A) \[\frac{2}{\sqrt{5}}\] done clear
B) \[\sqrt{5}\] done clear
C) \[\frac{1}{\sqrt{5}}\] done clear
D) \[5\sqrt{5}\] done clear
View Solution play_arrowquestion_answer2) The maximum area of a right angled triangle with hypotenuse h is:
A) \[\frac{{{h}^{2}}}{2\sqrt{2}}\] done clear
B) \[\frac{{{h}^{2}}}{2}\] done clear
C) \[\frac{{{h}^{2}}}{\sqrt{2}}\] done clear
D) \[\frac{{{h}^{2}}}{4}\] done clear
View Solution play_arrowA) a = b = 0 done clear
B) a = b = 1 done clear
C) a = b = 2 done clear
D) a = b = -1 done clear
View Solution play_arrowA) 45 done clear
B) 50 done clear
C) 60 done clear
D) 40 done clear
View Solution play_arrowquestion_answer5) The function \[f(x)=\frac{{{x}^{2}}}{{{e}^{x}}}\] monotonically increasing if
A) x < 0 only done clear
B) x > 2 only done clear
C) 0 < x < 2 done clear
D) \[x\in (-\infty ,0)\cup (2,\infty )\] done clear
View Solution play_arrowA) 0 done clear
B) 4 unit done clear
C) 8 unit done clear
D) 12 unit done clear
View Solution play_arrowA) Fog is always an increasing function done clear
B) Fog is always a decreasing function done clear
C) Fog is neither an increasing nor a decreasing function done clear
D) None of the above done clear
View Solution play_arrowA) \[{{\left( {{a}^{\frac{3}{2}}}+{{b}^{\frac{3}{2}}} \right)}^{\frac{2}{3}}}\] done clear
B) \[{{\left( {{a}^{\frac{2}{3}}}+{{b}^{\frac{2}{3}}} \right)}^{\frac{3}{2}}}\] done clear
C) \[{{\left( {{a}^{\frac{2}{3}}}+{{b}^{\frac{2}{3}}} \right)}^{3}}\] done clear
D) \[{{\left( {{a}^{\frac{3}{2}}}+{{b}^{\frac{3}{2}}} \right)}^{3}}\] done clear
View Solution play_arrowA) 2 done clear
B) 1 done clear
C) 0 done clear
D) 4 done clear
View Solution play_arrowquestion_answer10) The curve \[y=x{{e}^{x}}\] has minimum value equal to
A) \[-\frac{1}{e}\] done clear
B) \[\frac{1}{e}\] done clear
C) \[-e\] done clear
D) e done clear
View Solution play_arrowquestion_answer11) What is the minimum value of \[px+qy\] \[(p>0,q>0)\] when\[xy={{r}^{2}}\]?
A) \[2r\sqrt{pq}\] done clear
B) \[2pq\sqrt{r}\] done clear
C) \[-2r\sqrt{pq}\] done clear
D) \[2rpq\] done clear
View Solution play_arrowA) 1 done clear
B) 2 done clear
C) 3 done clear
D) Infinite done clear
View Solution play_arrowA) n = 1, 2 done clear
B) n = 3, 4, -5 done clear
C) n = 1, 2, 3 done clear
D) Any value of n done clear
View Solution play_arrowA) Is continuous on \[\left( 0,\frac{\pi }{2} \right)\] done clear
B) Is strictly increasing in \[\left( 0,\frac{\pi }{2} \right)\] done clear
C) Is strictly decreasing in \[\left( 0,\frac{\pi }{2} \right)\] done clear
D) Has global maximum value 2 done clear
View Solution play_arrowquestion_answer15) The function \[f(x)=2\,\,\log (x-2)-{{x}^{2}}+4x+1\]increases on the interval
A) (1, 2) done clear
B) (2, 3) done clear
C) (1/2, 3) done clear
D) (2, 4) done clear
View Solution play_arrowquestion_answer16) Consider the following statements:
1. \[f(x)=\] ln x is an increasing function on \[\left( 0,\infty \right).\] |
2. \[f(x)={{e}^{x}}-x(ln\,\,x)\] is an increasing function on \[\left( 1,\,\infty \right)\]. |
Which of the above statements is/are correct? |
A) 1 only done clear
B) 2 only done clear
C) Both 1 and 2 done clear
D) Neither 1 nor 2 done clear
View Solution play_arrowA) \[6\pi \,c{{m}^{2}}/s\] done clear
B) \[10\pi \,c{{m}^{2}}/s\] done clear
C) \[30\pi ;c{{m}^{2}}/s\] done clear
D) \[60\,\pi \,c{{m}^{2}}/s\] done clear
View Solution play_arrowA) \[\pi /6\] done clear
B) \[\pi /4\] done clear
C) \[\pi /2\] done clear
D) \[\pi /3\] done clear
View Solution play_arrowA) Neither a maximum nor a minimum done clear
B) Only one maximum done clear
