
Area bounded by the curve \[y=\log x\,,\] \[x\]axis and the ordinates \[x=1,\,\,x=2\] is [MP PET 2004]
A)
\[\log 4\]sq. unit done
clear
B)
\[(\log 4+1)\]sq. unit done
clear
C)
\[(\log 41)\]sq. unit done
clear
D)
None of these done
clear
View Solution play_arrow

Area bounded by the curve \[y=x{{e}^{{{x}^{2}}}},\] \[x\]axis and the ordinates \[x=0,\,\,x=a\]
A)
\[\frac{{{e}^{{{a}^{2}}}}+1}{2}\]sq. unit done
clear
B)
\[\frac{{{e}^{{{a}^{2}}}}1}{2}\]sq. unit done
clear
C)
\[{{e}^{{{a}^{2}}}}+1\]sq. unit done
clear
D)
\[{{e}^{{{a}^{2}}}}1\]sq. unit done
clear
View Solution play_arrow

Area bounded by the curve \[y=\sin x\] between \[x=0\] and \[x=2\pi \] is
A)
2 sq. unit done
clear
B)
4 sq. unit done
clear
C)
8 sq. unit done
clear
D)
None of these done
clear
View Solution play_arrow

Area bounded by the parabola \[y=4{{x}^{2}},\] \[y\]axis and the lines \[y=1,\,\,y=4\] is [MNR 1990]
A)
3 sq. unit done
clear
B)
\[\frac{7}{5}\]sq. unit done
clear
C)
\[\frac{7}{3}\]sq. unit done
clear
D)
None of these done
clear
View Solution play_arrow

Area bounded by the lines \[y=x,\,\,x=1,\,\,x=2\] and \[x\]axis is
A)
\[\frac{5}{2}\]sq. unit done
clear
B)
\[\frac{3}{2}\]sq. unit done
clear
C)
\[\frac{1}{2}\]sq. unit done
clear
D)
None of these done
clear
View Solution play_arrow

If the ordinate \[x=a\] divides the area bounded by the curve \[y=\left( 1+\frac{8}{{{x}^{2}}} \right)\,,\] \[x\]axis and the ordinates \[x=2,\] \[x=4\] into two equal parts, then \[a=\] [IIT 1983]
A)
8 done
clear
B)
\[2\sqrt{2}\] done
clear
C)
2 done
clear
D)
\[\sqrt{2}\] done
clear
View Solution play_arrow

Area between the curve \[y=\cos x\] and \[x\]axis when \[0\le x\] is [MP PET 1997]
A)
2 done
clear
B)
4 done
clear
C)
0 done
clear
D)
3 done
clear
View Solution play_arrow

Area bounded by curve \[y={{x}^{3}},\] \[x\]axis and ordinates \[x=1\] and \[x=4,\] is
A)
64 sq. unit done
clear
B)
27 sq. unit done
clear
C)
\[\frac{127}{4}\]sq. unit done
clear
D)
\[\frac{255}{4}\]sq. unit done
clear
View Solution play_arrow

Area bounded by curve \[xy=c,\] \[x\]axis between \[x=1\] and \[x=4,\] is
A)
\[c\log 3\]sq. unit done
clear
B)
\[2\log c\]sq. unit done
clear
C)
\[2c\log 2\]sq. unit done
clear
D)
\[2c\log 5\]sq. unit done
clear
View Solution play_arrow

Area bounded by curve \[y=k\sin x\]between \[x=\pi \] and \[x=2\pi ,\] is
A)
\[2k\] sq. unit done
clear
B)
0 done
clear
C)
\[\frac{{{k}^{2}}}{2}\] sq. unit done
clear
D)
\[k\] sq. unit done
clear
View Solution play_arrow

Area bounded by \[y=x\sin x\] and \[x\]axis between \[x=0\] and \[x=2\pi ,\] is [Roorkee 1981; RPET 1995]
A)
0 done
clear
B)
\[2\pi \] sq. unit done
clear
C)
\[\pi \] sq. unit done
clear
D)
\[4\pi \] sq. unit done
clear
View Solution play_arrow

