ENGLISH LANGUAGE

Reading Comprehension
Synonyms & Antonyms
English Language
Passage Completion
Synonyms
Similar Substitution
Double Synonms
Sentence Improvement
Homonyms
Idioms and Phrases
Spelling
Direct and Indirect Speech
Antonyms
Spotting the Errors
Deriving conclusion from passages
Theme Detection
Sentence Completion
Correct Usage of Preposition
Para Jumbles
One Word Substitution
Vocabulary Test
Cloze Test
Active and Passive Voice

QUANTITATIVE APTITUDE

Problem Based on Ages
Probability
Geometry
Time and Work / Pipe and Cistern
Permutation and Combination
Quantitative Aptitude
Mensuration
Square, Cube, Indices & Surds
Simple & Compound Interest
Number Series
Simple Interest
Profit, Loss & Discount
Data Interpretation
Simplification
Percentage
Distance, Speed and Time
Average
Ratio & Proportion
Alligation and Mixture
Compound Interest
Miscellaneous
Algebraic Expressions and Inequalities
Number System
LCM, HCF and Fraction

GENERAL AWARENESS

History of Banking & It's Development
Banking Product & Services
RBI & It's Monetary Policies
General Awareness
Micro Finance & Economics
Current Affairs
Foreign Trade
Books & Authors
Events/ Organisation/ Summits
Country and Capital
Banking Terminologies
Sports & Games
Current Banking
Awards & Honours
Socio-Eco_Political Environment of India
Appointment/ Election/ Resignation
Science & Technology
Government Schemes

COMPUTER AWARENESS

Computer Awareness
Modern Marketing/ Marketing in Banking Industry
Computer Fundamental/ Binary System/ OS
Fundamentals of Marketing, Product and Branding
Professional Knowledge (IT)
Softwares/ Programming
Market Situation, Distribution, Promotion & Advertising
Logic Gates
MS Office/ Commands & Shortcut Keys
Market Segmentation, Targeting & Positioning
DBMS (Database management system)
Computer Architecture
Internet, Networking & Computer Abbreviations
Data Structure Compiler

REASONING

Q 1.

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If (5, 1), (x, 7) and (3, -1) are 3 consecutive verticles of a square then x is equal to :

-3

-4

5

6

None of these

For the verticles to form a square, we know that the length of each side of the square should be equal. Therefore,

(x - 5){tex}^2{/tex} + (7 - 1){tex}^2{/tex} = (x - 3){tex}^2{/tex} + (7 + 1){tex}^2{/tex}

[x{tex}^2{/tex} + 5{tex}^2{/tex} - 2 (x) (5) ] + [36] = [x{tex}^2{/tex} + 3{tex}^2{/tex} - 2 (x) (3) ] + [64]

[5{tex}^2{/tex} + 36] - [9 + 64] = (10 - 6) x

x = -{tex}\frac{12}{4}{/tex} = - 3

This gives the side of the square x = - 3.

Q 2.

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What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150°?

24 sq units

48 sq units

24{tex}\sqrt 3{/tex}

48{tex}\sqrt 3{/tex}

Such a triangle does not exist

If two sides of a triangle and the included angle 'y' is known, then the area of the triangle can be found using the formula

{tex}\frac{1}{2}{/tex}* (product of sides) * sin y

Substituting the values in the formula, we get {tex}\frac{1}{2}{/tex}* 8 * 12 * sin 150 = 24 sq units

Q 3.

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What is the measure of the radius of the circle that circumscribes a triangles whose sides measure 9, 40 and 41?

6

4

24.5

20.5

12.5

From the measure of the length of the sides of the triangle 9, 40 and 41 we can infer that the triangle is a right angled triangle. 9, 40, 41 is a Pythagorean triplet.

In a right angled triangle, the radius of the circle that circumscribes the triangle is half the hypotenuse.

In the given triangle, the hypotenuse = 41

Therefore, the radius of the circle that circumscribes the triangle ={tex}\frac{41}{2}{/tex} = 20.5 units

Q 4.

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Verticles of a quadrilateral ABCD are A (0, 0), B (4, 5), C (9, 9) and D (5, 4). What is the shape of the quadrilateral?

Square

Rectangle but not a square

Rhombus

Parallelogram but not a rhombus

None of these

The lengths of the four sides AB, BC, CD and DA are all equal to {tex}\sqrt{41}{/tex}.

Hence, the given quadrilateral is either a Rhombus or a Square.

Now let us compute the lengths of the two diagonals AC and BD.

The length of AC is {tex}\sqrt{162}{/tex} and the length of BD is {tex}\sqrt{2}{/tex}

As the diagonals are not equal and the sides are equal, the given quadrilateral is a Rhombus.

Q 5.

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If the sum of the interior angles of a regular polygon measures upto 1440 degrees, how many sides does the polygon have?

10 sides

8 sides

12 sides

9 sides

None of these

We know that the sum of an exterior angle and an interior angle of a polygon = 180°

We also know that sum of all the exterior angles of a polygon = 360°

The question states that the sum of all interior angles of the given polygon = 1440°

Therefore, sum of all the interior and exterior angles of the polygon = 1440 + 360 = 1800

If there are ‘n' sides to this polygon, then the sum of all the exterior and interior angles = 180 x n = 10

Q 6.

