practice test 14-mathematical aptitude

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Practice Test 14-Mathematical Aptitude

Domain: Class X Test Code: TST2007AT20451643 Course:Admission Test

2013

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

Section Details:

Section 1

Subjects: Class X Maths

Topics: Geometry, Mensuration, Linear Equation in One variable, Quadratic Equations, General Topic, Polynomial

Total Questions: 10

Section 2

Subjects: Class X Maths

Topics: Trigonometry, 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. of

Questions:10

Subjects:Class X Maths

1. Ram visits the Recreation club after every 5 days, Harish visits after every 24 days, while Rajesh goes thereafter every 9 days. If all three of them met at the club last on a Sunday, The day of the week will all three meetagain is :

(A). Sunday (B). Thursday

(C). Wednesday (D). Monday

CorrectAnswer

C

Explanation

Ram visits every 5 days.

Harish visits every 24 days.

Rajesh visits every 9 days.

All three of them will meet on the LCM of 5, 24 and 9 days.

LCM = days.

weeks 3 days

If they last met on a Sunday, next time they will meet on a Wednesday.

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(Marks: 3.0, Negative Marks : 0.0).

2. A, B, C, D and E starts a partnership firm. Capital contributed by A is 3 times that contributed by D. E contributes

of A's contribution, B contributes of E's contribution and C contributes rd of A's contributed. If the

difference between combined shares of A, D and E and combined shares of B and C in the total profit of the firmis Rs. 13500 out of the total profit of the firm, the combined share of B, C and D in the profit of the firm will be :

(A). Rs. 15750 (B). Rs. 18000

(C). Rs. 13500 (D). Rs. 20250

CorrectAnswer

A

Explanation

Let the capital contributed by D be Rs. x

Capital contributed by




Shares of A, B, C, D and E in total profit are in the ratio

According to given condition,

(Shares of A, D and E) - (shares of B and C) = 13500

Total share of B, C and D in the profit

= Rs. 15750.(Marks: 3.0, Negative Marks : 0.0).

3.

If one root of the equation is m times the other, then = ?

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Explanation .

Thus,


5.When is divided by , then quotient and the reminder are

and , respectively, the value of a is :

(A). 2 (B). 5

(C). 7 (D). 9

CorrectAnswer

A

Explanation Comparing coefficient of


6.

If then

(A). 3 (B). -1

(C). -2 (D). 0

CorrectAnswer

D

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Explanation

Applying Componendo-Dividendo,

Again applying Componendo-Dividendo,


7. The sum of the ages of Mummy, Papa, Sonu, Sona and Sonia now is 96 years. Sonu is the youngest in thefamily. The year Sonu was born, the sum of the ages of all the members of the family was just 66 years. IfPapa's age now is 6 times that of Sonu's present age then Papa's age 10 years hence will be :

(A). 30 years (B). 36 years

(C). 40 years (D). 46 years

CorrectAnswer

D

Explanation

Let Sonu's present age be years.

Then, x years ago the sum of the ages will get reduced by 5x, as there are 5 members in the

family excluding Sonu. Thus, .

Thus, x = 6 and . Thus, Papa's age 10 years hence will be 46 years.


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8. Let ABCD be a rectangle, such that AB = 2BC. An equilateral triangle ABE is drawn as shown in the figure withM as the midpoint of BE. The value of

(A). (B).

(C). (D).

CorrectAnswer

C

Explanation

Let BC = a, Then, AB = 2a.

Also, BM = a (as M is the midpoint of BE)

In , (as ) and BC = a ; BM = a

[ is an isosceles ]


9.A can do as much work in 3 days as B can do in 5 days and B can do as much work in 2 days as C can do in 3days. All of them together can do a certain piece of work in 20 days. The no. of days A alone take to do the workwill be :

(A). 60 days (B). 40 days

(C). 65 days (D). 50 days

CorrectAnswer

B

Explanation

Capacity of A : B = 5 : 3

Capacity of B : C = 3 : 2

Capacity of A : C = 5 : 2

Capacity of (A + B + C) : A (5 + 3 + 2) : 5 = 2 : 1

Hence A will take 40 days.(Marks: 3.0, Negative Marks : 0.0).

10. Three spheres of radius 'r ' are kept inside a cylinder such that two of the spheres are at bottom touching eachother and sides of the cylinder while the third sphere is touching the two bottom spheres and the top of the

is :

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cylinder. Then the volume of the cylinder is :

(A). (B).

(C). (D).

CorrectAnswer

C

Explanation

Let A, B and C be the centres of the three circles.

Volume of the cylinder =

=

=


Section 2Section Title: Section 2

Total No. ofQuestions:

5

Subjects:Class X Maths

11. A quadrilateral is inscribed inside a rectangle such that its vertices are the mid-points of the four sides of therectangle. Similarly, another quadrilateral is inscribed inside the quadrilateral. The ratio of the areas of the innerquadrilateral to that of the outer rectangle is :

(A). 1 : 2 (B). 1 : 3

(C). 1 : 4 (D). None of these

CorrectAnswer

C

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Explanation

Let the length and breadth of the original rectangle ABCD be 2a and 2b, respectively.

Now, HEFG is a rhombus of side length

Also, HF || AB || DC and EG || AD || BC

Now, in , P and Q are midpoints of HE, and EF respectively.

PQ || HF and .

Similarly, PS || EG and

Also PSRQ is a rectangle with length 'a' and breadth 'b'.

Required ratio =


12. When a person is looking at the top of the tower from the foot B of the hill , the angle of elevation is . The

slope of the hill is and units. If the height of the tower is twice the height of the hill, then thedistance between the top of the hill and the tower is :

(A).

units

(B).units

(C).units

(D).units

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CorrectAnswer

A

Explanation

Slope of the hill = 45o

Hence

Also = 20 units

Height of the tower = 2(height of hill) = 40 units

Distance between top of the hill & tower = BM + BD = units


13. A man runs around a curved track as shown below, in which the radius of each semicircle increases by rmeters.

If the man's initial speed is and the man halves his speed after every semicircular track, the time hewill take to complete running around the track if there are 8 such semicircles and the smallest has radius r is :

(A). 22 min 12 sec (B). 29 min 53 sec

(C). 31 min 37 sec (D). 37 min 43 sec

CorrectAnswer

B

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Explanation

Distance covered in the first semicircle =

Time taken = 1 second.

Distance covered in the second track =

Time taken = seconds.

Time taken for the third track = seconds.

For the fourth track = seconds.

For the fifth track = seconds.

For the sixth track = seconds.

For the seventh track = seconds.

For the eighth track = seconds.

Total time = 1793 seconds

= 29 mins 53 seconds.(Marks: 5.0, Negative Marks : 0.0).

14. If , the value of is :

(A). 1 (B).

(C). (D).

CorrectAnswer

D

Explanation......... (i)

Or dividing,

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.......(ii)

Solving (i) and (ii)


15.A line is tangent to three circles with radii as shown. Then, which of the following is true ?

(A). (B).

(C). (D).

CorrectAnswer

D

Explanation

Let c1, c2 and c3 be centres of the circles with radii a, b and c respectively. Draw perpendiculars

c2P, c2Q and c3R as shown.

We have

= . . . . . (i)

Also,

= . . . . . (ii)

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But

i.e.,


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practice test 14-mathematical aptitude

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