Area under the curve \[y=\sin 2x+\cos 2x\] between \[x=0\] and \[x=\frac{\pi }{4},\] is [AI CBSE 1979]
A)
2 sq. unit done
clear
B)
1 sq. unit done
clear
C)
3 sq. unit done
clear
D)
4 sq. unit done
clear
View Solution play_arrow

Area under the curve \[y=\sqrt{3x+4}\] between \[x=0\] and \[x=4,\] is [AI CBSE 1979, 80]
A)
\[\frac{56}{9}\] sq. unit done
clear
B)
\[\frac{64}{9}\] sq. unit done
clear
C)
8 sq. unit done
clear
D)
None of these done
clear
View Solution play_arrow

If area bounded by the curves \[{{y}^{2}}=4ax\] and \[y=mx\] is \[{{a}^{2}}/3,\], then the value of \[m\] is
A)
2 done
clear
B)
\[2\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
None of these done
clear
View Solution play_arrow

Area bounded by parabola \[{{y}^{2}}=x\] and straight line \[2y=x\] is [MP PET 1996]
A)
\[\frac{4}{3}\] done
clear
B)
1 done
clear
C)
\[\frac{2}{3}\] done
clear
D)
\[\frac{1}{3}\] done
clear
View Solution play_arrow

Area bounded by lines \[y=2+x,\] \[y=2x\] and \[x=2\] is [MP PET 1996]
A)
3 done
clear
B)
4 done
clear
C)
8 done
clear
D)
16 done
clear
View Solution play_arrow

The ratio of the areas bounded by the curves \[y=\cos x\] and \[y=\cos 2x\] between \[x=0,\] \[x=\pi /3\] and \[x\]axis, is [MP PET 1997]
A)
\[\sqrt{2}:1\] done
clear
B)
\[1:1\] done
clear
C)
\[1:2\] done
clear
D)
\[2:1\] done
clear
View Solution play_arrow

The area bounded by the curve \[y={{x}^{3}},\] \[x\]axis and two ordinates \[x=1\] to \[x=2\] equal to [MP PET 1999]
A)
\[\frac{15}{2}\] sq. unit done
clear
B)
\[\frac{15}{4}\] sq. unit done
clear
C)
\[\frac{17}{2}\] sq. unit done
clear
D)
\[\frac{17}{4}\] sq. unit done
clear
View Solution play_arrow

The area bounded by the \[x\]axis and the curve \[y=\sin x\] and \[x=0,\] \[x=\pi \] is [Kerala (Engg.) 2002]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow

The area bounded by the parabola \[{{y}^{2}}=4ax,\] its axis and two ordinates \[x=4,\] \[x=9\] is
A)
\[4{{a}^{2}}\] done
clear
B)
\[4{{a}^{2}}.4\] done
clear
C)
\[4{{a}^{2}}(94)\] done
clear
D)
\[\frac{152\sqrt{a}}{3}\] done
clear
View Solution play_arrow

For \[0\le x\le \pi ,\] the area bounded by \[y=x\] and \[y=x+\sin x,\] is [Roorkee Qualifying 1998]
A)
2 done
clear
B)
4 done
clear
C)
\[2\pi \] done
clear
D)
\[4\pi \] done
clear
View Solution play_arrow

The area of the region bounded by the \[x\]axis and the curves defined by \[y=\tan x,\,(\pi /3\le x\le \pi /3)\] is [Kurukshetra CEE 1998]
A)
\[\log \sqrt{2}\] done
clear
B)
\[\log \sqrt{2}\] done
clear
C)
\[2\log 2\] done
clear
D)
0 done
clear
View Solution play_arrow

If a curve \[y=a\sqrt{x}+bx\] passes through the point (1, 2) and the area bounded by the curve, line \[x=4\] and xaxis is 8 sq. unit, then [MP PET 2002]
A)
\[a=3,\,b=1\] done
clear
B)
\[a=3,\,b=1\] done
clear
C)
\[a=3,\,b=1\] done
clear
D)
\[a=3,\,b=1\] done
clear
View Solution play_arrow

