Unit-6:
(a)Mensuration
(b)Trigonometry
(c)Geometry
(d)Co-ordinate geometry
Q1.
The length of diagonals of a rhombus are 10 cm and √300 cm , Find the perimeter of the rhombus.
(a) 40 cm (b) 10 cm (c) 60 cm (d) 50 cm
Solution.
(a) 40 cm
Note : 4a2 = d12 + d22
Solution
Q2.
The perimeter of an equilateral triangle is 30 cm, Find the radius of incircle.
(a) 5 (b) 5/√3 (c) 2√3 (d) 6/√3
Solution.
(b) 5/√3
Solution
Q3.
One side of an rectangle becomes 2 times and other becomes 3 times , find the change in percentage of area of the rectangle .
(a) 300% (b) 600% (c) 500 % (d) 100%
Solution.
(c) 500 %
Solution
Q4.
Length of arc is double than radius, find the angle center by arc.
(a) 2 Radian (b) 3 Radian (c) 4 Radian (d) 5 Radian
Solution.
(a) 2 Radian
Note: θ = l/r = Length of an arc/radius
Solution
Q5.
Find the value of
(1+tan2θ) (1 - sinθ)(1 + sinθ)
(a) 3 (b) 0 (c) 1 (d) 2
Solution.
(c) 1
Solution
Q6.
7sin2θ + 3cos2θ = 4
so,find the value of cotθ.
(a) 1 (b) √3
(c) 1/√3 (d) 2
Solution.
(b) √3
Solution
Q7.
Find the total number of diagonals in an 9 sided polygon.
(a) 18 (b) 20 (c) 24 (d) 27
Solution.
formula = n(n - 3)/2
= (9 x 6)/2
= 9 x 3 = 27
Solution
Q8.
How many triangles can be formed from 12 points out of 4 points are collinear.
(a) 89 (b) 200 (c) 216 (d) 62
Solution.
Formula = 12C3 - 4C3
= 12!/(3! x 9!) - 4!/(3! x 1!)
(12 x 11 x 10 x 9!)/(3 x 2 x 9!) - (4 x 3!)/3!
= 20 x 11 - 4
= 220 - 4
= 216
Solution
Q9.
If points are (a,0)(0,b) and (1,1) are collinear, then find the value of ab.
(a) b (b) a + b (c) a (d) None of these
Solution.
(b) a + b
Solution
Q10.
Find the equation of line which has equal intercept and passes through the point (2,3).
(a) x+y = 2 (b) x = y
(c) x + y = 5 (d) x + y = 7
Solution.
x/a + 4/b = 1
∴ a = b
x/a + y/a = 1
(x + y)/a = 1
x + y = a
2 + 3 = a
a = 5
x + y = 5
Solution
