Practice Test 15-Mathematical Aptitude

7/31/2019 Practice Test 15-Mathematical Aptitude

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Practice Test 15-Mathematical Aptitude

Domain: Class X Test Code: TST2007AT20456644 Course:Admission Test

2013

Total Questions: 15 Total Time: 90 min. Maximum Marks: 55.0

Section Details:

Section 1

Subjects: Class X Maths

Topics:General Topic, Quadratic Equations, Linear Equation in Two variables, Linear Equation in One variable, Mensuration,

Geometry, Circle

Total Questions: 10

Section 2

Subjects: Class X Maths

Topics: Mensuration, General Topic

Total Questions: 5

General Instructions:

1. This Test contains 15 questions spread across 2 Section(s).2. There are No Sectional Cut-Offs but the Student is expected to display his/her performance across all the sections.

3. Section Wise time indicates the Ideal Time which should be given to a particular section. You are free to give more or less time than

what is mentioned for a Section, but the Test should be Finished within the Specified time.4. The Test is to be given in One Single Attempt. Once the Test is Started, it can't be Paused for any Breaks.

5. If the Test is Not completed before the Test Time, then as soon as the Time for the Test is completed, the Test would Automatically

End and its Answer file would be generated.6. Use of Calculators and Log Tables is Not Permitted.

7. Use of Unfair means during the Test is Strictly Prohibited.

8. For fair Result and Performance evaluation, Please Do Not discuss the Test with your peers.

Section 1Section Title: Section 1

Total No. ofQuestions:

10

Subjects:Class X Maths

1. If is a factor of , then ?

(A). 4 (B). 0(C). -4 (D). 6

CorrectAnswer

A

Explanation

is a factor of P(a)

But

(a - 3) is a factor of P(a) 3p + q = -12 . . . . . . (i)

(a + 1) is is also factor P(a) -p + q = 20 . . . . . .(ii)

Solving (i) and (ii), we get :

p = -8 and q = 12

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As x > 30

x = 35.

Total numbers of mangos are

=

(Marks: 3.0, Negative Marks : 0.0).

4. In a circle with centre O and radius 'r ', another smaller circle is inscribed with centre D and radius half that of thebigger circle as shown in the figure. Tangents to the smaller circle from a point on the bigger

circle meet at E and F and meet its diameter when produced at B and C. Then, is :

(A). (B).

(C). (D).

CorrectAnswer

C

(by A-A symmetry)

BD = 3BE

Let BE= x BD = 3x

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Explanation

In , (DE)2 + (BE)2 = (BD)2

Therefore, .


5. is a regular hexagon of side I unit. Then, the ratio of the product of lengths

and to the perimeter of the hexagon is :

(A). (B).

(C). 1 : 1 (D). None of these

CorrectAnswer

C

Explanation

A0A1 = 1 ;

;

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Product of these lengths = = 6 and

perimeter of the hexagon = 6

Required ratio = 1 : 1.(Marks: 3.0, Negative Marks : 0.0).

6. Four horses are grazing within a circular field. In the diagram given, AB and CD are the perpendicular diameterof the field with centre O. Horses are tied at P,Q, Rand S such that they can graze only in their respectivecircles. The approximate percentage of area of the circle that can be grazed by the four horses is :

(A). 80 (B). 75

(C). 72 (D). 64

CorrectAnswer

C

Explanation

Let 2rbe the radius of the circular field.

Then r is the radius of the circles with centres Pand R.

Let x be the radius of the circles with centres S and Q.

In right angled

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= [Perimeter of ].


8. a, b and care the sides of a right-angled triangle in which c is the hypotenuse measuring meters. If

side a is increased by and side b is increased by then their total becomes 14 meter. The

values of a and b, if a and b are integers.

(A). 4, 6 meters (B). 3, 6 meters

(C). 6, 8 meters (D). Data insufficient

CorrectAnswer

B

Explanation

a, b and c are sides of right angled triangle

As per information gives i.e.,

Also,

i.e.,

i.e., 14a + 7b = 84

i.e., 2a + b = 12 or

Substituting this value in the equation,

i.e.,

i.e.,

i.e., or a = 3, taking the valid value, we get a = 3m and b = 6m.


9. A 10% sugar solution implies 10 gm sugar is dissolved in 100 gm water. Water evaporates on heating thesolution. On heating, 1 kg of the 10% solution is reduced to 0.5 kg. The concentration now is :

20% 18.2 %

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(A). (B).

(C). 22.2 % (D). 21.18 %

CorrectAnswer

C

Explanation

In a 10% solution, i.e., in 110 gm of solution ; there is 10 gm sugar.

1 kg of the solution has of sugar.

After heating, the amount of solution = 0.5 kg

Amount of water =

Solution percentage is = 22.2%.