If the area above the xaxis, bounded by the curves \[y={{2}^{kx}}\] and \[x=0\] and \[x=2\] is \[\frac{3}{\ln 2},\] then the value of k is [Orissa JEE 2003]
A)
\[\frac{1}{2}\] done
clear
B)
1 done
clear
C)
\[1\] done
clear
D)
2 done
clear
View Solution play_arrow

The area bounded by the xaxis, the curve \[y=f(x)\] and the lines \[x=1,\,x=b\] is equal to \[\sqrt{{{b}^{2}}+1}\sqrt{2}\] for all b > 1, then \[f(x)\] is \[\] [MP PET 2000; AMU 2000]
A)
\[\sqrt{x1}\] done
clear
B)
\[\sqrt{x+1}\] done
clear
C)
\[\sqrt{{{x}^{2}}+1}\] done
clear
D)
\[\frac{x}{\sqrt{1+{{x}^{2}}}}\] done
clear
View Solution play_arrow

The area bounded by the curve \[y=f(x)\], xaxis and ordinates x = 1 and \[x=b\]is \[\frac{5}{24}\pi \], then \[f(x)\] is [RPET 2000]
A)
\[3(x1)\cos (3x+4)+\sin (3x+4)\] done
clear
B)
\[(b1)\sin (3x+4)+3\cos (3x+4)\] done
clear
C)
\[(b1)\cos (3x+4)+3\sin (3x+4)\] done
clear
D)
None of these done
clear
View Solution play_arrow

The area of the region (in the square unit) bounded by the curve \[{{x}^{2}}=4y,\] line \[x=2\] and xaxis is [MP PET 2002]
A)
1 done
clear
B)
\[\frac{2}{3}\] done
clear
C)
\[\frac{4}{3}\] done
clear
D)
\[\frac{8}{3}\] done
clear
View Solution play_arrow

Area under the curve \[y={{x}^{2}}4x\]within the xaxis and the line \[x=2\], is [SCRA 1991]
A)
\[\frac{16}{3}sq.\,unit\] done
clear
B)
\[\frac{16}{3}sq.\,unit\] done
clear
C)
\[\frac{4}{7}sq.\,unit\] done
clear
D)
Cannot be calculated done
clear
View Solution play_arrow

Area bounded by the curve \[xy3x2y10=0,\]xaxis and the lines \[x=3,x=4\]is [AI CBSE 1991]
A)
\[16\log 213\] done
clear
B)
\[16\log 23\] done
clear
C)
\[16\log 2+3\] done
clear
D)
None of these done
clear
View Solution play_arrow

The area bounded by curve \[{{y}^{2}}=x,\] line \[y=4\] and yaxis is [Roorkee 1995; RPET 2003]
A)
\[\frac{16}{3}\] done
clear
B)
\[\frac{64}{3}\] done
clear
C)
\[7\sqrt{2}\] done
clear
D)
None of these done
clear
View Solution play_arrow

The measurement of the area bounded by the coordinate axes and the curve \[y={{\log }_{e}}x\] is [MP PET 1998]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
\[\infty \] done
clear
View Solution play_arrow

Area bounded by the parabola \[{{y}^{2}}=2x\] and the ordinates \[x=1,x=4\] is
A)
\[\frac{4\sqrt{2}}{3}sq.\,unit\] done
clear
B)
\[\frac{28\sqrt{2}}{3}sq.\,unit\] done
clear
C)
\[\frac{56}{3}\text{ }sq. unit\] done
clear
D)
None of these done
clear
View Solution play_arrow

The area bounded by the straight lines \[x=0,x=2\]and the curves \[y={{2}^{x}},y=2x{{x}^{2}}\]is [AMU 2001]
A)
\[\frac{4}{3}\frac{1}{\log 2}\] done
clear
B)
\[\frac{3}{\log 2}+\frac{4}{3}\] done
clear
C)
\[\frac{4}{\log 2}1\] done
clear
D)
\[\frac{3}{\log 2}\frac{4}{3}\] done
clear
View Solution play_arrow

