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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
Exam Prep: Bank Exams

Q:

In a circle of radius 8 cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC?

A) 2√6 cm B) 3√6 cm
C) 3√7 cm D) 6√7 cm
 
Answer & Explanation Answer: D) 6√7 cm

Explanation:
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Filed Under: Volume and Surface Area
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Q:

The angles of a triangle are in the ratio 1 : 1 : 4. If the perimeter of the triangle is k times its largest side, then what is the value of k?

A) 1 + 2/√3 B) 1 - 2/√3
C) 2 + 2/√3 D) 2
 
Answer & Explanation Answer: A) 1 + 2/√3

Explanation:
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Filed Under: Area
Exam Prep: Bank Exams

Q:

A 12 m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle?

A) 12/π+4 B) 6/π+4
C) 3/π+4 D) 6/π+2√2
 
Answer & Explanation Answer: B) 6/π+4

Explanation:
As it is clear that 2r = a where a is the side of the square and
R is the radius of circle
It is given that 2πr + 4a = 12
a = 12/(π+4)
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Filed Under: Simplification
Exam Prep: Bank Exams

Q:

The perimeter of a right-angled triangle is k times the shortest side. If the ratio of the other side to hypotenuse is 4 : 6, then what is the value of k?

 

A) 2 B) 3
C) 4 D) 5
 
Answer & Explanation Answer: C) 4

Explanation:
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Filed Under: Area
Exam Prep: Bank Exams

Q:

A rectangular red carpet of size 6 ft ×12 ft has a dark red border 6 inches wide. What is the area of the dark red border?

 

A) 9 square feet B) 15 square feet
C) 17 square feet D) 18 square feet
 
Answer & Explanation Answer: C) 17 square feet

Explanation:
Initially carpet is 6×12 = 72 sq feet
Since red border is 6 inches wide from all 4 side
So area without border = 5× 11 = 55 sq feet
Area of border = total–area without border = 72–55 = 17 sq feet
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Filed Under: Volume and Surface Area
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Q:

Two circles are drawn with the same centre. The circumference of the smaller circle is 44 cm and that of the bigger circle is double the smaller one. What is the area between these two circles?A. 154 square cmB. 308 square cmC. 462 square cmD. 616 square cm

A) 154 square cm B) 308 square cm
C) 462 square cm D) 616 square cm
 
Answer & Explanation Answer: C) 462 square cm

Explanation:
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Q:

The corners of a square of side ‘a’ are cut away so as to form a regular octagon. What is the side of the octagon?

A) a(√2 –1) B) a(√3 –1)
C) a/√2+2 D) a/3
 
Answer & Explanation Answer: A) a(√2 –1)

Explanation:

Since we are forming a regular octagon

so AE = AL = FB = BG and so on

So AE = SB = x/√2

AE + EF + FB = side of square = a (Given)

So x/√2 + x + x/√2 = a

X = a/(√2+1) = a(√2 -1)

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