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This mock test of SSC CPO Mock Test (Quant Apt) 9 for SSC helps you for every SSC entrance exam.
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QUESTION: 1

Solution:

QUESTION: 2

Solution:
Let Price of each paper weight be Rs. x and ball Pens be Rs. y

9x + 7y = 300 .....(i)

6x + 13y = 300 .....(ii)

Solving (i) & (ii) we get

y = 12 & x = 24

9x + 7y = 300 .....(i)

6x + 13y = 300 .....(ii)

Solving (i) & (ii) we get

y = 12 & x = 24

QUESTION: 3

If one root of the quadratic equation 3x^{2} - 10x + p = 0 is 1 3 , then the value of p and other root respectively are

Solution:

Let 1/3 , α be the roots of the

QUESTION: 4

The square root of (272^{2}-128^{2}) is

Solution:

QUESTION: 5

x^{2} varies directly as y^{3} and when x=6,y=3.Which of the following equation correctly represents the relationship between x and y?

Solution:

x^{2} ∝ y^{3}

⇒ x^{2} = Ky^{3}

or, x = 6, y = 3

⇒ K = 4/3

So, 3x^{2} = 4y^{3}

QUESTION: 6

The average of marks obtained by 120 candidates in a certain examination is 35. If the average marks obtained by passed candidates is 39 and that of the failed candidates is 15, what is the number of candidates who passed the examination?

Solution:

QUESTION: 7

The area of the circumcircle of the equilateral triangle whose one side lies on the diagonal of a square with side 4 cm is (use π = 3.14)

Solution:

QUESTION: 8

Size of a tile is 9 inches by 9 inches. The number of tiles needed to cover a floor of 12 feet by 12 feet is

Solution:

Length of floor = 12 feet

Breath of floor = 12 feet

So Area of floor = 12 × 12 = 144 feet

Area of tile = 9/12 × 9/12 = 9/16 feet

QUESTION: 9

Area of a square field is 1 hectare. The length of another square field is 1% more than the length of this square field. The difference in their areas is

Solution:

1 hectare = 10000 m^{2}

Area of a square field = 10000 m^{2}

let length of a square field be x m

then x^{2} = 10000

x = 100m

length of other square field = 100 + 100 x 1/100 = 101

Area of Another square field = (101)^{2} = 10201 m^{2}

∴ Difference in their areas = 10201 - 10000

= 201 m^{2}

QUESTION: 10

The average of three numbers is 135. The largest number is 180 and the difference of the others is 25. The smallest number is

Solution:

⇒ x + y + z = 405

But let x = largest number i.e. 180

⇒ y + z = 225 .....(1)

Also, y - z = 25 .....(2)

Solving (1) and (2)

We get 2y = 250

⇒ y = 125

⇒ z = 125 - 25 = 100

Hence, the smallest number among the three numbers is 100

QUESTION: 11

The equation of the straight line which is perpendicular to y = x and passes through (3, 2) is :

Solution:
y = x

⇒ x - y = 0

⇒ y + x + λ = 0

⇒ 2 + 3 + λ = 0

⇒ λ = -5

⇒ x + y = 5

⇒ x - y = 0

⇒ y + x + λ = 0

⇒ 2 + 3 + λ = 0

⇒ λ = -5

⇒ x + y = 5

QUESTION: 12

How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

Solution:

QUESTION: 13

Which of the following is a perfect square as well as a cube? 343,125,81 or 64

Solution:

QUESTION: 14

The value of [(0.051×0.051×0.051+0.041×0.041×0.041)/(0.051×0.051-0.051×0.041+0.041×0.041)] is :

Solution:

QUESTION: 15

A specific type of cloth costs Rs 50 a metre and a buyer gets 8% discount on the total cost,if he buys 125 metres or more. The cost of 625 metres of cloth is

Solution:

QUESTION: 16

Diagonals AC and BD of || gm ABCD meet at O. If AP = QC then quadrilateral PBQD is a

Solution:
DO = OB and AO = OC. Also AP = CQ

$\Rightarrow $ AO - AP = OC - CQ

$\Rightarrow $ OP = OQ

Hence, PBQD is a || gm.

$\Rightarrow $ AO - AP = OC - CQ

$\Rightarrow $ OP = OQ

Hence, PBQD is a || gm.

QUESTION: 17

In the given figure AD bisects ΔBAC. If AB = 10 cm, AC = 6 cm and BD = 12cm, then length of CD is

Solution:

By internal angle bisector theorem, the bisector of vertical angle of triangle divides the base in the ratio of the other two sides

QUESTION: 18

If the two angles of a triangle are equal to the corresponding angles of another triangle, then the triangles are called :

Solution:

QUESTION: 19

(1095/1168) when expressed in simplest form is :

Solution:

QUESTION: 20

A pole is standing erect on the horizontal ground.The tip of the pole is tied tight with a rope of length √12 at a point on the ground. If the rope is making an angle of 30� with the horizontal,then the height of the pole is

Solution:

QUESTION: 21

The correct statement out of the following is

Solution:
∠A = ∠F; ∠B = ∠E and ∠C = ∠D

Hence, ∆ABC$\sim $∆FED.

