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This mock test of SSC CPO Mock Test (Quant Apt) 2 for SSC helps you for every SSC entrance exam.
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QUESTION: 1

Solution:

QUESTION: 2

Solution:
All equations are resulting 2x^{2} - 3xy + y^{2}

except (B) gives

2x^{2} - xy - y^{2}

except (B) gives

2x

QUESTION: 3

Solution:
x^{2} (y - z) + y^{2} (z - x) + z^{2} (x - y)

= x^{2}y - x^{2}z + y^{2}z - y^{2}x + z^{2}x - z^{2}y

= xy(x - y) - xz (x - y) - zy (x - y) + z^{2} (x - y)

= (x - y) [xy - xz - zy + z^{2}]

= (x - y) [x(y - z) - z (y - z)]

= (x - y) (y - z) (x - z)

= - (x - y) (y - z) (z - x)

= x

= xy(x - y) - xz (x - y) - zy (x - y) + z

= (x - y) [xy - xz - zy + z

= (x - y) [x(y - z) - z (y - z)]

= (x - y) (y - z) (x - z)

= - (x - y) (y - z) (z - x)

QUESTION: 4

In a certain party,there was a bowl of rice for every two guests,a bowl of broth for every three of them and a bowl of meat for every four of them. If in all,there were 65 bowls of food,then how many guests were there in the party?

Solution:

Let the number of rice bowls be x, number of broth bowls be y

and number of meat bowls be z

∴ x + y + z = 65 .....(1)

and 2x = 3y = 4z .....(2)

By solving both the equation we get x = 30, y = 20 and z = 15 So, number of guests = 30 × 2 = 20 × 3 = 15 × 4 = 60

QUESTION: 5

The average of 50 numbers is 30. If two numbers, 35 and 40 are discarded,then the average of the remaining numbers is nearly

Solution:

QUESTION: 6

If the roots of the quardratic equation x²-px+q = 0 differ by unity, then

Solution:

QUESTION: 7

A circular running path is 726 metres in circumference. Two men start from the same point and walk in opposite directions at the speed of 3.75 km. per hour and 4.5 km per hour respectively. Then when will they meet for first chance:

Solution:

The two men walk in opposite directions @ 62.5 metres/minute and 75 metres/minute respectively

∴ They will meet for the first time after

QUESTION: 8

The sides of a triangle are in the ratio 13:14:15 and its perimeter is 168cm. The length of the altitude corresponding to the longest side is

Solution:

Ratio of sides = 13 : 14 : 15

Perimeter of triangle = 168 cm

Let the sides are 13x, 14x, and 15x

∴ 13x + 14x + 15x = 168

⇒ 42x = 168

⇒ x = 4

∴ sides are 13 × 4 = 52 cm

14 × 4 = 56 cm

15 × 4 = 60 cm

QUESTION: 9

The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is:

Solution:

Weight of the teacher = (35.4 × 25 - 35 × 24) kg = 45 kg

QUESTION: 10

The equation x² - 7xy + 12y² = 0 represents

Solution:

QUESTION: 11

A sum of money lent out at simple interests amounts to Rs. 720 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is :

Solution:

Principal + SI for 2 years = Rs 720 ……(I)

Principal + SI for 7 years = Rs 1020 ……(II)

Subtracting equation (I) from (II),

S.I. for 5 years = (1020 – 720) = Rs 300

∴ S.I. for 2 years = 300 x 2/5 = Rs 120

∴ Principal = (720 – 120) = Rs 600

QUESTION: 12

The value of

Solution:

QUESTION: 13

After getting two successive discoubts,a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.5% the first discount is

Solution:

QUESTION: 14

About a quadrilateral it is known that all its sides are equal. The quadrilateral is certainly a

Solution:

QUESTION: 15

Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by

Solution:

QUESTION: 16

A square is inscribed in a circle of radius 10 units. The area of the circle not included in the square......(use π = 3.14)

Solution:

Let the side of square be x unit.

sider the right triangle ABD

have x^{2} + x^{2} = (10 + 10)^{2}

⇒ 2x^{2} = 400

x^{2} = 200

Area of square = 200 sq units

One of circle = πr^{2} = 22/7 x (10)^{2} = 314 sq units

One of shaded region not included in square

= 314 sq unit - 200 sq unit

= 114 sq unit.

