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Q:

A plane is going in circles around an airport. The plane takes 3 minutes to complete one round. The angle of elevation of the plane from a point P on the ground at time t seconds is equal to that at time (t + 30) seconds. At time (t + x) seconds, the plane flies vertically above the point P. What is x equal to?

A) 75 seconds B) 90 seconds
C) 105 seconds D) 135 seconds
 
Answer & Explanation Answer: C) 105 seconds

Explanation:
Let the plane be at point A at t se
conds and at point B
after t + 30 seconds
Since the motion is uniform, we can say that at time t+15 seconds, the plane is above the point is
diametrically opposite to the point P from where the angle is same.
Now since the time taken to cover the full circ
le is 3 minutes (180
seconds), the time taken by the plane
to reach the diametrically opposite point will be 90 seconds.
So the time after which the plane reaches the point P will be = t+ 15 + 90 seconds = (t + 105 )seconds
 
 
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Filed Under: Time and Distance
Exam Prep: Bank Exams

Q:

Consider a regular hexagon ABCDEF. Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is 30 deg, and the angle of elevation to the top of the tower at C is 45 deg. What is the ratio of the height of towers at B and C?

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

Explanation:

Let the side of regular hexagon be ‘a’

Let height of the tower 1 be h1 and tower 2 be h2

Height of tower 1 = h1 = (distance between A and B)* (tan 30o)= a.1/√3

Distance between A and C = 2*√3.a/2= √3a

Height of tower 2 = h2 = (distance between A and C)* (tan 45o) = √3a.1 = √3a

Ratio of height of towers at B and C respectively =a/√3/√3a = 1/3.

 

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Filed Under: Simplification
Exam Prep: Bank Exams

Q:

What is the percentage decrease in the area of a triangle if its each side is halved?

A) 75% B) 50%
C) 25% D) No change
 
Answer & Explanation Answer: A) 75%

Explanation:
Area of triangle of = ½*a*b* sinθ = A
Where a and b are sides of the triangle and θ be the angle between them
After decreasing each side
New area = ½*(a/2)*(b/2)*sinθ = ¼ A
%decrease = [(A–¼ A)/A ]*100 = 75%
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Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

Q:

In a rectangle, length is three times its breadth. If the length and the breadth of the rectangle are increased by 30% and 100% respectively, then its perimeter increases by

A) 40/3% B) 20%
C) 25% D) 27%
 
Answer & Explanation Answer: C) 25%

Explanation:
Let the breadth of the rectangle = x
Length of the the rectangle will be = 3 times of breadth = 3x
So the initial perimeter = 2(length + breadth) = 2(x + 3x) = 8x
New breadth after increase = x + 10x/100 = 1.1x
New length after increase = 3x + 30*3x/100 = 3.9x
New perimeter = 2(1.1x + 3.9x) = 10x
Percentage change in perimeter = ( 10x-8x)*100/8x = 25%
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Filed Under: 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

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

Q:

ABC is a right angled triangle in which ∠A = 90°, AB = 5 cm and AC = 12 cm. What is the approximate volume (in cm3) of the double cone formed by rotating the triangle about its hypotenuse?

A) 145 B) 290
C) 435 D) 580
 
Answer & Explanation Answer: B) 290

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

Q:

How many triangles are there in the given figure?

A) 8 B) 9
C) 10 D) 12
 
Answer & Explanation Answer: B) 9

Explanation:
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Filed Under: Verbal Reasoning - Mental Ability
Exam Prep: Bank Exams

Q:

Consider the following statements:

1) The perimeter of a triangle is greater than the sum of its three medinas.

2) In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD.

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:
Let ABC be the triangle and D. E and F are midpoints of BC, CA and AB respectively.
Recall that the sum of two sides of a triangle is greater than twice the median bisecting the third side,(Theorem to be remembered)
Hence in ΔABD, AD is a median
⇒
AB + AC > 2(AD)
Similarly, we get
BC + AC > 2CF
BC + AB > 2BE
On adding the above inequations, we get
(AB + AC) + (BC + AC) + (BC + AB )> 2AD + 2CD + 2BE
2(AB + BC + AC) > 2(AD + BE + CF)
∴
AB + BC + AC > AD + BE +CF
 
2.
To prove: AB + BC + CA > 2AD
Construction: AD is joined
Proof: In triangle ABD,
AB + BD > AD [because, the sum of any two sides of a triangle is always greater than the
third side]
----
1
In triangle ADC,
AC + DC > AD [because, the sum of any two
sides of a tri
angle is always greater than the
third side]
----
2
Adding 1 and 2 we get,
AB + BD + AC + DC > AD + AD
=> AB + (BD + DC) + AC > 2AD
=> AB + BC + AC > 2AD
Hence proved
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Filed Under: Volume and Surface Area
Exam Prep: Bank Exams