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This mock test of SSC CPO Mock Test (Quant Apt) 3 for SSC helps you for every SSC entrance exam.
This contains 50 Multiple Choice Questions for SSC SSC CPO Mock Test (Quant Apt) 3 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Solution:

QUESTION: 2

Solution:

QUESTION: 3

Factors of(2x-3y)³+(3y-5z)³+(5z-2x)³ are

Solution:

QUESTION: 4

If 2x+3y=26; 2y+z=19 and x+2z=29,what is the value of of x+y+z?

Solution:
2x + 3y = 26 .....(i)

2y + z = 19 .....(ii)

x + 2z = 29 .....(iii)

from (ii) and (iii)

x + 2(19 - 2y) = 29

x + 38 - 4y = 29

x - 4y = - 9 .....(iv)

from (i), (ii) and (iv) we get

y = 4, x = 7, z = 11

∴ x + y + z = 4 + 7 + 11 = 22

2y + z = 19 .....(ii)

x + 2z = 29 .....(iii)

from (ii) and (iii)

x + 2(19 - 2y) = 29

x + 38 - 4y = 29

x - 4y = - 9 .....(iv)

from (i), (ii) and (iv) we get

y = 4, x = 7, z = 11

∴ x + y + z = 4 + 7 + 11 = 22

QUESTION: 5

If α, β, γ and Δ are the roots of the polynominal equation (x^{2} - 3x + 4)(x^{2} + 2x + 5)= 0, then the quardratic equation whose roots are α + β + γ + Δ and αβγΔ is

Solution:

α + β = 3, α.β = 4

γ + Δ = -2, γ.Δ = 5

α + β + γ + Δ = 3 - 2 = 1

α.β.γ.Δ = 4 × 5 = 20

Required quadratic equation is

x^{2} - (α + β + γ + Δ)x + (αβγΔ) = 0

x^{2} - x + 20 = 0

QUESTION: 6

Diameter of two circular plates are respectively 18cm and 80 cm. The diameter of the plate which has an area equal to the combined area of two given plates is

Solution:

Combined area of two plates = π (9)^{2} + π (40)^{2}

= π (81 + 1600)

= 1681 π cm^{2}.

Let R be the Radius of plate, whose area is combined area of two plates.

Area of plate = πR^{2} = 1681 π

⇒ R^{2} = 1681

⇒ R = 41 cm.

Diameter = 2 x 41 = 82 cm

QUESTION: 7

The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?

Solution:

Let the cricket player makes x runs in his next innings

∴ 32 × 10 + x = 11 × 36

∴ x = 396 - 320 = 76

QUESTION: 8

OABC is a rhombus whose vertices A, B and C lie on a circle with centre at O. If radius of circle is 10cm. The area of the rhombus

Solution:

If A, B, and C lie on the circle, O is the center of the circle, and the radius is 10 cm, then OA, OB, OC, AB, and BC must all measure 10 cm because OA, OB, and OC are all radii, and AB and BC are congruent because of congruent sides of a rhombus.

Hence, the area of the rhombus is twice the area of an equilateral triangle with sides that measure 10 cm.

QUESTION: 9

Diagonals of a rhombus are in the ratio 3:4 and its area is 2400 cm^{2}. Side of the rhombus is

Solution:

Let the diagonals of a rhombus are 3K and 4K. Then

Area of rhombus = 1/2 x product of diagonals

2400 = 1/2 x 3K x 4K

or 400 = K^{2}

or K = 200

∴ The Diagonals are 60 cm and 80 cm

we know that, if a be side of the rhombus and AC and BD be its diagonals then

(AC)^{2} + (BD)^{2} = 4 × a^{2}

or (60)^{2} + (80)^{2} = 4 × a^{2}

or 3600 + 6400 = 4 × a^{2}

or 10000 = 4a^{2}

or 2500 = a^{2}

or a = 50 cm

QUESTION: 10

The average of 5 numbers is 27. If one number is excluded,the average becomes 25. The excluded number is

Solution:

QUESTION: 11

The equation x² + Kxy + y² - 5x - 7y + 6 = 0 represents a pair of st. lines, then K is

Solution:

QUESTION: 12

Find Compound Interest on Rs 15625 for 9 months at 16% p.a compounded quarterly.

Solution:

QUESTION: 13

A shopkeeper marks his goods 20% above the cost price but allows 30% discount for cash. His net loss is

Solution:

Let C.P. of goods = Rs. 100

∴ Marked price = 100 + 20

= Rs 120

∴ Selling price after allowing 30% discount for cash

QUESTION: 14

Which one of the following is the least?

Solution:

QUESTION: 15

Simplify : [(0.2×0.2+0.2×0.02)/(0.044)]

Solution:

QUESTION: 16

In ∆ABC, ∠B = 90�, AB = 6 cm and BC = 8 cm. Its circum radius is

Solution:
Using Pythogorous theorem AC = 10 cm. Circum radius of a right triangle is half the hypotenuse. Hence r = 5 cm.