QUESTION: 17

Diagonals of a parallelogram are equal. The quadrilateral is a

Solution:

QUESTION: 18

AB∥CD and P is a point between the lines, the measure of the angles ∠ABP+∠BPD+∠CDP is

Solution:

QUESTION: 19

Which of the following is the least perfect square which is exactly divisible by 2,3,4,5 and 6?

Solution:

QUESTION: 20

ABC is a triangle. ∠A = 80º, ∠C = 60º. The measure of (yº - xº) is

Solution:

∠ABC = 180º - (∠BAC + ∠ACB)

∠ABC = 180º - 140º

∠ABC = 40º

But ∠ABC = 2xº

⇒ 2x = 40º

⇒ xº = 20º

Hence,

∠BOC = 180º - (20º + 30º)

∠BOC = 130º

⇒ yº - xº = 130º - 20º

yº - xº = 110º

QUESTION: 21

From a point P on a level ground, the angle of elevation of the top of a tower is 30º. If the tower is 100 m high, the distance of point P from the foot of the tower is:

Solution:

QUESTION: 22

If 2579*84 is divisible by 11,the missing digit is

Solution:

QUESTION: 23

5% income of A is equal to 15% income of B and 10% income of B is equal to 20% income of C.If the income of C is Rs 2000,then the total income of A,B and C (in Rs) is

Solution:

QUESTION: 24

10% of the voters did not cast their vote in an election between two candidates. 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1620 votes. The number of voters enrolled on the voters list was:

Solution:

QUESTION: 25

A cistern can be filled by a tap in 4 hrs while it can be emptied by another tap in 9 hrs. If both the taps are opened simultaneously, after how much time will the cistern get filled?

Solution:

QUESTION: 26

A house worth Rs 150000 is sold by X at 5% profit to Y. Y sells the house back to X at a 2% loss. Then, in the entire transaction

Solution:

QUESTION: 27

At what percent above the cost price must a shopkeeper mark his goods so that he gains 20% even after giving a discount of 10% on the marked price?

Solution:

QUESTION: 28

If a:b=2:5,then (3a+4b):(5a+6b) is equal to

Solution:

QUESTION: 29

The equation ax^{2} + bx + c = 0, where a, b, c are the sides of a ΔABC , and the equation x^{2} + √2x + 1 = 0 have a common root. The measure of ∠C is

Solution:

Clearly, the roots of x^{2} + √2x + 1 = 0 are nonreal complex. So, one root common implies both roots are common.

QUESTION: 30

An alloy contains copper and Zinc in the ratio 5:2 and another alloy containing Zinc and tin in the ratio 3:4. If two parts of first alloy and one part of second alloy are melted together to form a new alloy of copper,zinc and tin, the ratio of metals in the new alloy will be

Solution:
Allay A contains Copper and Zinc in the ratio 5 : 2

Alloy B contains Zinc and tin in the ratio 3 : 4

The new alloy contains 2 parts of alloy A that means copper and zinc ratio is 10 : 4

And

One part of alloy B that means zinc and tin ratio is 3 : 4

So copper = 10

Zinc = 4 + 3 = 7

tin = 4

So the ratio of metals in the new alloy will be 10 : 7 : 4

Alloy B contains Zinc and tin in the ratio 3 : 4

The new alloy contains 2 parts of alloy A that means copper and zinc ratio is 10 : 4

And

One part of alloy B that means zinc and tin ratio is 3 : 4

So copper = 10

Zinc = 4 + 3 = 7

tin = 4

So the ratio of metals in the new alloy will be 10 : 7 : 4

QUESTION: 31

11³ + 12³ + 13³ + ... + 20³ is

Solution:

QUESTION: 32

What sum of money will amount to Rs 520 in 5 yrs and to Rs 568 in 7 yrs at simple interest?

Solution:

QUESTION: 33

The positive square root of 45.5625 is

Solution:

QUESTION: 34

Walking at 3/4 of his usual pace, a man reaches his office 20 minutes late. Find his usual time.