The area of smaller part between the circle \[{{x}^{2}}+{{y}^{2}}=4\]and the line \[x=1\] is [RPET 1999]
A)
\[\frac{4\pi }{3}\sqrt{3}\] done
clear
B)
\[\frac{8\pi }{3}\sqrt{3}\] done
clear
C)
\[\frac{4\pi }{3}+\sqrt{3}\] done
clear
D)
\[\frac{5\pi }{3}+\sqrt{3}\] done
clear
View Solution play_arrow

The area between the curve \[y={{\sin }^{2}}x,\] \[x\]axis and the ordinates \[x=0\] and \[x=\frac{\pi }{2}\] is [RPET 1996]
A)
\[\frac{\pi }{2}\] done
clear
B)
\[\frac{\pi }{4}\] done
clear
C)
\[\frac{\pi }{8}\] done
clear
D)
\[\pi \] done
clear
View Solution play_arrow

The area bounded by the circle \[{{x}^{2}}+{{y}^{2}}=4,\] line \[x=\sqrt{3}y\] and \[x\]axis lying in the first quadrant, is [RPET 1997; Kurukshetra CEE 1998]
A)
\[\frac{\pi }{2}\] done
clear
B)
\[\frac{\pi }{4}\] done
clear
C)
\[\frac{\pi }{3}\] done
clear
D)
\[\pi \] done
clear
View Solution play_arrow

The area of the triangle formed by the tangent to the hyperbola \[xy={{a}^{2}}\] and coordinate axes is [RPET 2000]
A)
\[{{a}^{2}}\] done
clear
B)
\[2{{a}^{2}}\] done
clear
C)
\[3{{a}^{2}}\] done
clear
D)
\[4{{a}^{2}}\] done
clear
View Solution play_arrow

The area formed by triangular shaped region bounded by the curves \[y=\sin x,\,y=\cos x\] and \[x=0\] is [MP PET 2000]
A)
\[x={{y}^{2}}\] done
clear
B)
1 done
clear
C)
\[\sqrt{2}\] done
clear
D)
\[1+\sqrt{2}\] done
clear
View Solution play_arrow

The part of straight line \[y=x+1\] between \[x=2\] and \[x=3\] is revolved about xaxis, then the curved surface of the solid thus generated is [UPSEAT 2000]
A)
\[37\pi /3\] done
clear
B)
\[7\pi \sqrt{2}\] done
clear
C)
\[37\pi \] done
clear
D)
\[y={{x}^{2}}\] done
clear
View Solution play_arrow

The area bounded by the curve \[y=4x{{x}^{2}}\] and the \[x\]axis, is [MP PET 1999, 2003]
A)
\[\frac{30}{7}\] sq. unit done
clear
B)
\[\frac{31}{7}\] sq. unit done
clear
C)
\[\frac{32}{3}\] sq. unit done
clear
D)
\[\frac{34}{3}\] sq. unit done
clear
View Solution play_arrow

Area of the region bounded by the curve \[y=\tan x,\] tangent drawn to the curve at \[x=\frac{\pi }{4}\] and the xaxis is [DCE 2001]
A)
\[\frac{1}{4}\] done
clear
B)
\[\frac{4}{3}\] done
clear
C)
\[\log \sqrt{2}\frac{1}{4}\] done
clear
D)
None of these done
clear
View Solution play_arrow

The area between the curve \[y=4+3x{{x}^{2}}\] and xaxis is [RPET 2001]
A)
125/6 done
clear
B)
125/3 done
clear
C)
125/2 done
clear
D)
None of these done
clear
View Solution play_arrow

The area bounded by the curve \[y=x,\] xaxis and ordinates \[x=1\] to \[x=2\] is [RPET 2001]
A)
0 done
clear
B)
1/2 done
clear
C)
3/2 done
clear
D)
5/2 done
clear
View Solution play_arrow