Hence, ∆ABC$\sim $∆FED.

QUESTION: 22

Two numbers are in the ratio 5:4 and there difference is 10.What is the largest number?

Solution:

QUESTION: 23

What percentage of numbers from 1 to 70 have squares that end in the digit 1?

Solution:

The numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1.

Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69

Number of such number = 14

∴ Required percentage = (14/70 × 100)% = 20%

QUESTION: 24

A district has 64000 inhabitants. If the population increases at the rate of 2(1/2)% per annum, then the number of inhabitants at the end of 3 years will be

Solution:

QUESTION: 25

A tap can fill a tank in 6 hrs. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

Solution:

QUESTION: 26

A man gains 20% by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be:

Solution:

QUESTION: 27

A man purchased a box full of pencils at the rate of 7 for Rs 9 and sold all of them at the rate of 8 for Rs 11. In this transaction, he gained Rs. 10. How many pencils did the box contain?

Solution:

QUESTION: 28

In Δ A B C ,

Solution:

QUESTION: 29

Rs 6400 are divided among three workers in the ratio The share of the second worker (in rupees)is

Solution:

QUESTION: 30

In a factory,the ratio of male to female workers was 5:3. If the number of female workers was less by 40,then what was the total number of workers in the factory?

Solution:

QUESTION: 31

The two geometric means between 1 and 64 are

Solution:

QUESTION: 32

A sum of Rs 600 amounts to Rs 720 in 4 yrs. What will it amount to if the rate of interest is increased by 2%?

Solution:

QUESTION: 33

In a garden, there are n rows and n columns with a tree in each cell. If the total number of trees is 225 in the garden, then the value of n is

Solution:

QUESTION: 34

A gun is fired at a distance of 3.32 km from Barbar. He hears the sound 10 sec later. Find the speed of the sound.

Solution:

Distance = 3.32 × 1000 = 3320 m

Time = 10s

∴ Speed = 3320/10 = 332 m/s

QUESTION: 35

If 4 workers can make 42 toys in 6 days, how many toys can 12 workers make in 3 days?

Solution:

QUESTION: 36

If cosec A + cot A = 11/2, then tan A is

Solution:

QUESTION: 37

Maximum value of cos²x+cos²y-cos²z is

Solution:

QUESTION: 38

The length of an edge of a hollow cube open at one face is √3 metres. What is the length of the largest pole that it can accomodate?

Solution:

QUESTION: 39

What is the volume of a cube (in cubic cm) whose diagonal measures 4√3 cm?

Solution:

Length of the diagonal of the cube = 4√3 cm

So side = 4cm

Volume = (4)^{3} = 64 cubic cm

QUESTION: 40

The greatest value of 3 cos θ + 4 sin θ is :

Solution:

QUESTION: 41

The volumes of two cubes are in the ratio 8:27. The ratio of their surface areas is :

Solution:

QUESTION: 42

**The above graph shows the number of 5 Star Hotels in Delhi from 2000 to 2004. Observe the above line graph and answer the following question:**

**Q. **Percentage increase in the number of 5-Star Hotels in 2004 as compared to 2000 is

Solution:

QUESTION: 43

**The above graph shows the number of 5 Star Hotels in Delhi from 2000 to 2004. Observe the above line graph and answer the following question:**

**Q. **What percentage of number of 5-star hotels in 2000 is the number in 2004?

Solution:

QUESTION: 44

**The above graph shows the number of 5 Star Hotels in Delhi from 2000 to 2004. Observe the above line graph and answer the following question:**

**Q. **The ratio of number of 5-star hotels in 2001 to the number of 5-star hotels in 2003 is:

Solution:

Required ratio = 18 : 28 = 9 : 14

QUESTION: 45

**Q. **The year in which growth as compared to the previous year is maximum in

Solution:

Clearly maximum growth is in 2003 (+8)

QUESTION: 46

**Percentage of students in various courses( A,B,C,D,E,F) and Percentage of girls out of these.
Total Students : 1200
(800 girls + 400 boys)
Percentage in various courses**

**Q. **For which course is the number of boys the minimum ?

Solution:

QUESTION: 47

**Percentage of students in various courses( A,B,C,D,E,F) and Percentage of girls out of these.
Total Students : 1200
(800 girls + 400 boys)
Percentage in various courses**

**Q. **How many girls are there in course *C* ?

Solution:

QUESTION: 48

**Percentage of students in various courses( A,B,C,D,E,F) and Percentage of girls out of these.
Total Students : 1200
(800 girls + 400 boys)
Percentage in various courses**

**Q. **For course *D* what is the respective ratio of boys and girls ?

Solution:

QUESTION: 49

*A,B,C,D,E,F*) and Percentage of girls out of these.

Total Students : 1200

(800 girls + 400 boys)

Percentage in various courses

**Q. **For which pair of courses is the number of boys the same ?

Solution:

QUESTION: 50

*A,B,C,D,E,F*) and Percentage of girls out of these.

Total Students : 1200

(800 girls + 400 boys)

Percentage in various courses

**Q. **For course E, the number of girls is how much percent more than the boys for course E ?

Solution:

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