12th Class Mathematics MCQS Integration Online Test 2

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-let-f-be-a-differentiable-function-on-the-interval-28-a-2-c-b-29then-f-is-a-decreasing-on-28-a-2-c-b-29-if-for-each-x-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-22-font-family-3-a-symbol-22-3-e-3-cspan-style-3-d-22-color-3-ablack-22-3-e-c-3-8-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-28-a-2-c-b-29-3-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-f-5-c-27-28-x-29-26-lt-3-b-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-the-maclaurin-series-expansion-is-valid-only-if-it-is-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-econvergent-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-the-inequality-x-26-gt-3-b-a-is-the-open-half-plane-to-the-of-the-boundary-line-x-3-d-a-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-eright-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,3-cp-3-e-are-tangent-to-c-2-a-0-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-5-c-5-cfrac-7-bx-5-e-2-7-d-7-ba-5-e-2-7-d-5-c-5-cfrac-7-by-5-e-2-7-d-7-bb-5-e-2-7-d-3-d-1-5-c-5-c-29-3-c-2-fspan-3-e-for-all-values-of-m-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-dmx-5-c-5-c-2-c-5-c-5-cpm-5-c-5-c-2-c-5-c-5-csqrt-7-ba-5-e-2-m-5-e-2-b-5-e-2-7-d-5-c-5-c-29-3-c-2-fspan-3-e-3-c-2-fp-3-e,3-cp-3-e-inverse-of-c-2-a-0-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-f-28-x-29-3-d-5-c-5-csqrt-7-bx-2-b-1-7-d-5-c-5-c-29-3-c-2-fspan-3-e-is-3-a-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-f-5-e-7-b-1-7-d-28-x-29-3-dx-5-e-2-1-5-c-5-c-29-3-c-2-fspan-3-e-3-c-2-fp-3-e,3-cp-3-ea-vector-c-2-a-0-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-5-c-5-cunderline-v-5-c-5-c-29-3-c-2-fspan-3-e-c-2-a-0-is-to-a-vector-c-2-a-0-3-cspan-class-3-d-22-math-tex-22-3-e-5-c-5-c-28-k-5-c-5-cunderline-v-5-c-5-c-29-3-c-2-fspan-3-e-2-c-where-k-is-a-scalar-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-eparallel-3-c-2-fspan-3-e-3-c-2-fspan-3-e-3-c-2-fstrong-3-e-3-c-2-fp-3-e,5-c-28-5-cint-5-climits-0-5-e-3-7-b-0-crac-7-b-1-7-d-7-b-7-b-5-csqrt-7-b-9-7-bx-5-e-2-7-d-7-d-7-d-7-d-7-d-5-c-29-is-equal-to-3-a_-_5-c-28-0-crac-7-b-7-b-5-cpi-7-d-7-d-7-b-2-7-d-5-c-29,5-c-28-5-cint-5-climits-1-5-e-2-7-ba-7-b-7-d-5-exdx-7-d-5-c-29-equals-3-a_-_5-c-28-0-crac-7-b-7-b-7-ba-5-e-2-7-d-7-d-7-d-7-b-7-b-5-cln-a-7-d-7-d-0-crac-7-ba-7-d-7-b-7-b-5-cln-a-7-d-7-d-5-c-29,5-c-28-5-cint-5-climits-7-b-0-crac-7-b-1-7-d-7-b-7-b-5-csqrt-2-7-d-7-d-7-d-5-e-7-b-0-crac-7-b-7-b-5-csqrt-3-7-d-7-d-7-b-2-7-d-7-d-7-b-0-crac-7-b-7-bdx-7-d-7-d-7-b-7-b-5-csqrt-7-b-1-7-bx-5-e-2-7-d-7-d-7-d-7-d-7-d-3-d-5-c-29_-_5-c-28-0-crac-7-b-5-cpi-7-d-7-b-12-7-d-5-c-29,5-c-28-5-cint-5-climits-a-5-eb-7-bf-28-x-29-dx-7-d-5-c-29-as-the-area-under-the-curve-y-3-d-f-28-x-29-from-x-3-d-a-to-x-3-d-b-and-the-x-axis-is-called-3-a_-_definite-integral,5-c-28-5-cint-7-b-0-crac-7-b-1-7-d-7-b-7-b-5-csqrt-7-b-1-7-bx-5-e-2-7-d-7-d-7-d-7-d-7-d-dx-3-d-5-c-5-c-5-c-5-c-5-c-3-a-5-c-29_-_sin-3-csup-3-e-1-3-c-2-fsup-3-ex,5-c-28-5-cint-7-b-0-crac-7-b-7-b-7-b-7-b-5-csec-7-d-5-e-2-7-dx-7-d-7-d-7-b-7-b-5-csqrt-7-b-09-an-x-7-d-7-d-7-d-7-d-dx-5-c-29-is-equal-to-3-a_-_5-c-282-5-csqrt-7-b-09-an-x-7-d-2-b-c-5-c-29,5-c-28-5-cint-7-b-5-ccos-ec-28-ax-2-b-b-29-5-ccot-28-ax-2-b-b-29-dx-3-d-5-ccos-ec-28-ax-2-b-b-29-2-b-c-2-c-28-a-0-ae-0-29-7-d-5-c-29_-_5-c-28-0-crac-7-b-1-7-d-7-ba-7-d-5-c-29,5-c-28-5-cint-7-b-5-cln-xdx-3-d-7-d-5-c-29_-_5-c-28-x-5-cln-x-x-2-b-c-5-c-29,5-c-28-5-cint-7-b-7-b-7-b-5-csin-7-d-5-e-2-7-dxdx-7-d-3-d-3-f-5-c-29_-_5-c-28-0-crac-7-b-1-7-d-7-b-2-7-d-5-cleft-28-7-bx-0-crac-7-b-7-b-5-csin-2-x-7-d-7-d-7-b-2-7-d-7-d-0-dight-29-2-b-c-5-c-29,5-c-28-f-7-be-5-ex-7-d-28-5-ccos-x-2-b-5-csin-x-29-dx-3-d-5-c-29_-_5-c-28-7-be-5-ex-7-d-5-csin-x-2-b-c-5-c-29,5-c-28-f-7-be-5-ex-7-d-28-x-2-b-1-29-dx-3-d-5-c-29_-_5-c-28-x-7-be-5-ex-7-d-5-c-29,if-the-graph-of-f-is-entirely-below-the-x-axis-2-c-then-the-definite-integral-is-3-a_-_negative,solution-of-differential-equation-5-c-28-0-crac-7-b-7-bdy-7-d-7-d-7-b-7-bdx-7-d-7-d-3-d-5-ccos-x-5-c-29-is-3-a_-_5-c-28-y-3-d-5-csin-x-2-b-c-5-c-29,solution-of-differential-equation-5-c-28-0-crac-7-b-7-bdy-7-d-7-d-7-b-7-bdx-7-d-7-d-3-d-y-5-c-29-is-3-a_-_5-c-28-y-3-d-c-7-be-5-e-7-b-x-7-d-7-d-5-c-29,the-solution-of-differential-equation-5-c-28-0-crac-7-b-7-bdy-7-d-7-d-7-b-7-bdx-7-d-7-d-3-d-7-b-5-csec-5-e-2-7-dx-5-c-29-is-3-a_-_y-3-d-tanx-2-b-c,the-term-5-c-28-dy-5-c-2-c-28-or-5-c-2-cdf-29-3-d-7-bf-5-e-27-7-d-28-x-29-5-cdelta-x-5-c-29-is-called-the-of-the-dependent-variable-y_-_differential