Unit-6:
(a)Mensuration
(b)Trigonometry
(c)Geometry
(d)Co-ordinate geometry
Q1.
A rhombus of side 40 cm has two angles of 60o each. find the length of diagonals.
(a) 10,20 (b) 20,40
(c) 40√3, 20 (d) 40√3, 40
Solution.
(d) 40√3, 40
= cos 30
o AO/AB
√3/2 = AO/40
AO = 20√3
sin 30
o = OB/AB
1/2 = OB/AB
= 20
Solution
Q2.
A parallelogram circumscribing a circle is a ___________.
(a) Rectangle (b) Trapezium (c) Square
(d) Rhombus
Solution.
(d) Rhombus
Solution
Q3.
ABC is a right triangle right - angled at B such that BC = 6 cm and AB = 8 cm . find the radius of its circle.
(a) 8 cm (b) 2 cm (c) 4 cm (d) 10 cm
Solution.
r = (AB + BC + AC)/2
r = (8 + 6 - 10)/2
= 4/2
r = 2
Solution
Q4.
In a right triangle ABC, right angled at C. If tanB = 1 the 2 sinB . cosB = _______
(a) 4 (b) 3 (c)
1 (d) 2
Solution.
(c) 1
Solution
Q5.
If θ is an acute angle and tanθ + cotθ = 2, find the value of ( tanθ + cotθ)2
(a) 5 (b) 4 (c) 2 (d) 3
Solution.
On solving tanθ + cotθ = 2
θ = 45o
= tan2θ + cot2θ + 2 tanθ . cotθ
= 2 + 2 = 4
Solution
Q6.
Find the value of cosθ . sin(90o - θ ) + sinθ . cos(90o - θ)
(a) 1 (b) 2 (c) 3 (d) 4
Solution.
(a) 1
Solution
Q7.
Determine the ratio in which the line 3x + y = 9 divides the segment joining the points (1,3) and (2,7)
(a) 3:1 (b) 2:1 (c) 3:4 (d) 1:1
Solution.
(c) 3:4
let line divides the segment A and B in the ratio k:1 of point C , so the coordinates of C are
[(2k + 1)/(k + 1) , (7k + 3)/(k + 1)]
[3(2k + 1)/(k + 1) , (7k + 3)/(k + 1)] - 9 = 0
k = 3/4
Solution
Q8.
If three points (3,√3)(0,0)(3,a) form an triangle whose each angle is 600, find a.
(a) 1 (b) 2
(c) 3 (d) none of these
Solution.
(d) none of these
Solution
Q9.
The length of the minute hand of a clock is 44 cm . find the area swept by the minute hand in 5 minute.
(a) 199 cm2 (b) 322.6 π cm2 (c) 308 π cm2 (d) 176 cm2
Solution.
A = θ/360 x πr2
θ = 30o
A = 30o/360o x π x 44 x 44
= 1/6 x π x 44 x 44
A = [(22 x 44)/3] π
= 322.6 π cm2
Solution
Q10.
A cone and a hemisphere have equal bases. If their height are also equal then what is the ratio of their curved surface ?
(a) √2 : 3 (b) 1: √2 (c) 1 : 1 (d) 1 : 3
Solution.
(b) 1: √2
Solution