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What is the radius of the in circle of the triangle whose sides measure 5, 12 and 13 units?

2 units

12 units

6.5 units

6 units

7.5 units

The triangle given is a right angled triangle as its sides are 5, 12 and 13 which is one of the Pythagorean triplets.

Note: In a right angled triangle, the radius of the incircle is given by the following relation

{tex}\frac{sum\ of\ perpendicular\ sides - hypotenuse}{2}{/tex}

As the given triangle is a right angled triangle, radius of its incircle = {tex}\frac{5+12-13}{2}{/tex}= 2 units

Q 7.

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How many diagonals does a 63 sided convex polygon have?

3780

1890

3843

3906

1953

The number of diagonals of an n-sided convex is {tex}\frac{n(n-3)}{2}{/tex}

This polygon has 63 sides. Hence, {tex}n{/tex} = 63

Therefore, number of diagonals = {tex}\frac{63\times60}{2}{/tex} = 1890

Q 8.

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If 10, 12 and ‘x' are sides of an acute angled triangle, how many integer values of ‘x' are possible?

7

12

9

13

11

For any triangle sum of any two sides must be greater than the third side.

The sides are 10, 12 and ‘x'.

From Rule 2, x can take the following values : 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 - A total of 19 values.

When x = 3 or x = 4 or x = 5 or x = 6, the triangle is an OBTUSE angled triangle.

The smallest value of x that satisfies both conditions is 7. (10{tex}^{2}{/tex} + 7{tex}^{2}{/tex} > 12{tex}^{2}{/tex})

The highest value of x that satisfies both conditions is 15. (10{tex}^{2}{/tex} + 12{tex}^{2}{/tex} + 15{tex}^{2}{/tex})

When x = 16 or x = 17 or x = 18 or x = 19 or x = 20 or x = 21, the triangle is an OBTUSE angled triangle.

Hence, the values of x that satisfy both the rules are x = 7, 8, 9, 10, 11, 12, 13, 14, 15. A total of 9 values.

Q 9.

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Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are 6 inches and 8 inches.

10 inches

11 inches

18 inches

20 inches

None of these

Test the ratio of the lengths to see if it fits the 3n : 4n : 5n ratio.

6 : 8 : ?= 3 (2) : 4 (2) : ?

Yes, it is a 3-4-5 triangle for n =

Calculate the third side 5n = 5 x 2 = 10

The length of the hypotenuse is 10 inches.

Q 10.

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Find the length of one side of a right triangle if the length of the hypotenuse is 15 inches and the length of the other side is 12 inches.

8 inches

7 inches

9 inches

13 inches

None of these

Test the ratio of the lengths to see if it fits the 3n : 4n : 5n ratio.

? : 12 : 15 = ? : 4 (3) : 5 (3)

Yes, it is a 3-4-5 triangle for n = 3

Calculate the third side 3n = 3 x 3 = 9

The length of the side is 9 inches.

Q 11.

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Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are both 3 inches.

{tex}5{/tex} inches

{tex}3\sqrt{4}{/tex} inches

{tex}6{/tex} inches

{tex}3\sqrt{2}{/tex} inches

None of these

This is a right triangle with two equal sides so it must be a 45° - 45° - 90° triangle. You are given that the both the sides are 3. If the first and second value of the ratio n : n : n{tex}\sqrt{2}{/tex} is 3 then the length of the third side is 3{tex}\sqrt{2}{/tex}

The length of the hypotenuse is 3{tex}\sqrt{2}{/tex} inches.

Q 12.

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Find the lengths of the other two sides of a right triangle if the length of the hypotenuse is 4{tex}\sqrt{2}{/tex} inches and one of the angles is 45°.

4 inches

9 inches

8 inches

7 inches

None of these

This is a right triangle with a 45° so it must be a 45° - 45° - 90° triangle.

You are given that the hypotenuse is 4{tex}\sqrt{2}{/tex} . If the third value of the ratio n : n : n{tex}\sqrt{2}{/tex} is 4{tex}\sqrt{2}{/tex} then the lengths of the other two sides must 4.

The lengths of the two sides are both 4 inches.

Q 13.

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Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are 4 inches and 4{tex}\sqrt{3}{/tex} inches.

8 inches

9 inches

10 inches

11 inches

None of these

Test the ratio of the lengths to see if it fits the n : n{tex}\sqrt{3}{/tex} : 2n ratio.

4 : 4{tex}\sqrt{3}{/tex} : ? n : n{tex}\sqrt{3}{/tex} : 2n

Yes, it is a 30° - 60° - 90° triangle for n = 4

Calculate the third side

2n = 2 x 4 = 8

The length of the hypotenuse is 8 inches.

Q 14.

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What is the area of the following square, if the length of BD is 2{tex}\sqrt{2}{/tex} ?

1

2

3

4

5

We need to find the length of the side of the square in order to get the area.

