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Q:

Consider the following statements:

1) The number of circles that can be drawn through three non-collinear points is infinity.

2) Angle formed in minor segment of a circle is acute.

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: D) Neither 1 nor 2

Explanation:

(1)

Only one circle can be drawn through 3 non collinear points

Angle in the minor segment is always obtuse

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Filed Under: Volume and Surface Area
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Q:

Two equal circles intersect such that each passes through the centre of the other. If the length of the common chord of the circles is 10√3 cm, then what is the diameter of the circle?

A) 10 cm	B) 15 cm
C) 20 cm	D) 30 cm

Answer & Explanation Answer: C) 20 cm

Explanation:

Let there be 2 circles with centre O1 and OAB is the common chord

Since both passes through the center of each other as shown in figure

So O1O is the radius of both

Let O1O = r = AO1= AO

AX = AB / 2 = 5√3 cm (since OX perpendicular to chord bisects it)

AOO1 forms an equilateral triangle with on side = radius = r

Sin 60 = √3/2 = AX / AO = 5√3/r

So r = 10 cm

So diameter = 20 cm

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Filed Under: Simplification
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 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:

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:

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
Exam Prep: Bank Exams

Q:

Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible?

A) Only one	B) Only two
C) Only three	D) Infinitely many

Answer & Explanation Answer: A) Only one

Explanation:

let n-1, n, n+1 be 3 consecutive integers

So

(n+1)^2= n^2+ (n-1)^2

(n+1)^2-(n-1)^2= n^2

4n = n^2

So n = 0 or n = 4

n can’t be 0 as n-1 will be negative then

So 3,4 and 5 is the only triplet formed.

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

Q:

A person divided a sum of Rs. 17,200 into three parts and invested at 5%. 6% and 9% per annum simple interest. At the end of two years, he got the same interest on each part of money. What is the money invested at 9%?

A) Rs. 3,200	B) Rs. 4,000
C) Rs. 4,800	D) Rs. 5000

Answer & Explanation Answer: B) Rs. 4,000

Explanation:

Let sum invested @ 5% be P1, @ 6% be P2 then @ 9% =17200-(P1+P2)

So according to question

P1*5*2/100 = P2*6*2/100 or P1 = (6/5) P2

Also P2*6*2/100 = [17200-(P1+P2)]*9*2/100

Or 2 P2 = [17200–(11/5)P2] * 3

Or (2 + 33/5)P2 = 17200 * 3

P2 = 17200 * 3 * 5 / 43 = 6000

So P1 = 6/5 P2 = 7200

So Sum invested @ 9% = 17200–(6000+7200) = Rs 4000

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Filed Under: Simple Interest
Exam Prep: Bank Exams

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