Multiple Choice QuestionsBE and CF are two altitudes of a Δ ABC. If AB = 6 cm, AC = 5 cm and CF = 4 cm, then the length of BE is
4.8 cm
7.5 cm
3.33 cm
5.5 cm
A.
4.8 cm
In Δ AFC,
(AC)2 = (AF)2 + (FC)2
(5)2 = (AF)2 + (4)2
(AF)2 = 25 - 16 = 9
AF = 3 cm,
FB = AB - AF = 6 - 3 = 3 cm
In Δ BFC ,
(BC)2 = (FB)2 + (FC)2
(BC)2 = (3)2 + (4)2
BC = 5 cm
In Δ BEC,
(BC)2 = (BE)2 + (EC)2
(5)2 = (BE)2 + x2
(BE)2 = 25 - x2 ...(i)
In Δ AEB,
(AB)2 = (BE)2 + (AE)2
(6)2 = (BE)2 + (5 - x)2
(BE)2 = 36 - 25 - x2 + 10x
(BE)2 = 11 -x2 + 10x ...(ii)
From (i) and (ii),
25 - x2 = 11 - x2 + 10x
10x = 14
x = 1.4
In Δ BEC,
(BC)2 = (BE)2 + (EC)2
(5)2 = (BE)2 + (1.4)2
(BE)2 = 25 - 1.96 = 23.04
∴ BE = 4.8 cm
The circular measure of the included angle formed by the hour hand and minute hand of a clock at 3 p.m. will be
π/4
π/3
5π/12
π/2
The average of 100 observations was calculated as 35. It was found later, that one of the observations was misread as 83 instead of 53. The correct average is
32.7
34.7
35.7
36.7
O is a centre of a circle and AB is the tangent to it touch at B. If OB = 3 cm and OA = 5 cm, then the measure of AB (in cm) is
√34
2
8
4
The volume of the largest sphere (in cm3) that can be drawn inside a cube of side 18 cm is
Switch
is
then 
then the value of 
, the value of 
is
