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Practice Test 01-Mathematical Aptitude

Domain: Total Questions: Section Details: Class X 15 Test Code: Total Time: TST2007AT204548630 90 min. Course: Admission Test Maximum Marks: 55.0

Section 1

Subjects: Topics: Total Questions: Class X Maths Linear Equation in One variable, Mensuration, Geometry, Trigonometry 10

Section 2

Subjects: Topics: Total Questions: Class X Maths Trigonometry, Mensuration 5

Section 1

Section Title: Total No. of Questions: Section 1 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). (C).

(B). (D).

Correct Answer

C

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

Explanation

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). (C).

3 hrs 4 hrs

(B). (D).

Correct Answer

A

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)

Explanation

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

is an isosceles triangle. The area

(A). (C).

12 sq. cm 24 sq. cm

(B). (D).

16 sq. cm None of these

Correct Answer

B

Let O be the centre of the circle. From symmetry, let RO = OS = x i.e., RS = 2x Vidyamandir Classes Admission test for IITJEE

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Other sides of the square are also equal to 2x. PR = PQ = QS = 2x Now, . . . . . .(i) angle subtended at circumference is 900 and CE = ED

CED is a right angled triangle [

Hence,

Explanation

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). (C).

30 sec 36 sec

(B). (D).

24 sec 40 sec

Correct Answer

B

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Page 4 of 14

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) travel in opposite directions).

(

Relative speed will be v1 + v2, when they

Similarly , travel in the same direction)

. . (iii) (Relative speed will be

, when they

Explanation

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.

(Marks: 3.0, Negative Marks :...