Area inside the parabola \[{{y}^{2}}=4ax,\]between the lines \[x=a\]and\[x=4a\]is equal to [Pb. CET 2002; Karnataka CET 2005]
A)
\[4{{a}^{2}}\] done
clear
B)
\[8{{a}^{2}}\] done
clear
C)
\[28\frac{{{a}^{2}}}{3}\] done
clear
D)
\[35\frac{{{a}^{2}}}{3}\] done
clear
View Solution play_arrow

The area bounded by \[y={{x}^{2}}+2x+3\]and\[y=0\] is [Orissa JEE 2004]
A)
\[32\] done
clear
B)
\[\frac{32}{3}\] done
clear
C)
\[\frac{1}{32}\] done
clear
D)
\[\frac{1}{3}\] done
clear
View Solution play_arrow

The area enclosed between the curves \[y={{x}^{3}}\]and \[y=\sqrt{x}\] is, (in square units) [Karnataka CET 2004]
A)
\[\frac{5}{3}\] done
clear
B)
\[\frac{5}{4}\] done
clear
C)
\[\frac{5}{12}\] done
clear
D)
\[\frac{12}{5}\] done
clear
View Solution play_arrow

The area between the parabola \[y={{x}^{2}}\] and the line \[y=x\] is [UPSEAT 2004]
A)
\[\frac{1}{6}\]sq. unit done
clear
B)
\[\frac{1}{3}\]sq. unit done
clear
C)
\[\frac{1}{2}\]sq. unit done
clear
D)
None of these done
clear
View Solution play_arrow

Area bounded by the parabola \[{{y}^{2}}=4ax\] and its latus rectum is [RPET 1997, 2000, 02]
A)
\[\frac{2}{3}{{a}^{2}}\]sq. unit done
clear
B)
\[\frac{4}{3}{{a}^{2}}\]sq. unit done
clear
C)
\[\frac{8}{3}{{a}^{2}}\]sq. unit done
clear
D)
\[\frac{3}{8}{{a}^{2}}\]sq. unit done
clear
View Solution play_arrow

Area enclosed by the parabola \[ay=3({{a}^{2}}{{x}^{2}})\] and xaxis is
A)
\[4\,{{a}^{2}}\]sq. unit done
clear
B)
\[12\,{{a}^{2}}\]sq. unit done
clear
C)
\[4\,{{a}^{3}}\]sq. unit done
clear
D)
None of these done
clear
View Solution play_arrow

Area of the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is [Karnataka CET 1993]
A)
\[\pi \,ab\]sq. unit done
clear
B)
\[\frac{1}{2}\pi \,ab\]sq. unit done
clear
C)
\[\frac{1}{4}\pi \,ab\]sq. unit done
clear
D)
None of these done
clear
View Solution play_arrow

The area of the region bounded by \[y=\,\,x1\] and \[y=1\] is [IIT Screening 1994]
A)
2 done
clear
B)
1 done
clear
C)
\[\frac{1}{2}\] done
clear
D)
None of these done
clear
View Solution play_arrow

The area between the curve \[{{y}^{2}}=4ax,\] xaxis and the ordinates \[x=0\] and \[x=a\] is [RPET 1996]
A)
\[\frac{4}{3}{{a}^{2}}\] done
clear
B)
\[\frac{8}{3}{{a}^{2}}\] done
clear
C)
\[\frac{2}{3}{{a}^{2}}\] done
clear
D)
\[\frac{5}{3}{{a}^{2}}\] done
clear
View Solution play_arrow

The area of the curve \[x{{y}^{2}}={{a}^{2}}(ax)\] bounded by yaxis is [RPET 1996]
A)
\[\pi {{a}^{2}}\] done
clear
B)
\[2\pi {{a}^{2}}\] done
clear
C)
\[3\pi {{a}^{2}}\] done
clear
D)
\[4\pi {{a}^{2}}\] done
clear
View Solution play_arrow

The area enclosed by the parabolas \[y={{x}^{2}}1\] and \[y=1{{x}^{2}}\] is [AMU 1999]
A)
1/3 done
clear
B)
2/3 done
clear
C)
4/3 done
clear
D)
8/3 done
clear
View Solution play_arrow

