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Q:

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:3 and area of ΔABC is 100 sq cm, what is the area (in sq cm) of quadrilateral BDEC?

A) 84 B) 16
C) 25 D) 75
 
Answer & Explanation Answer: A) 84

Explanation:
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Filed Under: Area
Exam Prep: Bank Exams

Q:

There are two parallel streets each directed north to south. A person in the first street travelling from south to north wishes to take the second street which is on his right side. At some place, he makes a 150 deg turn to the right and he travels for 15 minutes at the speed of 20 km/hr. After that he takes a left turn of 60 deg and travels for 20 minutes at the speed of 30 km/hr in order to meet the second street. What is the distance between the two streets?

A) 7.5 km B) 10.5 km
C) 12.5 km D) 15 km
 
Answer & Explanation Answer: C) 12.5 km

Explanation:
Initially the person is travelling from south to north i.e. D to A
He takes 150 deg right turn and moves AB distance and then he takes 60 deg left turn travels BC
AB = 20km/hr * 15/60 hr = 5km
BC = 30 * 20/60 = 10 km
We know that distance between both the streets is DC = DB + BC
DB = AB cos 60o= 5. ½ =2.5 km
So the distance between streets = 12.5 km
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Filed Under: Height and Distance
Exam Prep: Bank Exams

Q:

If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm, then what is the distance between these two chords?

A) 1 cm or 7 cm B) 2 cm or 14 cm
C) 3 cm or 21 cm D) 4 cm or 28 cm
 
Answer & Explanation Answer: B) 2 cm or 14 cm

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Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

Q:

PQ is a diameter of a circle with centre O. RS is a chord parallel to PQ subtends an angle of 40° at the centre of the circle. If PR and QS are produced to meet at T, then what will be the measure (in degrees) of ∠PTQ?

A) 55 B) 60
C) 70 D) 90
 
Answer & Explanation Answer: C) 70

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Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

Q:

Consider the following statements:

1) An isosceles trapezium is always cyclic.

2) Any cyclic parallelogram is a rectangle.

Which of the above statements is/are correct?

A) 1 only B) 2 only
C) Both 1 and 2 D) Neither 1 nor 2
 
Answer & Explanation Answer: C) Both 1 and 2

Explanation:

Since it is an isosceles trapezium

So angle C = angle D = x

let A = 180 –D = 180 –x (since AB is parallel to CD)

B = 180-x

A+C = 180 –x + x = 180 degrees (Property of cyclic quadrilateral)

ABCD is cyclic parallelogram with AB // CD and AD // BC

Considering angles A = C = y (Property of parallelogram) and B=D = x Also since it is cyclic A+C = B+D = 180 degrees

So x=y=90 degrees And also opposite sides are equal being a parallelogram

Thus ABCD is a rectangle

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Filed Under: Volume and Surface Area
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Q:

In ΔPQR, PQ = PR = 18 cm, AB and AC are parallel to lines PR and PQ respectively. If A is the mid-point of QR, then what is the perimeter (in cm) of quadrilateral ABPC?

A) 18 B) 28
C) 32 D) 36
 
Answer & Explanation Answer: D) 36

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Filed Under: Volume and Surface Area
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Q:

In ΔPQR, PQ = PR = 18 cm, AB and AC are parallel to lines PR and PQ respectively. If A is the mid-point of QR, then what is the perimeter (in cm) of quadrilateral ABPC?

A) 18 B) 28
C) 32 D) 36
 
Answer & Explanation Answer: D) 36

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Filed Under: Volume and Surface Area
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Q:

The lengths of two parallel sides of a trapezium are 21 cm and 9 cm. If its height is 10 cm, then what is the area (in cm2) of the trapezium?

A) 35 B) 75
C) 150 D) 225
 
Answer & Explanation Answer: C) 150

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Filed Under: Volume and Surface Area
Exam Prep: Bank Exams