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Welcome to ICOME Quiz Corner

Q1. If x:y = 3:2, So find the value of
x2 - y2 / (x - y)


(a) 3 (b) 5 (c) 2 (d) 1

Solution.
(x - y)(x + y) / (x - y)


= (x + y)

= 5
Solution

Q2. If A:B = 2:3 and B:C = 3:7 , find the value of (A + B):(B + C):(C - A)

(a) 2:2:1 (b) 2:1:1 (c) 1:2:1 (d) 1:1:2

Solution.
A:B:C = 2:3:7

5:10:5 = 1:2:1
Solution

Q3. A set of 15 points, in which 6 are collinear, find how many triangles can be formed.

(a) 290 (b) 195 (c) 400 (d) 435

Solution.
= 15 c3 - 6 c3

=
15! / 3! x 12!
-
6! / 3! x 3!


=
15 x 14 x 13 x 12! / 3 x 2 x 12!
-
6 x 5 x 4 x 3! / 3 x 2 x 3!


= 5 x 7 x 13 - 2 x 5 x 2

= 35 x 13 - 20

= 455 - 20 = 435
Solution

Q4. Line 8x + 15y = 120 cuts x and y axis at A and B respectively. Find the distance between A and B .

(a) 17 (b) 8 (c) 15 (d) 20

Solution.


AB2 = OB2 + AO2

AB2 = 64 + 225

AB = 17
Solution

Q5. Find the ∠BAC + ∠OBC in the given figure.


(a) 800 (b) 1200 (c) 750 (d) 900

Solution.
∠BOC = 2∠BAC

BO = OC

∠OBC = ∠OCB

∠BOC + 2∠OBC = 1800

2∠BAC + 2∠OBC = 1800

∠BAC + ∠OBC = 900
Solution

Q6. If sinθ + cosθ = √3 cos(900 - θ), find the value of tanθ .

(a) (√3-1)/2 (b) 1/2 (c) √3 - 1 (d) (√3 + 1)/2

Solution.
sinθ + cosθ = √3 sinθ

sinθ - √3 sinθ = cosθ

sinθ (1 - √3) = cosθ

tanθ = 1/(1 - √3) x (1 - √3)/(1 + √3) = (1 - √3)/(1 - √3) = (1 - √3)/(-2)

= (√3 - 1)/2
Solution

Q7. If A,B,C and D are angles of a cyclic quadrilateral , find the value of cosA + cosB + cosC + cosD .

(a) 3 (b) 1 (c) 0 (d) 2

Solution.
A + C = 180

A = 180 - C

cosA = -cosC

Similarly cosB = -cosD

= cosA + cosB + cosC + cosD

= - cosC - cosD + cosC + cosD

= 0
Solution

Q8. Find the value of
a2 + b2 + c2 / bc + ca + ab
, if a + b + c = 0

(a) -2 (b) -3 (c) 2 (d) 3

Solution.
(a) -2

(a + b + c)2 = a2 + b2 + c2 + 2(ab + ac + bc)
Solution

Q9. If logy x . logx y = x and x2 + y = 3 , find the value of x and y .

(a) (1,1) (b) (1,2) (c) (1,3) (d) (2,4)

Solution.
(logx/logy) . (logy/logx) = x

x = 1

(1)2 + y = 3

1 + y = 3

y = 2
Solution

Q10. If S.D of x is 1, find the S.D of y = (x - a)/b

(a) 1/b (b) b (c) 1 (d) a

Solution.
(a) 1/b
Solution