The area of the smaller segment cut off from the circle \[{{x}^{2}}+{{y}^{2}}=9\] by \[x=1\] is [RPET 2002]
A)
\[\frac{1}{2}(9{{\sec }^{1}}3\sqrt{8})\] done
clear
B)
\[9{{\sec }^{1}}(3)\sqrt{8}\] done
clear
C)
\[\sqrt{8}9{{\sec }^{1}}(3)\] done
clear
D)
None of these done
clear
View Solution play_arrow

The area of the region bounded by the curves \[y=x2,\] \[x=1,\,\,x=3\]and the xaxis is [AIEEE 2004]
A)
4 done
clear
B)
2 done
clear
C)
3 done
clear
D)
1 done
clear
View Solution play_arrow

The area enclosed between the parabolas \[{{y}^{2}}=4x\] and \[{{x}^{2}}=4y\] is [Karnataka CET 1999, 2003]
A)
\[\frac{14}{3}\] sq. unit done
clear
B)
\[\frac{3}{4}\] sq. unit done
clear
C)
\[\frac{3}{16}\] sq. unit done
clear
D)
\[\frac{16}{3}\] sq. unit done
clear
View Solution play_arrow

The area bounded by the curves \[{{y}^{2}}=8x\] and \[y=x\] is
A)
\[\frac{128}{3}\] sq. unit done
clear
B)
\[\frac{32}{3}\] sq. unit done
clear
C)
\[\frac{64}{3}\] sq. unit done
clear
D)
32 sq. unit done
clear
View Solution play_arrow

The area bounded by the curves \[y={{\log }_{e}}x\] and \[y={{({{\log }_{e}}x)}^{2}}\] is [RPET 2000]
A)
\[3e\] done
clear
B)
\[e3\] done
clear
C)
\[\frac{1}{2}(3e)\] done
clear
D)
\[\frac{1}{2}(e3)\] done
clear
View Solution play_arrow

The area between the parabola \[{{y}^{2}}=4ax\]and \[{{x}^{2}}=8ay\] is [RPET 1997]
A)
\[\frac{8}{3}{{a}^{2}}\] done
clear
B)
\[\frac{4}{3}{{a}^{2}}\] done
clear
C)
\[\frac{32}{3}{{a}^{2}}\] done
clear
D)
\[\frac{16}{3}{{a}^{2}}\] done
clear
View Solution play_arrow

The area of the region bounded by the curves \[y={{x}^{2}}\] and \[y=\,x\] is [Roorkee 1999]
A)
1/6 done
clear
B)
1/3 done
clear
C)
5/6 done
clear
D)
5/3 done
clear
View Solution play_arrow

The area bounded by curves \[y=\cos x\] and \[y=\sin x\] and ordinates \[x=0\] and \[x=\frac{\pi }{4}\] is [Karnataka CET 2002]
A)
\[\sqrt{2}\] done
clear
B)
\[\sqrt{2}+1\] done
clear
C)
\[\sqrt{2}1\] done
clear
D)
\[\sqrt{2}(\sqrt{2}1)\] done
clear
View Solution play_arrow

The area in the first quadrant between \[{{x}^{2}}+{{y}^{2}}={{\pi }^{2}}\] and \[y=\sin x\] is [MP PET 1997]
A)
\[\frac{({{\pi }^{3}}8)}{4}\] done
clear
B)
\[\frac{{{\pi }^{3}}}{4}\] done
clear
C)
\[\frac{({{\pi }^{3}}16)}{4}\] done
clear
D)
\[\frac{({{\pi }^{3}}8)}{2}\] done
clear
View Solution play_arrow

The area bounded by the curves \[{{y}^{2}}x=0\] and \[y{{x}^{2}}=0\] is [MP PET 1997]
A)
\[\frac{7}{3}\] done
clear
B)
\[\frac{1}{3}\] done
clear
C)
\[\frac{5}{3}\] done
clear
D)
1 done
clear
View Solution play_arrow

