3-e-1-3-c-2-fsub-3-e_-_5-c-28-7-bf-5-e-27-7-d-28-7-bx-1-7-d-29-3-d-0-5-c-29,the-notation-used-by-lagrange-for-derivation-is-3-a_-_5-c-28-7-bf-5-e-27-7-d-28-x-29-5-c-29