C) Only one minimum done clear
D) Only one maximum and only one minimum done clear
View Solution play_arrowA) \[162\,\,c{{m}^{3}}/s\] done clear
B) \[172\,\,c{{m}^{3}}/s\] done clear
C) \[182\,\,c{{m}^{3}}/s\] done clear
D) \[192\,\,c{{m}^{3}}/s\] done clear
View Solution play_arrowA) \[0<x<3\] done clear
B) \[-3<x<0\] done clear
C) \[0<x<9\] done clear
D) \[-3<x<3\] done clear
View Solution play_arrowA) \[\frac{1}{2}S\frac{dr}{dt}\] done clear
B) \[\frac{1}{2}r\frac{dS}{dt}\] done clear
C) \[r\frac{dS}{dt}\] done clear
D) \[\frac{1}{2}{{r}^{2}}\frac{dS}{dt}\] done clear
View Solution play_arrowA) \[\frac{3\sqrt{3}}{4}{{R}^{2}}\] done clear
B) \[\frac{\sqrt{3}}{2}{{R}^{2}}\] done clear
C) \[\frac{3\sqrt{3}}{8}{{R}^{2}}\] done clear
D) \[{{R}^{2}}\] done clear
View Solution play_arrowA) \[f\{g(x)\}\ge f\{g(0)\}\] done clear
B) \[g\{f(x)\}\le g\{f(0)\}\] done clear
C) \[f\{g(2)\}=7\] done clear
D) None of these done clear
View Solution play_arrowA) \[x+2y=1\] done clear
B) \[x+2y=\pi /2\] done clear
C) \[x+2y=\pi /4\] done clear
D) None of these done clear
View Solution play_arrowquestion_answer26) The range of the function\[f(x)=2\sqrt{x-2}+\sqrt{4-x}\] is
A) \[\left( \sqrt{2},\sqrt{10} \right)\] done clear
B) \[\left[ \sqrt{2},\sqrt{10} \right)\] done clear
C) \[\left( \sqrt{2},\sqrt{10} \right]\] done clear
D) \[\left[ \sqrt{2},\sqrt{10} \right]\] done clear
View Solution play_arrowA) 0 done clear
B) 1 done clear
C) 2 done clear
D) None of these done clear
View Solution play_arrowA) 7/6 done clear
B) 6/7 done clear
C) 1 done clear
D) 5/6 done clear
View Solution play_arrowA) 1 s done clear
B) \[(log\,\,10)s\] done clear
C) \[2\text{(}log\text{ }10)s\] done clear
D) \[10s\] done clear
View Solution play_arrowA) -1500 ft/s done clear
B) 1500 ft/s done clear
C) -1600 ft/s done clear
D) 1600 ft/s done clear
View Solution play_arrowA) 1 done clear
B) 2 done clear
C) \[\frac{\pi }{4}\] done clear
D) \[\frac{\pi }{2}\] done clear
View Solution play_arrowquestion_answer32) The approximate value of \[{{(0.007)}^{1/3}}\]
A) \[\frac{23}{120}\] done clear
B) \[\frac{27}{120}\] done clear
C) \[\frac{19}{120}\] done clear
D) \[\frac{17}{120}\] done clear
View Solution play_arrowA) \[3y=x+8\] done clear
B) \[x=3y+4\] done clear
C) \[y=2x+8\] done clear
D) \[y=3x\] done clear
View Solution play_arrowA) \[\frac{1}{4}\] done clear
B) 1 done clear
C) \[\frac{1}{3}\] done clear
D) \[\frac{1}{2}\] done clear
View Solution play_arrowA) 1s done clear
B) 2s done clear
C) 3s done clear
D) 4s done clear
View Solution play_arrowA) Square of radius done clear
B) Square root of radius done clear
C) Inversely proportional to radius done clear
D) Cube of the radius done clear
View Solution play_arrowA) \[\frac{1}{3}\] done clear
B) \[\frac{2}{3}\] done clear
C) \[\frac{4}{3}\] done clear
D) \[\frac{5}{3}\] done clear
View Solution play_arrowA) \[180{}^\circ \] done clear
B) \[90{}^\circ \] done clear
C) \[0{}^\circ \] done clear
D) None of these done clear
View Solution play_arrowquestion_answer39) \[f(x)=\frac{\log (\pi +x)}{\log (e+x)}\] is
A) Increasing in \[[0,\infty )\] done clear
B) Decreasing in \[[0,\infty )\] done clear
C) Decreasing in \[\left[ 0,\frac{\pi }{e} \right]\] & increasing in \[\left[ \frac{\pi }{e},\infty \right]\] done clear
D) Increasing in \[\left[ 0,\frac{\pi }{e} \right]\] & decreasing in \[\left[ \frac{\pi }{e},\infty \right)\] done clear
View Solution play_arrowA) 2 done clear
B) 0 done clear
C) 1 done clear
D) Infinite done clear
View Solution play_arrowquestion_answer41) How many tangents are parallel to x-axis for the curve\[y={{x}^{2}}-4x+3\]?