Solution:

QUESTION: 35

A contractor undertakes to excute a certain work by 10 days and engages 12 men. He finds that half the work is done in 6 days. Number of additional men that he must now employ to fulfill his contract is

Solution:

QUESTION: 36

A circular wire of radius 7 cm is cut and bend again into an arc of a circle of radius 12 cm. The angle subtended by the are at the centre is

Solution:

QUESTION: 37

The least value of cosÎ¸+sinÎ¸ is

Solution:

QUESTION: 38

CosÎ¸/1-tanÎ¸ + sinÎ¸/1-cotÎ¸ is equal to

Solution:

QUESTION: 39

A hollow spherical metallic ball has an external diameter 6 cm and is ( 1/2 ) cm thick. The volume of metal used in the ball is :

Solution:

QUESTION: 40

The curved surface of a right circular cone of height 15 cm and base diameter 16 cm is :

Solution:

QUESTION: 41

If the height of a cone can be doubled and radius of base remains the same, then the ratio of the volume of the given cone to that of the second cone will be :

Solution:

QUESTION: 42

**Number of Vehicles Manufactured by Two companies ove the Years (Number in Thousands)**

**Q. **What is the difference between the total production of the two companies in the given years ?

Solution:

Productions of Company X in the years 1997, 1998, 1999, 2000, 2001 and 2002 are 119000, 99000, 141000, 78000, 120000 and 159000 and those of Company Y are 139000, 120000,100000, 128000, 107000 and 148000 respectively.

Total production of Company X from 1997 to 2002

= 119000 + 99000 + 141000 + 78000 + 120000 + 159000 = 716000

and total production of Company Y from 1997 to 2002

= 139000 + 120000 + 100000 + 128000 + 107000 + 148000 = 742000

Difference = (742000 - 716000) = 26000

QUESTION: 43

**Number of Vehicles Manufactured by Two companies ove the Years (Number in Thousands)**

**Q. **What is the difference between the number of vehicles manufactured by company Y in 2000 and 2001 ?

Solution:

Required difference = (128000 - 107000) = 21000.

QUESTION: 44

**Number of Vehicles Manufactured by Two companies ove the Years (Number in Thousands)**

**Q. **What is the average number of vehicles manufactured by company X over the given period? (rounded off to the nearest integer)

Solution:

Average number of vehicles manufactured by Company X

= 1/6 × (119000 + 99000 + 141000 + 78000 + 120000 + 159000) = 119333.

QUESTION: 45

**Number of Vehicles Manufactured by Two companies ove the Years (Number in Thousands)**

**Q. **In which of the following years, the difference between the productions of companies X and Y was the maximum amoung the given years ?

Solution:

The difference between the productions of Companies X and Y in various years are:

For 1997 (139000 - 119000) = 20000.

For 1998 (120000 - 99000) = 21000.

For 1999 (141000 - 100000) = 41000.

For 2000 (128000 - 78000) = 50000.

For 2001 (120000 - 107000) = 13000.

For 2002 (159000 - 148000) = 11000.

Maximum difference was in 2000.

QUESTION: 46

**These questions refer to the following circle graph showing the expenditure distribution of a certain family.**

**Q. **If the family spends Rs.6,500 per month, how much are its annual taxes ?

Solution:

QUESTION: 47

**These questions refer to the following circle graph showing the expenditure distribution of a certain family.**

**Q. ** How many degrees should there be in the central angle showing clothing , taxes and transportation combined ?

Solution:

Required angle

= 360/100 × 35 = 126°

QUESTION: 48

**These questions refer to the following circle graph showing the expenditure distribution of a certain family.**

**Q. **How much more money per month is spent by the family on food as compared to the rent ?

Solution:

QUESTION: 49

**Q. **If the expenditure budget of the family is raised to Rs.8,000 per month and distribution on various items remain the same , then the monthly expenses on both , the entertainment and the transport, will be :

Solution:

Expenses on entertainment and transport

= 8000 × 18%

= Rs 1440

QUESTION: 50

**The following questions are based on the following pie chart which gives the expenditure incurred in printing a magazine.**

**Q. **What is the angle for the sector representing paper cost ?

Solution:

Angle for sector representing paper cost = 360/100 × 10 = 36°

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