The area of region \[\{\,(x,\,y):{{x}^{2}}+{{y}^{2}}\le 1\le x+y\}\] is [Kerala (Engg.) 2002]
A)
\[\frac{{{\pi }^{2}}}{5}\] done
clear
B)
\[\frac{{{\pi }^{2}}}{2}\] done
clear
C)
\[\frac{{{\pi }^{2}}}{3}\] done
clear
D)
\[\frac{\pi }{4}\frac{1}{2}\] done
clear
View Solution play_arrow

The area of figure bounded by \[y={{e}^{x}},\,y={{e}^{x}}\] and the straight line \[x=1\] is [Karnataka CET 1999]
A)
\[e+\frac{1}{e}\] done
clear
B)
\[e3\] done
clear
C)
\[e+\frac{1}{e}2\] done
clear
D)
\[e+\frac{1}{e}+2\] done
clear
View Solution play_arrow

The volume of the solid formed by rotating the area enclosed between the curve \[y={{x}^{2}}\] and the line \[y=1\] about \[y=1\] is (in cubic units [UPSEAT 2003]
A)
\[9\pi /5\] done
clear
B)
\[4\pi /3\] done
clear
C)
\[8\pi /3\] done
clear
D)
\[7\pi /5\] done
clear
View Solution play_arrow

The volume of the solid generated by revolving about the yaxis the figure bounded by the parabola \[y={{x}^{2}}\] and \[x={{y}^{2}}\] is [UPSEAT 2002]
A)
\[\frac{21}{5}\pi \] done
clear
B)
\[\frac{24}{5}\pi \] done
clear
C)
\[\frac{2}{15}\pi \] done
clear
D)
\[\frac{5}{24}\pi \] done
clear
View Solution play_arrow