10. A circus trope was performing in a village. One evening all the 120 villagers went to the circus and Rs. 120 werecollected in all. The charges were Rs. 5 per male, Rs. 2 per female and 10 paise, per child. The no. of manyladies in the village were :

(A). 13 (B). 17

(C). 30 (D). 19

CorrectAnswer

A

Explanation

Let the number of men, women and children be 'm', 'w' and 'c' respectively,

5m + 2w+ 0.1c= 120 ---------(1)

m + w+ c= 120 ------------(2)

m, w, care integers

0.1cshould be an integer which is possible only ifc is a multiple of 10

So 'c' could be any of 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110 or 120

Considerc= 10

5m + 2w= 119 and m + w= 110.

These equations give m which is not possible

Similarly c= 20, 30,.... 60 gives m negative. Forc= 70, 5m + 2w= 113 and m + w= 50 whichgives non integral value ofm and w. Similarly, m is a non integer value forc= 80, 100, 110 and120. m is an integer only forc= 90

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Substitute forc= 90 in (1) and (2)5m + 2w+ 0.1 (90) = 120m + w+ 90 = 1205m + 2w= 111m + w= 30solve to get w= 13


Section 2Section Title: Section 2

Total No. ofQuestions:

5

Subjects:Class X Maths

11. There is a piece of cheese in the shape of a square. A rat smells the cheese and starts eating it. Rat eats theportion ADFE before sighting a cat and leaves the place. The approximate ratio AC : EC is :

(A). 1.66 (B). 1.73

(C). 1.82 (D). 1.91

Correct

Answer B

As AD is the diagonal of square ABDC, similarlyEF will be the diagonal of square .

Let O be the point of intersection of diagonals of square ABCD.

Now AO = CO and hence .

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Explanation

Given, BD = 10 cm and hence which gives us

And hence

Another simpler and direct solution for the same question....

AC = 10 cm, AE = cm EC = cm.... and solve....


12. 8 sphere of radius 10 cm each are placed on a table with their centres vertically above the vertices of a regularoctagon drawn on the table and each sphere touching its two neighbors. A sphere of radius r is placed in thecentre so that it touches the table and each of the 8 spheres, then r is ?

(A).cm

(B).cm

(C).cm

(D).cm

CorrectAnswer

C

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Explanation

Let radius of the central sphere be 'r' and 'd' be the distance between the centres of

the neighboring sphere and itself.

. . . . .(i)

By cosine rule,

From (i)

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13. A and B are efficient workers and can complete a job in 12 days together. They work for 4 days after which the

project gets stopped for 15 days. After 15 days, th of the remaining work is added. Thereafter, A works thrice

as fast and finishes the work in 6 days. If B had worked alone and at thrice his speed in the latter part, no.of days (approximately) in which B finished the entire work alone would be :

(A). 15 days (B). 22 days

(C). 13 days (D). 17 days

CorrectAnswer

B

Explanation

For According to Question,

. . . . .(i)

In 4 days, they do rd of the work

Work left = 2/3

After 15 days, work left =

. . . . .(ii)

11/9 of the work is completed by A working at thrice the speed in 6 days.

Thus, he completes 11/9 work working at normal speed in 18 days.

He can complete the entire work in

days

B completes the work working at normal speed in days.

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Working at thrice his speed, he completes it in days.


PASSAGE

There are four outlet pipes of the same capacity fixed one above the other to a water tank. The first pipe is at thebottom level and the fourth pipe is at three-fourths of the height of the tank. The third pipe is equidistant from thesecond pipe and the fourth pipe, the second pipe is equidistant from the first and the third. The capacity of eachpipe is such that it can empty a full tank in four hours, whereas one inlet pipe can fill the empty tank in one hour.The pipe is opened to fill the empty tank and after one hour it is closed, then all the outlet pipes are opened

14. Time (in minutes) in which the tank will be empty is :

(A). 125 minutes (B). 90 minutes

(C). 100 minutes (D). 60 minutes

CorrectAnswer

A

Explanation

Let the volume of the tank be 100 litres.

Each outlet empties 25 litre in 1 hour.

Now, outlet 4 works only till upper 1/4th part of the tank is emptied i.e., for 15 minutes.

Now, three outlets work.

They can empty 75 litres from the tank in 60 minutes

They can empty 25 litres from the tank in 20 minutes

Now, two outlets work

They can empty 50 litres in 60 minutes.

They can empty 25 litres in 30 minutes

Now, only the first pipe works till the tank is emptied

i.e., till 25 litres are emptied i.e., for 60 minutes

Total time required = 15 + 20 + 30 + 60 = 125 minutes.(Marks: 5.0, Negative Marks : 0.0).

15. When the tank is full, all the four pipes are opened together and shut after one hour. If the inlet pipe is openednow, the time in which the tank will be full is :

(A). 60 minutes (B). 42.5 minutes

(C). 17.5 minutes (D). 10 minutes

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CorrectAnswer

B

Explanation

In 15 minutes, 25 litres from the tank are emptied.

In the next 20 minutes, 25 litres are emptied

In the next 30 minutes, 25 litres are emptied

For minutes, i.e., for the last 25 minutes, two pipes are open

In that time, litres are emptied

In an hour, litres are emptied

The inlet pipe fills the entire tank in 1 hour.

It fills 70.83 litres in


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Practice Test 15-Mathematical Aptitude

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