A) 1 done clear
B) 2 done clear
C) 3 done clear
D) No tangent is parallel to x-axis done clear
View Solution play_arrowA) \[68\,\,c{{m}^{2}}\] done clear
B) \[70\,\,c{{m}^{2}}\] done clear
C) \[71.25\,\,c{{m}^{2}}\] done clear
D) \[72.25\,\,c{{m}^{2}}\] done clear
View Solution play_arrowA) \[k<3\] done clear
B) \[k\le 3\] done clear
C) \[k>3\] done clear
D) \[k\ge 3\] done clear
View Solution play_arrowA) \[\left( \frac{1}{2},\frac{5}{24} \right)\] and \[\left( -1,-\frac{1}{6} \right)\] done clear
B) \[\left( \frac{1}{2},\frac{4}{9} \right)\] and \[(-1,0)\] done clear
C) \[\left( \frac{1}{3},\frac{1}{7} \right)\] and \[\left( -3,\frac{1}{2} \right)\] done clear
D) \[\left( \frac{1}{3},\frac{4}{47} \right)\] and \[\left( -1,-\frac{1}{3} \right)\] done clear
View Solution play_arrowA) \[\frac{5\sqrt{3}}{2}\] done clear
B) \[\frac{5\sqrt{5}}{2}\] done clear
C) \[\frac{2\sqrt{5}}{3}\] done clear
D) \[\frac{3\sqrt{5}}{2}\] done clear
View Solution play_arrowA) \[(-1,1)\] done clear
B) \[\left( -\sqrt{\frac{2}{3},}0 \right)\cup \left( \sqrt{\frac{2}{3}},\infty \right)\] done clear
C) \[\left( -\sqrt{\frac{2}{3}},\sqrt{\frac{2}{3}} \right)\] done clear
D) None of these done clear
View Solution play_arrowA) (1/2, 2) done clear
B) (4/3, 2) done clear
C) (0, 2) done clear
D) (0, 4/3) done clear
View Solution play_arrowA) \[a=b=1\] done clear
B) \[a=b=0\] done clear
C) \[a=1,b=0\] done clear
D) \[a=b=2\] done clear
View Solution play_arrowA) 1/4 done clear
B) 1/2 done clear
C) 3/4 done clear
D) 1 done clear
View Solution play_arrowA) \[162\,\,c{{m}^{3}}/s\] done clear
B) \[172\,\,c{{m}^{3}}/s\] done clear
C) \[182\,\,c{{m}^{3}}/s\] done clear
D) \[192\,\,c{{m}^{3}}/s\] done clear
View Solution play_arrowA) \[x={{e}^{-2}}\] done clear
B) \[x=e\] done clear
C) \[x={{e}^{-1}}\] done clear
D) \[x=2{{e}^{-1}}\] done clear
View Solution play_arrowA) 400 done clear
B) 300 done clear
C) 200 done clear
D) 100 done clear
View Solution play_arrowA) Cuts at right angle done clear
B) Touch each other done clear
C) Cut at an angle \[\frac{\pi }{3}\] done clear
D) Cut at an angle \[\frac{\pi }{4}\] done clear
View Solution play_arrowA) 10 done clear
B) 20 done clear
C) 30 done clear
D) 40 done clear
View Solution play_arrowA) a sin 2t done clear
B) \[\frac{a}{2}\sin 2t\] done clear
C) 2a sin 2t done clear
D) 2a done clear
View Solution play_arrowA) \[\frac{3\sqrt{3}}{2}\] done clear
B) \[\frac{3\sqrt{3}}{2}-2\] done clear
C) \[\frac{3\sqrt{3}}{2}+2\] done clear
D) None of these done clear
View Solution play_arrowA) \[15{}^\circ \] done clear
B) \[30{}^\circ \] done clear
C) \[60{}^\circ \] done clear
D) \[75{}^\circ \] done clear
View Solution play_arrowA) 8 times the original done clear
B) 16 times the original done clear
C) 32 times the original done clear
D) 64 times the original done clear
View Solution play_arrowA) 75 done clear
B) 91 done clear
C) 84 done clear
D) 96 done clear
View Solution play_arrowA) \[\frac{1}{\sqrt{3}}\] done clear
B) \[\frac{1}{3}\] done clear
C) \[3\] done clear
D) \[\sqrt{3}\] done clear
View Solution play_arrowA) f has a local extremum at x = c done clear
B) f has neither local maximum nor minimum at x = c done clear
