-
question_answer1)
In \[\Delta ABC,\ \,2{{R}^{2}}\sin A\sin B\sin C=\]
A)
\[{{s}^{2}}\] done
clear
B)
\[ab+bc+ca\] done
clear
C)
\[\Delta \] done
clear
D)
None of these done
clear
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question_answer2)
In \[\Delta ABC,\]if \[b=6,\,c=8\,\]and \[\angle A=90{}^\circ \], then R=
A)
3 done
clear
B)
4 done
clear
C)
5 done
clear
D)
7 done
clear
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question_answer3)
If the sides of a triangle are in ratio 3 : 7 : 8, then R : r is equal to
A)
2 : 7 done
clear
B)
7 : 2 done
clear
C)
3 : 7 done
clear
D)
7 : 3 done
clear
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question_answer4)
If the sides of triangle are 13, 14, 15, then the radius of its incircle is [EAMCET 1987]
A)
\[\frac{67}{8}\] done
clear
B)
\[\frac{65}{4}\] done
clear
C)
4 done
clear
D)
24 done
clear
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question_answer5)
The inradius of the triangle whose sides are 3, 5, 6, is [EAMCET 1982]
A)
\[\sqrt{8/7}\] done
clear
B)
\[\sqrt{8}\] done
clear
C)
\[\sqrt{7}\] done
clear
D)
\[\sqrt{7/8}\] done
clear
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question_answer6)
In an equilateral triangle of side \[2\sqrt{3}\]cm, the circum-radius is [EAMCET 1978]
A)
1 cm done
clear
B)
\[\sqrt{3}\]cm done
clear
C)
2 cm done
clear
D)
\[2\sqrt{3}\]cm done
clear
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question_answer7)
In an equilateral triangle the inradius and the circum-radius are connected by [EAMCET 1983]
A)
\[r=4R\] done
clear
B)
\[r=R/2\] done
clear
C)
\[r=R/3\] done
clear
D)
None of these done
clear
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question_answer8)
In any triangle ABC, \[a\cot A+b\cot B+c\cot C=\]
A)
\[r+R\] done
clear
B)
\[r-R\] done
clear
C)
\[2(r+R)\] done
clear
D)
\[2(r-R)\] done
clear
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question_answer9)
If the radius of the circumcircle of an isosceles triangle \[PQR\] is equal to \[PQ(=PR),\]then the angle P is [IIT Screening 1992; Pb. CET 2004]
A)
\[\frac{\pi }{6}\] done
clear
B)
\[\frac{\pi }{3}\] done
clear
C)
\[\frac{\pi }{2}\] done
clear
D)
\[\frac{2\pi }{3}\] done
clear
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question_answer10)
In a triangle ABC, \[a:b:c=4:5:6\]. The ratio of the radius of the circumcircle to that of the incircle is [IIT 1996]
A)
\[\frac{16}{9}\] done
clear
B)
\[\frac{16}{7}\] done
clear
C)
\[\frac{11}{7}\] done
clear
D)
\[\frac{7}{16}\] done
clear
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question_answer11)
Which is true in the following [UPSEAT 1999]
A)
\[a\cos A+b\cos B+c\cos C=R\sin A\sin B\sin C\] done
clear
B)
\[a\cos A+b\cos B+c\cos C=2R\sin A\sin B\sin C\] done
clear
C)
\[a\cos A+b\cos B+c\cos C=4R\sin A\sin B\sin C\] done
clear
D)
\[a\cos A+b\cos B+c\cos C=8R\sin A\sin B\sin C\] done
clear
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question_answer12)
If \[x,\,y,\,z\]are perpendicular drawn \[a,\,b\] and \[c\], then the value of \[\frac{bx}{c}+\frac{cy}{a}+\frac{az}{b}\]will be [UPSEAT 1999]
A)
\[\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{2R}\] done
clear
B)
\[\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{R}\] done
clear
C)
\[\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{4R}\] done
clear
D)
\[\frac{2({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}{R}\] done
clear
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question_answer13)
If the length of the sides of a triangle are 3, 4 and 5 units, then R (the circumradius) is [UPSEAT 2000]
A)
2.0 unit done
clear
B)
2.5 unit done
clear
C)
3.0 unit done
clear
D)
3.5 unit done
clear
View Solution play_arrow
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question_answer14)
If R is the radius of the circumcircle of the \[\Delta ABC\]and \[\Delta \]is its area, then [Karnataka CET 2000]
A)
\[R=\frac{a+b+c}{\Delta }\] done
clear
B)
\[R=\frac{a+b+c}{4\Delta }\] done
clear
C)
\[R=\frac{abc}{4\Delta }\] done
clear
D)
\[R=\frac{abc}{\Delta }\] done
clear
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question_answer15)
The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is [AIEEE 2003]
A)
\[a\cot \left( \frac{\pi }{n} \right)\] done
clear
B)
\[\frac{a}{2}\cot \left( \frac{\pi }{2n} \right)\] done
clear
C)
\[a\cot \left( \frac{\pi }{2n} \right)\] done
clear
D)
\[\frac{a}{2}\cot \left( \frac{\pi }{2n} \right)\] done
clear
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question_answer16)
In a \[\Delta ABC,\ {{r}_{1}}<{{r}_{2}}<{{r}_{3}},\]then [EAMCET 2003]
A)
\[a<b<c\] done
clear
B)
\[a>b>c\] done
clear
C)
D)
\[a<c<b\] done
clear
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question_answer17)
The radius of the in circle of triangle when sides are 18, 24 and 30 cms is [Pb. CET 2004]
A)
2 cm done
clear
B)
4 cm done
clear
C)
6 cm done
clear
D)
9 cm done
clear
View Solution play_arrow
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question_answer18)
If the sides of the triangle are \[5K,\ 6K,\ 5K\]and radius of incircle is 6 then value of K is equal to [Pb. CET 2004]
A)
4 done
clear
B)
5 done
clear
C)
6 done
clear
D)
7 done
clear
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question_answer19)
\[\frac{a\cos A+b\cos B+c\cos C}{a+b+c}=\] [Orissa JEE 2004]
A)
1/r done
clear
B)
r/R done
clear
C)
R/r done
clear
D)
1/R done
clear
View Solution play_arrow
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question_answer20)
In a triangle\[ABC\], if \[b=2,\,B=30{}^\circ \]then the area of circumcircle of triangle ABC in square units is [Karnataka CET 2004]
A)
\[\pi \] done
clear
B)
\[2\pi \] done
clear
C)
\[4\pi \] done
clear
D)
\[6\pi \] done
clear
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question_answer21)
The circum-radius of the triangle whose sides are 13, 12 and 5 is [Karnataka CET 2005]
A)
15 done
clear
B)
13/2 done
clear
C)
15/2 done
clear
D)
6 done
clear
View Solution play_arrow
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question_answer22)
The area of the equilateral triangle which containing three coins of unity radius is [IIT Screening 2005]
A)
\[6+4\sqrt{3}\ sq.\ units\] done
clear
B)
\[8+\sqrt{3}\] sq. units done
clear
C)
\[4+\frac{7\sqrt{3}}{2}\] sq. units done
clear
D)
\[12+2\sqrt{3}\]sq. units done
clear
View Solution play_arrow
