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Continuity and, Differentiability, , , , >> Multiple Choice Questions (MCQs) \—— >»? 6, Ifa fimetion ffx) is defined as, , RECTIONS : Shis section co, , questions. Eac, , , , witiple choice x0, , , , , , , , , , . b), fc) and (&, , , , que:, , , , , , , , , , , , , , , , , , , , , , , , + val then, out of whi 0 x=0, when x50 (a) ix) is coutinuous at x = 0 bat a fferentiable at, Il =4.whend 1 x, x* ~3x,whenl <x <2 (b} 4x) is continuous as well as differentiable at x = 0, Ax +4, when x22 (e} mlinuenis at x ~ 0, (a) f(x) is continuous at x = 0 (d) these:, (b) f(x) & continuous at 1-2, (c) (x) is discontinuous at x = 1 |, (d) Na these % If f(x)= 42x then fix) is, o, : fx= “ 1, 2 ire(x}= 4x 1 Saini (a) discontinuous every where, 7 ifx== (>) continuous as well as differentiable for all x, * (¢) continuous for all x but no; differentiuble al x 0, then a is equal t (d} neither differentiable aor continuous atx =, (a) 4 {b) 2 (c) 1 ) 4 (J-! oy, 8. WE {xp} x1 then fix) is, wax . 0 ,x=1, #2, 3 Let f(xj= (x- (a) coetinuous as well as differentiable at x = 1, k (>) differentiable but not continuous at x = |, If x) is continuoes far all x, th (c) coetinuous but not differentiable at x = 1, (a) 3 ib) 5 (c) 7 {d) 9 (d) neither continuous nor differentiable at x = 1, , 4, Ja the interval [7, 9] the, discontinuous at, greatest integer flanetion, , n Bx) = [x] 38 9, At bow many points between the interval (20, 20) is the, [x] denotes the function f (x) — sin x is not differentiable., , , , , , , , (a) O (>) 7, (a) 2 tb) 4 (c) 6, (c} 9 (d) 3, 5. The point of descontimuity of f (x) = oh dy, m y ’ 1. Ifsiny=x sin * is equal to, than x=-I are “, (a) (b) x= { ?, via, 5 > a) ——;, 2m+l 2m—! sin {a+ y) sina, (c) x= (d) 1==, 1-2 2m+! i, , (c} sin (a+ y) (d) None of these
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m-46, , dy, Ify = log (log x), then the value oe? is:, , (a), , l, {b), x, , , , 4., , . dy, if y=e™ , tha“ =, y=e oF, , (a) wWi+log. x), , (ec) ye“{l log, x), , {b) yx" (+log. x), , {d) Nowe of these, , o, Ify* =oF—*, then 7 is equal to, , , , _— Ltlogy, (@) “ylogy, l-logy, (ec) (logy, tf y= 22) ana 2, ao, a 22, ae, , , , Ifs — ft) and y — eft), then, , e), , (a), ” T(t), , (tstogy?*, yhuy, (I+loe y?, ner, , {b), , (d), , , , @ 12, ¥ ax, , {d) Nowe of these., , 4, rr is oquall to, , e'(tyr(t)-2', , , , 3, ° (ri), , (yr (y—2'|, (ri), (d) None of these, , (oh, , , , , , 19., , 20., , 2., , 22., , i., , Mathematics, If? +y7= 1, then, , (a) yy"-(2y'P+1=0 0b) yy?-(y'P +1=0, , , , = (d) yy?-2ly'F+t=0, , If fix) = 2x and a(x)=-+1, then which of the, following can be a discontinuous function?, , (ch yy"-ly, , (a) Ax) + gix) (d) fix) = wix), - a(x}, (c} Axdalx) (d) F(x), , 4-2, , , , ‘The function f(x), (a) discontinuous at caly ane point, , (b} discontinuous at exactly two points, (c} discontinuoes at exactly three paints, (d)} None of the above, , The set of points where the function f given by, f(x) > [2x ~ || sin x as differentiable is, , (ry, , , , , , , , a) 2 (oy R, (c} (0, 2) (d) None of these, The function ffx) ~ cot x is discontinuous on the set, , (a) [x=nx,ne@ 7} (b) [x =2nz,n.¢ 7}, , (c) 4, , 1& | fom, AntljojneZ> (d) (X=—ineZ, , , , 2, , , , ‘The function f(x) = el* is, , (a) cont:nvous everywhere bat not differentiable at x= 0, (b} coetinucus and differentiable everywhere, , (c} net continuous at c= 0, , (d) None of the above, , i. 1, If F[x)=x° sin, where x = 0, then the value of the, , function fat x = 0, so that the function is cantinuous at, a=0, is, , fa) 0 (o) -1, , «@t (d) Nowe of these, , cay | 2 ; ®, if flx)=) = S continuous at =>,, , then, , an, (a) m=I,n=0 Qasr, (c} = () m=n= =
