Practice Test 01-Mathematical Aptitude

Practice Test 01-Mathematical Aptitude

Domain: Class X Test Code: TST2007AT204548630 Course:Admission Test

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

Section Details:

Section 1

Subjects: Class X Maths

Topics: Linear Equation in One variable, Mensuration, Geometry, Trigonometry

Total Questions: 10

Section 2

Subjects: Class X Maths

Topics: Trigonometry, Mensuration

Total Questions: 5

Section 1Section Title: Section 1

Total No. of

Questions:10

Subjects:Class X Maths

1. A job was wrongly estimated to be completed in 10 days by x machines. By deploying 3 extra machines, the job was completed in 12 days. If only one additional machine was used, the no. of days more than that estimated it has taken to complete the job will be :

(A).

(B).

(C).

(D).

Correct Answer

C

Explanation

Machine-days required = (x + 3).12 = 12x + 36 = (x + 1).d

days.

Extra days = (Marks: 3.0, Negative Marks : 0.0).

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2. Water is pouring into a tank at a constant rate. When the tank is full, 10 pumps of equal capacity empty the tank in 12 hrs, while 15 pumps of the same capacity empty the tank in 6 hrs. The time which 25 pumps of the same capacity take to empty the tank, if the tank is initially full, will be : (All the pipes pouring water into the tank are always open)

(A). 3 hrs (B).

(C). 4 hrs (D).

Correct Answer

A

Explanation

If rate of filling the tank is 1/y per hr and each pump can empty it with a rate 1/x per hr then,

. . . . .(i)

. . . . (ii)

Solving (i) and (ii) we get, x = 60 and y = 12

If there are 25 pumps then of tank will be empty in 1hr

the entire tank will be empty in 3 hrs. (Marks: 3.0, Negative Marks : 0.0).

3. In the above figure, "CD " is the diameter, PQSR is a square and a is an isosceles triangle. The area

of the square, if area of the biggest triangle is 36 sq. cm is :

(A). 12 sq. cm (B). 16 sq. cm

(C). 24 sq. cm (D). None of these

Correct Answer

B

Let O be the centre of the circle.

From symmetry, let RO = OS = x

i.e., RS = 2x

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Explanation

Other sides of the square are also equal to 2x.

PR = PQ = QS = 2x

Now, . . . . . .(i)

CED is a right angled triangle [ and CE = ED

Hence,

From triangle EPL : PL = EL = x

From equation (i) . . . . . . (ii)

From question, we know that area of triangle is 36 sq. cm.

From (ii), we have, .

One side of the square =

Hence, area of the square = 42 = 16 sq. cm

(Marks: 3.0, Negative Marks : 0.0).

4. Two trains going on a parallel line in opposite directions take 10 seconds to cross each other. But if they are going in the same direction the longer train crosses the shorter train in 30 seconds. If the length of the longer train is decreased by 50%, the time taken to cross the shorter train while going in the same direction decreases by 8 seconds. The time taken by the longer train to cross a tunnel twice its length, if the difference between the length of the trains is 25 m is :

(A). 30 sec (B). 24 sec

(C). 36 sec (D). 40 sec

Correct Answer

B

angle subtended at circumference is 900

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Explanation

Let l1, v1 and l2, v2 be the lengths and speeds of the two trains. According to the question :

. . . . . .(i)

When, they are moving in opposite directions

. . . . (ii) ( Relative speed will be v1 + v2, when they

travel in opposite directions).

Similarly , . . (iii) (Relative speed will be , when they

travel in the same direction)

Again, when the length of the longer train will be decreased by 50% then

. . . . .(iv)

Solving equations (ii), (iii) and (iv) we get :

, ,

Time taken by longer train to cross the tunnel double its length = (length of tunnel + length of

train) / speed

seconds.


5. I see a bird flying away at a constant speed of 1.7568 kmph in the sky. The angle of elevation is . After 1/2

minute, I see the bird again and this time the angle of elevation is . The perpendicular (horizontal) distance

of the bird from me now will be :

(A). 10 m (B).

(C). 20 m (D).

Correct Answer

D

Let A be the initial position of the bird and B be the final position of the bird, i.e., after 30 seconds

Let E be my position (my eye).

Time required to cover the distance. From A to B = 30 seconds.

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Explanation

Constant speed of the bird = 1.7568 kmph. =

Distance traveled by Bird in 30 seconds.=

AB = DC = 14.64 m and AD = BC

In right angled

In right angled

As EC = ED + DC

The perpendicular distance of the bird from me = .


6. A hoarding is fitted above a building. The height of the building is 12 m. When I look at the lights fitted on top of the hoarding from a nearby bus stop, the angle of elevation is and when I look at the top of the building

(terrace) from the same bus stop, the angle of elevation is . If the height of a flat on each floor is equal to

the height of the hoarding, the maximum number of floors in the building are : ( )

(A). 2 (B). 4

(C). 5 (D). 7

Correct Answer

C

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Explanation

Let AB denote the height of the building = 12 m and AC denotes the hoarding fitted on top of the building.