QUESTION: 17

If the magnitude of angle θ is three times that of the angle φ in the given figure, then ∠φ is equal to

Solution:

QUESTION: 18

If AB and CD are two parallel straight lines and EF is a transversal which cuts AB at P and CD at Q, then the angles APQ and PQD are called :

Solution:

QUESTION: 19

Lines l and m are parallel. If p and q are two distinct lines such that p $\perp $ l and q $\perp $ m, then

Solution:
If two distinct lines are perpendicular to two parallel lines then they are parallel to each other.

QUESTION: 20

The least number, which when divided by 4,5 and 6 leaves the remainder 1,2 and 3 respectively, is

Solution:

QUESTION: 21

How much is the greatest number of three digits less than the smallest number of three digits?

Solution:

QUESTION: 22

The angle of elevation of the top of an incomplete tower at a point 40 m from its base is 45°,If the elevation of the completed tower at the same point is 60°,then the height through which the tower has been raised is

Solution:

QUESTION: 23

When the price of a product was increased by 15% the number sold was decreased by 20%. What was the net effect?

Solution:

QUESTION: 24

Rajeev buys goods worth Rs.6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @10%. Find the amount he will have to pay for the goods.

Solution:

QUESTION: 25

2 pipes A and B can fill a cistern in 20 minutes and 25 minutes respectively, Both are opened together but at the end of 5 minutes B is turned off. Total time taken to fill the cisten is

Solution:

QUESTION: 26

A merchant bought 10 items for Rs 200 each. He sold 5 of them at a profit of 10%. The trader wants to have on overall profit of 15%. The price at which he should sell each of the remaining items is

Solution:

QUESTION: 27

A man sells two articles at Rs 99 each. On one he gains 10% and on other he loses 10%. What is his gain or loss percent on the whole transaction?

Solution:

QUESTION: 28

In ΔABC , if a , b , c , are in A.P . , then tan A/2 tan C/2 =

Solution:

QUESTION: 29

A sum of money is to be divided among P,Q and R in the ratio of 3:7:13 respectively. If the total share of P and Q together is Rs 20,000, what is the difference between the shares of Q and R?

Solution:

QUESTION: 30

Two numbers are in the ratio of 5:7. On diminishing each of them by 40, they become in the ratio 17:27. The difference of the numbers is

Solution:

QUESTION: 31

Let the harmonic means and the geometric mean of two positive numbers be in the ratio 4 : 5. The two numbers are in the ratio

Solution:

QUESTION: 32

A money lender charged Rs 120 as simple interest on a sum of Rs 400 for four months. The rate of interest per annum will be

Solution:

QUESTION: 33

The square root of 0.9 is equal to

Solution:

QUESTION: 34

Points A and B are 60 km apart. One bus starts from A and another bus starts from B at the same time. If they go in the same direction, they meet after 6 hrs and if they go in opposite directions they meet after 2 hrs. The speed of the bus with the greater speed is

Solution:

QUESTION: 35

Rama can complete a job in 8 days. Shyamu can complete the same job in 12 days. However, Monu takes 12 days to complete 3/4th of the same job. Ramu works for 2 days and then leaves a job. The number of days will be taken by Shyamu and Monu to complete the balance together is

Solution:

QUESTION: 36

Solution:

QUESTION: 37

If x sin³α+y cos³α=sinα cosα and x sinα-y cosα=0, then x²+y²=

Solution:

QUESTION: 38

A solid cylindrical block of radius 12 cm and height 18 cm is mounted with a conical block of radius 12 cm and height 5 cm. The total lateral surface of the solid thus formed is :

Solution:

Lateral surface of the solid = Curved surface of cone + Curved surface of cylinder + Surface area of bottom

= πrl + 2πrh + πr^{2}, where h is the height of the cylinder

QUESTION: 39

1+cos2x+cos4x+cos6x=

Solution:

QUESTION: 40

The edges of a cuboid are in the ratio 1:2:3 and its surface area is 88 cm². The volume of the cuboid is :

Solution:

QUESTION: 41

The volumes of two spheres are in the ratio of 64:27. The ratio of their surface areas is :

Solution:

QUESTION: 42

**Study the graph given below to answer these questions.**

**Q. **In which year, were the gross sales proceeds the highest?

Solution:

Sales proceeds in the year

1992 = 180 × 210 = Rs 37800 million

Sales proceed in the year

1993 = 160 × 207 = Rs 33120 million

Sales proceeds in the year

1994 = 150 × 210 = Rs 31500 million

Sales in the year

1995 = 195 × 210 = Rs 40950 million

It is highest in the year 1995

QUESTION: 43

**Study the graph given below to answer these questions.**

**Q. **Which year was the least profitable from the fiscal point of veiw ?

Solution:

QUESTION: 44

**Study the graph given below to answer these questions.**

**Q. **In which year the number of cars sold was the lowest but financial turnover , the maximum ?

Solution:

The year 1996 the number of cars sold is least and financial turnover maximum

QUESTION: 45

**Study the graph given below to answer these questions.**

**Q. **In which year, the maximum profit was generated vis-a-vis in ?

Solution:

In the 1991 profit generated is the maximum

QUESTION: 46

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

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 pie chart given below shows the funding arrangements for National Highways Development Projects: phase I. Study the chart carefully to answer these questions.**

**Q. **Near about 25% of the funding arrangement is through :

Solution:

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