Advanced maths Quiz For SSC CGL and Bank 3/3/2016

#everydayquiz #10Questions

1.ABCD is a parallelogram with AB = 21 cm, BC = 13 cm and BD= 14 cm. Find the length of AC.

A. 32

B. 42

C. 34

D. 36

2. In triangle DEF shown below, points A, B, and C are taken on DE, DF and EF respectively such that EC = AC and CF = BC. If angle D = 40° then what is angle ACB in degree

A. 120

B. 100

C. 140

D. 150

3.In the figure (not drawn to scale) given below, if AD = CD = BC, and ∠BCE = 96°, how much is ∠DBC?

A. 32

B. 64

C. 96

D. 16

Direction(4-6): In the adjoining figure, I and II are circles with centres P and Q respectively. The two circles touch each other and have a common tangent that touches them at points Rand S

respectively. This common tangent meets the line joining P and Q at O. The diameters of I and II are in the ratio 4: 3. It is also known that the length of PO is 28 cm.

4.What is the ratio of the length of PQ to that of QO?

A. 1 : 4

B. 1 : 3

C. 3 : 8

D. 3 : 4

5.What is the radius of the circle II?

A. 2 cm

B. 3 cm

C. 4 cm

D. 5 cm

6.The length of SO is

A. 8√3 cm

B. 10√3 cm

C. 12√3 cm

D. 14√3 cm

7.In the figure given below (not drawn to scale), A, B and C are three points on a circle with centre O. The chord BA is extended to a point T such that CT becomes a tangent to the circle

at point C. If ∠ATC = 30° and ∠ACT = 50°, then the angle ∠BOA is

A. 100°

B. 150°

C. 80°

D. not possible to determine

8.A regular polygon with n sides has interior angles measuring 178°  . What is the value of 180/n ?

A. 1

B. 2

C. 3

D. 4

9.A regular hexagon is inscribed in a circle of radius 6. What is the area of the hexagon?

A. 54 √3.

B. 64 √3.

C. 84 √3.

D. 64 √3.

10.A rhombus has diagonals measuring 6 cm and 10 cm. What is its area in square centimeters?

A. 30

B. 32

C. 60

D. 64

ANSWER AND SOLUTION:

1.Answer: The figure is shown below

 Let AC and BD intersect at O. O bisects AC and BD. Therefore, OD is the median in triangle ADC.

⇒ AD^2 + CD^2 = 2(AO^2 + DO^2) ⇒ AO = 16. Therefore, AC = 32.

2.Answer: Let ∠AEC = ∠EAC = α and ∠CBF = ∠CFB = β. We know that α + β = 180° − ∠D = 140°. ∠ACB = 180° − (∠ECA + ∠BCF) = 180° − (180° − 2α + 180° − 2β) = 100°.

3.Answer: Let ∠DAC = ∠ACD = α and ∠CDB = ∠CBD = β. As ∠CDB is the exterior angle of triangle ACD, β = 2α. Now ∠ACD + ∠DCB + 96° = 180° ⇒ α + 180° − 2β + 96° = 180° ⇒ 3α = 96° ⇒ α = 32° ⇒ β = 64°

(4-6).

Join R and P, and S and Q. ∠PRO = ∠QSO = 90°. Therefore, ΔPRO and ΔQSO are similar. Therefore,

PR/SQ =PO/QO⇒ QO = 3/4xPO = 21⇒ PQ=1/4xPO = 7

⇒PQ:QO= 1:3.Also,PQ=7 and the radii are in the ratio 4: 3. Therefore,

radius of circle II = 3. 

7.Answer: Tangent TC makes an angle of 50° with chord AC. Therefore, ∠TBC = 50°. In triangle TBC,∠BCT = 180° − (30° + 50°) = 100°. Therefore, ∠BCA = ∠BCT − ∠ACT = 100° − 50° = 50°. ∠BOA  =2∠BCA = 100°.

8.Exterior angle = 180 – 178 = 2°

⇒ 360/n = 2 so 180/n = 1

9.As all the sides of a regular hexagon makes an equilateral Δ with the

centre of hexagon

.

⇒ 2a = 2r = 2× 6 ⇒ a = 6.

So area of the hexagon = 3√3/2 x 6^2= 54 √3.

10.Area of rhombus = 1/2xd1d2 = 1/2x6x10= 30sqcm

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