7. A robber received one third of a loot as his share. He spent Rs.144 on food and drinks and then donated half of

the remained share to a temple. The balance left with him was 1/24th of the total loot. The robber's share was :

(A). Rs.1728 (B). Rs.576

(C). Rs.192 (D). Rs.432

Correct Answer

C

Explanation

Let the total loot be 'x' rupees.

Robbers share = . (Marks: 3.0, Negative Marks : 0.0).

8.

In bisectors of and meet each other at X. Line AX cuts side BC at Y. Hence, = ?

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(A).

(B).

(C).

(D). None of these

Correct Answer

B

Explanation

In is the bisector of .

Similarly, in is the bisector of

(equal ratios)

.


9. A three-digit number in which the digit in the units place is the smallest of the three digits is such that the sum of the squares of the digits is 149. If each of the digits is replaced by its predecessor, the new number formed has two digits common with the original number. The digit in the units place of the original number is :

(A). 4 (B). 5

(C). 6 (D). 7

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Correct Answer

C

Explanation

Let the three digit number be 100x + 10y + z ..........(i)

According to question

When elements are replaced by their predecessors, the number formed is 100(x - 1) + 10(y - 1) + (z - 1) ....... (ii)

(i) and (ii) has two digits same, then the digits used should be consecutive.

Using (A), and considering digits to be n - 1, n and n + 1, we have

So, n = 7

Hence, digits are 6,7 and 8

Min {6,7,8} = 6 (Marks: 3.0, Negative Marks : 0.0).

10. As per the figure, two circles intersect each other at points P and Q. Point A is on PQ produced and AMD and ASR are the secants to the circles. If AM = 3, MD = 5, AS = 4, The value of SR is :

(A). 2 (B). 1

(C). 4 (D). 3

Correct Answer

A

AD = AM + MD = 3 + 5 = 8

and

As per theorem of secants from an external point.

. . . . . .(i)

.......(A)

3n2 + 2 = 149

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Explanation

. . . . . .(ii)

From (i) and (ii) :

and .


Section 2Section Title: Section 2

Total No. of

Questions:5

Subjects:Class X Maths

11. One cubic meter piece of copper is melted and recast into a bar 36 meters long with a square cross-sectional

area. An exact cube is cut off from this bar. The cost of this cube, if 1 m3 of copper costs Rs. 216 will be :

(A). Rs.1.50 (B). Rs.1.75

(C). Rs.1.00 (D). Rs.1.36

Correct Answer

C

Explanation

Volume of the bar = Volume of the piece of copper.

Length of the bar = 36m

Cross sectional area of the bar is

Side of square cross-section =

Volume of the cube which is cut from the bar =

Cost is .


12.

In the given figure ABCD is a square with side 15 and BCE is an equilateral triangle. The ratio of the shaded

region to the unshaded region is :

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(A).

(B). 1 : 2

(C). 2 : 1 (D).

Correct Answer

A

Explanation

Area of sq units

A (unshaded region) =

A (shaded region) = A (entire figure)

The required ratio = . (Marks: 5.0, Negative Marks : 0.0).

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13. Lines l and m are tangents to the circles as shown. Segment AB is divided in the ratio 3 : 1 by point O (AO >

OB). The distance between the centres C1 and C2 is 20 cm. . The area of the shaded region

is :

(A). 62.5 cm2 (B). 49.6 cm2

(C). 45.75 cm2 (D). 56.25 cm2

Correct Answer

C

Explanation

Also,

(By A A A similarity)

Since

Then

C1O = 15 cm and C2O = 5 cm

and are triangles.

and

Also, and

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Area of shaded region

=

=

=

=

=


14. In the given figure, there are two concentric circles with radii 10 cm and 20 cm. Also, AB and AC are tangents to the circle with radius 10 cm at P and Q respectively, PQ = 19 cm and BC is a tangent to the circle with radius 20

cm. The area of in (cm2) is : (Take and ).

(A). 885.5 cm2 (B). 306.5 cm2

(C). 353.5 cm2 (D). 994.5 cm2

Correct Answer

A

From the figure, is a right angled triangle

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Explanation

.

BCRS is a rectangle, cm.

Now, and also

This means PQ and BC are parallel.

Now, ; where x = AM


15.

Four points L, M, N and P are chosen on the circumference of a circle as shown in the figure. If the length of

arcs : where R is the radius of the circle. The measure of the angle is:

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(A). 112.5o (B). 135o

(C). 90o (D). 120o

Correct Answer

C

Explanation

Length of arc MN = implies i.e. M, A, N are collinear and MN is the

diameter of the circle.

We know that P lies on semi-circular arc. So,

The length of arc NP and arc LM were not needed and were given just to confuse. (Marks: 5.0, Negative Marks : 0.0).

Page 14 of 14


Practice Test 01-Mathematical Aptitude

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