C) f is necessarily a constant function done clear
D) it is difficult to say whether or (b) done clear
View Solution play_arrowA) \[a>0\] done clear
B) \[a\le \sqrt{3}\] done clear
C) \[-\sqrt{3}\le a\le \sqrt{3}\] done clear
D) None of these done clear
View Solution play_arrowA) One-one and onto done clear
B) Onto but not one-one done clear
C) One-one but not onto done clear
D) Neither one-one nor onto done clear
View Solution play_arrowA) \[-\frac{4}{125}rad/s\] done clear
B) \[-\frac{2}{25}rad/s\] done clear
C) \[-\frac{1}{625}rad/s\] done clear
D) None of these done clear
View Solution play_arrowA) 8a/27 done clear
B) 27/8b done clear
C) 8b/27 done clear
D) 8/27 done clear
View Solution play_arrowA) \[-\frac{5{{l}_{2}}}{2}m/s\] done clear
B) \[-\frac{2{{l}_{2}}}{5}m/s\] done clear
C) \[-\frac{{{l}_{2}}}{2}m/s\] done clear
D) \[-\frac{{{l}_{2}}}{5}m/s\] done clear
View Solution play_arrowquestion_answer67) Let \[f'(x)<0\] and \[g'(x)>0\] for all real x, then
A) \[f(g(x+1))>f(g(x+5))\] done clear
B) \[f(g(x))<f(g(f(x+2))\] done clear
C) \[g(f(x))<g(f(x+2))\] done clear
D) \[g(f(x))>g(f(x-2))\] done clear
View Solution play_arrowA) Has a local maximum done clear
B) done clear
C) Is discontinuous done clear
D) None of these done clear
View Solution play_arrowA) 1 done clear
B) -2 done clear
C) 4 done clear
D) None of these done clear
View Solution play_arrowA) \[1600\,{{m}^{2}}\] done clear
B) \[2100\,{{m}^{2}}\] done clear
C) \[2400\,{{m}^{2}}\] done clear
D) \[2500\,{{m}^{2}}\] done clear
View Solution play_arrowA) \[\frac{\pi }{4}\] done clear
B) \[\frac{\pi }{2}\] done clear
C) \[\pi \] done clear
D) \[\frac{3\pi }{2}\] done clear
View Solution play_arrowA) \[4\pi \] done clear
B) \[2\pi \] done clear
C) \[6\pi \] done clear
D) \[3\pi \] done clear
View Solution play_arrowA) \[x+y=1\] done clear
B) \[x-y=1\] done clear
C) \[x+y=-1\] done clear
D) \[x-y=-1\] done clear
View Solution play_arrowA) \[\frac{7}{2}v\] m/minute done clear
B) 5 v m/minute done clear
C) v m/minute done clear
D) None of these done clear
View Solution play_arrowA) 0 done clear
B) 1 done clear
C) -1 done clear
D) 2 done clear
View Solution play_arrowA) \[{{e}^{1/2}}\] done clear
B) \[{{e}^{-1/2}}\] done clear
C) \[{{(2e)}^{-1}}\] done clear
D) \[2{{e}^{-1/2}}\] done clear
View Solution play_arrowA) 1 done clear
B) 2 done clear
C) 3 done clear
D) None of these done clear
View Solution play_arrowquestion_answer78) Find the minimum value of\[{{e}^{(2{{x}^{2}}-2x-1){{\sin }^{2}}x}}\].
A) 1 done clear
B) 2 done clear
C) 0 done clear
D) None of these done clear
View Solution play_arrowA) \[e(x+y)=1\] done clear
B) \[y+ex=1\] done clear
C) \[y+x=e\] done clear
D) None of these done clear
View Solution play_arrowquestion_answer80) A ball is dropped from a platform 19.6m high. Its position function is ?
A) \[x=-4.9{{t}^{2}}+19.6(0\le t\le 1)\] done clear
B) \[x=-4.9{{t}^{2}}+19.6(0\le t\le 2)\] done clear
C) \[x=-9.8{{t}^{2}}+19.6(0\le t\le 2)\] done clear
D) \[x=-4.9{{t}^{2}}-19.6(0\le t\le 2)\] done clear
View Solution play_arrowYou need to login to perform this action.
You will be redirected in
3 sec