A frustum of sphere is made by cutting two parallel planes of any sphere. If radius of sphere is 5 cm and distance between the plane is 1 cm, then what will be the curved surface of frustum when the distance of first plane from the centre of sphere is 2 cm [UPSEAT 1999]
A)
\[5\pi \,c{{m}^{2}}\] done
clear
B)
\[10\pi \,c{{m}^{2}}\] done
clear
C)
\[15\pi \,c{{m}^{2}}\] done
clear
D)
\[40\pi \,c{{m}^{2}}\] done
clear
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The area enclosed by the parabola \[{{y}^{2}}=4ax\] and the straight line \[y=2ax,\] is [MP PET 1993]
A)
\[\frac{{{a}^{2}}}{3}\] sq. unit done
clear
B)
\[\frac{1}{3{{a}^{2}}}\] sq. unit done
clear
C)
\[\frac{1}{3a}\] sq. unit done
clear
D)
\[\frac{2}{3a}\] sq. unit done
clear
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The part of circle \[{{x}^{2}}+{{y}^{2}}=9\] in between \[y=0\] and \[y=2\] is revolved about yaxis. The volume of generating solid will be [UPSEAT 1999]
A)
\[\frac{46}{3}\pi \] done
clear
B)
\[12\pi \] done
clear
C)
\[16\pi \] done
clear
D)
\[28\pi \] done
clear
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Area bounded by the curve \[{{x}^{2}}=4y\] and the straight line \[x=4y2\] is [SCRA 1986; IIT 1981; Pb. CET 2003]
A)
\[\frac{8}{9}\] sq. unit done
clear
B)
\[\frac{9}{8}\] sq. unit done
clear
C)
\[\frac{4}{3}\] sq. unit done
clear
D)
None of these done
clear
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The area of the region bounded by the curve \[y=xx\], xaxis and the ordinates \[x=1,\,\,x=1\]is given by [Pb. CET 2004]
A)
Zero done
clear
B)
\[\frac{1}{3}\] done
clear
C)
\[\frac{2}{3}\] done
clear
D)
1 done
clear
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Area included between the two curves \[{{y}^{2}}=4ax\] and \[{{x}^{2}}=4ay,\] is [SCRA 1986; Roorkee 1984; RPET 1999; Kerala (Engg.) 2002, 05]
A)
\[\frac{32}{3}\,{{a}^{2}}\] sq. unit done
clear
B)
\[\frac{16}{3}\] sq. unit done
clear
C)
\[\frac{32}{3}\] sq. unit done
clear
D)
\[\frac{16}{3}\,{{a}^{2}}\] sq. unit done
clear
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If the area bounded by \[y=a{{x}^{2}}\]and \[x=a{{y}^{2}}\], \[a>0\], is 1, then \[a=\] [IIT Screening 2004]
A)
1 done
clear
B)
\[\frac{1}{\sqrt{3}}\] done
clear
C)
\[\frac{1}{3}\] done
clear
D)
None of these done
clear
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The area bounded by the curves \[y=\sqrt{x},\] \[2y+3=x\] and \[x\]axis in the 1st quadrant is [IIT Screening 2003]
A)
9 done
clear
B)
\[\frac{27}{4}\] done
clear
C)
36 done
clear
D)
18 done
clear
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The area enclosed between the curve \[y={{\log }_{e}}(x+e)\]and the coordinate axes is [AIEEE 2005]
A)
3 done
clear
B)
4 done
clear
C)
1 done
clear
D)
2 done
clear
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The parabolas \[{{y}^{2}}=4x\] and \[{{x}^{2}}=4y\] divide the square region bounded by the lines \[x=4\], \[y=4\]and the coordinate axes. If \[{{S}_{1}},{{S}_{2}},{{S}_{3}}\] are respectively the areas of these parts numbered from top to bottom, then \[{{S}_{1}}:{{S}_{2}}:{{S}_{3}}\] is [AIEEE 2005]
A)
\[2:1:2\] done
clear
B)
\[1:1:1\] done
clear
C)
\[1:2:1\] done
clear
D)
\[1:2:3\] done
clear
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If A is the area of the region bounded by the curve \[y=\sqrt{3x+4}\], x axis and the line \[x=1\] and \[x=4\]and B is that area bounded by curve \[{{y}^{2}}=3x+4\], x axis and the lines \[x=1\]and \[x=4\] then \[A:B\] is equal to [J& K 2005]
A)
\[1:1\] done
clear
B)
\[2:1\] done
clear
C)
\[1:2\] done
clear
D)
None of these done
clear
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The area of the region bounded by the curve \[9{{x}^{2}}+4{{y}^{2}}36=0\] is [Karnataka CET 2005]
A)
\[9\pi \] done
clear
B)
\[4\pi \] done
clear
C)
\[36\pi \] done
clear
D)
\[6\pi \] done
clear
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The area bounded by the curve \[y={{(x+1)}^{2}},\,y={{(x1)}^{2}}\] and the line \[y=\frac{1}{4}\] is [IIT Screening 2005]
A)
1/6 done
clear
B)
2/3 done
clear
C)
1/4 done
clear
D)
1/3 done
clear
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Let \[f(x)\] be a nonnegative continous function such that the area bounded by the curve \[y=f(x)\], xaxis and the ordinates \[x=\frac{\pi }{4}\], \[x=\beta >\frac{\pi }{4}\] is \[\left( \beta \sin \beta +\frac{\pi }{4}\cos \beta +\sqrt{2}\beta \right)\]. Then \[f\ \left( \frac{\pi }{2} \right)\] is [AIEEE 2005]
A)
\[\left( 1\frac{\pi }{4}\sqrt{2} \right)\] done
clear
B)
\[\left( 1\frac{\pi }{4}+\sqrt{2} \right)\] done
clear
C)
\[\left( \frac{\pi }{4}+\sqrt{2}1 \right)\] done
clear
D)
\[\left( \frac{\pi }{4}\sqrt{2}+1 \right)\] done
clear
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Area bounded by curves \[y={{x}^{2}}\] and \[y=2{{x}^{2}}\] is [Orissa JEE 2005]
A)
8/3 done
clear
B)
3/8 done
clear
C)
3/2 done
clear
D)
None of these done
clear
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Let y be the function which passes through (1, 2) having slope \[(2x+1)\]. The area bounded between the curve and xaxis is [DCE 2005]
A)
6 sq. unit done
clear
B)
5/6 sq. unit done
clear
C)
1/6 sq. unit done
clear
D)
None of these done
clear
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