The diagonal BD makes two 45° - 45° - 90° triangles with the sides of the square.

Using the 45° - 45° - 90° special triangle ratio n: n : n{tex}\sqrt{2}{/tex}. If the hypotenuse is 2{tex}\sqrt{2}{/tex} then the legs must be 2. So, the length of the side of the square is 2.

Area of square = 5{tex}^{2}{/tex} = 2{tex}^{2}{/tex} = 4

Q 15.

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In the figure below, what is the value of y?

40

50

60

100

120

Vertical angles being equal allows us to fill in two angles in the triangle that y° belongs to.

Sum of angles in a triangle = 180°

So, y° + 40° + 80° = 180°

y° + 120° = 180°

y° = 60°

Q 16.

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Two circles both of radii 6 have exactly one point in common. If A is a point on one circle and B is a point on the other circle, what is the maximum possible length for the line segment AB?

12

15

18

20

24

Sketch the two circles touching at one point.

The furthest that A and B can be would be at the two ends as shown in the above diagram.

If the radius is 6 then the diameter is 2 x 6 = 12 and the distance from A to B would be 2 x 12 = 24

Q 17.

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A right circular cylinder has a radius of 3 and a height of 5. Which of the following dimensions of a rectangular solid will have a volume closest to the cylinder?

4, 5, 5

4, 5, 6

5, 5, 5

5, 5, 6

5, 6, 6

Write down formula for volume of cylinder

V = {tex}\pi{/tex}r{tex}^2{/tex}h

Plug in the values

V = {tex}\pi{/tex} x 3{tex}^2{/tex} x 5 = 45 {tex}\pi{/tex}

V = 45 x 3.142 = 141.39

We now have to test the volume of each of the rectangular solids to find out which is the closest to 141.39

(A) 4 x 5 x 5 = 100

(B) 4 x 5 x 6 = 120

(C) 5 x 5 x 5 = 125

(D) 5 x 5 x 6 = 150

(E) 5 x 6 x 6 = 180

Q 18.

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Note: Figures not drawn to scale.

In the figures above, x = 60, How much more is the perimeter of triangle ABC compared with the triangle DEF.

0

2

4

6

8

Note: Figures not drawn to scale
Since x = 60°, triangle ABC is an equilateral triangle with sides all equal.
The sides are all equal to 8.
Perimeter of triangle ABC = 8 + 8 + 8 = 24
Triangle DEF has two angles equal, so it must be an isosceles triangle.
The two equal sides will be opposite the equal angles

So, the length of DF = length of DE = 10

Perimeter of triangle DEF = 10 + 10 + 4 = 24 Subtract the two perimeters.

24 - 24 = 0

Q 19.

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A right triangle has one other angle that is 35°. What is the size of the third angle?

55°

65°

90°

180°

None of these

A right triangle has one angle = 90°. Sum of known angles is 90° + 35° = 125°

The sum of all the angles in any triangle is 180°. Subtract sum of known angles from 180°. 180° 125° = 55°

The size of the third angle is 55°

Q 20.

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An equilateral triangle has one side that measures 5 in. What is the size of the angle opposite that side?

55°

70°

110°

60°

None of these

Since it is an equilateral triangle all its angles would be 60°. The size of the angle does not depend on the length of the side.

The size of the angle is 60°.

Q 21.

Correct1

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An isosceles triangle has one angle of 96°. What are the sizes of the other two angles?

24°

34°

42°

96°

None of these

Since it is an isosceles triangle it will have two equal angles. The given 96° angle cannot be one of the equal pair because a triangle cannot have two obtuse angles.

Let x be one of the two equal angles. The sum of all the angles in any triangle is 180°.

x + x + 96° = 180°

2x = 84°

x = 42°

The sizes of the other two angles are 42° each.

Q 22.

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Find the circumference of the circle with a diameter of 8 inches?

25 inches

25.163 inches

29.45 inches

35.62 inches

None of these

Formula C = {tex}\pi {/tex}d

C = 8{tex}\pi {/tex}

The circumference of the circle is 8{tex}\pi {/tex} = 25.163 inches

Q 23.

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Find the area of the circle with a diameter of 10 inches?

55.78 sq. inches

99.75 sq. inches

92 inches

78.55 sq. inches

None of these

Formula A = {tex}\pi {/tex}r{tex}^{2}{/tex}

Change diameter to radius r = {tex}\frac{1}{2}{/tex}d = {tex}\frac{1}{2}{/tex}x 10 = 5

Plug in the value: A = {tex}\pi {/tex}5{tex}^{2}{/tex} = 25 {tex}\pi {/tex}

The area of the circle is 25{tex}\pi {/tex}

78.55 sq. inches

Q 24.

Correct1

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Find the area of the circle with a radius of 10 inches?

314.2 sq. inches

115 inches

320.29 sq. inches

56.12 sq. inches

None of these

Formula A = {tex}\pi {/tex}r2

Plug in the value A = {tex}\pi {/tex}102 = 100 {tex}\pi {/tex}

The area of the circle is 100 {tex}\pi {/tex}

314.2 sq. inches

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