aieee maths 2010

8/2/2019 aieee maths 2010

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Q. 1. R be a differentiable function with f(0)=-1and f(0)=1,Let g(x)= .then

1. 4

2. 03. 2

4. 4

Sol :

Answer: (1)

Q. 2. There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two

balls are taken out at random and then transferred to the other. The number of ways in which this can be done is.

1. 36

2. 66

3. 108

4. 3

Sol :

Total number of ways

Q. 3. An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn

at random without replacement from the urn. The probability that the three balls have different colours is.

1.

2.

3.

4.

Sol :

Required probability=

Answer: (1)


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Q. 4. For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are

given to be 2 and 4, respectively. The variance of the combined data set is

1.

2.

3.

4.

Sol :

Answer: (1)

Q. 5 . Let be a continuous function defined by . .

Statement-1: , for some . .

Statement-2: for all .

1. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

2. Statement-1 is true, Statement-2 is false.

3. Statement-1 is false, Statement-2 is true.

4. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Sol :


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Answer: (4)

Q. 6. For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false

statement among the following is.

1. There is a regular polygon with




Sol :

If O is centre of polygon and AB is one of the side, then by figure:

Answer : (2)

Q. 7. If two tangents drawn from a point P to the parabola are at right angles, then the locus of p is.

1. 2x +1=0

2. x = -1

3. 2x +1=0

4. x = 1

Sol.

Locus of point P is directrix of parabola i.e., x=-1

Answer: (2)

Q. 8. If the vectors and are mutually orthogonal ,

then

1. (2,-3)

2. (-2,3)

3. (3,-2)

4. (-3,2)


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Sol :

Answer (c)

Q. 9. Consider the following relations:

R = {(x, y) | x, y are real numbers and x=wy for some rational number w };

Then

1. neither R nor S is an equivalence relation

2. S is an equivalence relation but R is not an equivalence relation

3. R and S both are equivalence relations

4. R is an equivalence relation but S is not an equivalence relation

Sol :

R is not equivalence but

S in equivalence

Answer : (2)

Q. 10. be defined by . If f has a local minimum at x = -1 ,

then a possible value of k is.

1. 0

2.

3. -1

4. 1

Sol :


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Answer : (3)

Q. 11. The number of 3 X 3 non-singular matrices, with four entries as 1 and all other entries as 0, is

1. 5

2. 6

3. at least 7

4. less than 4

Sol :

are 6 non-singular matrices because 6 blanks will be filled by 5 zeros and 1 one.

Similarly, are 6 non-singular matrices.

So, required cases are more than 7.

Answer: (3)

Directions: Questions number 12 to 16 are Assertion-Reason type questions. Each of these questions

contains two statements:

Statement-1 : (Assertion) and

Statement-2 : (Reason).

Each of these questions also has four alternative choices, only one of which is the correct answer.

You have to select the Answer.

Q. 12.Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ,20}.

Statement-1: The probability that the chosen numbers when arranged in some order will form an AP is.

Statement-2: If the four chosen numbers form an AP, then the set of all possible values of common difference is






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Sol :

Required probability =

Statement -2 is false because common difference can also be 6.

Answer: (2)

Q. 13. Statement-1: The point is the mirror image of the point

in the plane .

Statement-2: The plane bisects the line segment joining and



3. Statement-1 is false, Statement-2 is true.4. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Sol :

Statement I and II both are true but statement II is not the correct explanation.

Plane is not just bisector but it is perpendicular bisector of AB.

Answer: (1)

Q. 14. Let

Statement-1:

Statement-2:


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Sol :

Answer (2)

Q 15. Let A be a 2 x 2 matrix with non-zero entries and let A2 =1 , where I is 2 x2 identity matrix. Define Tr=(A)

sum of diagonal elements of A and = determinant of matrix A.

Statement-1: = Tr(A) =0

Statement-2: =




4. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

Sol :

Answer: (2)

Q.16. Solution of the differential equation is.

1. ysecx = ten x + c

2. ytanx=secx + c

3. tanx = (secx +c)y

4. secx =(tanx +c )y

Sol :


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Q. 17. The area bounded by the curves

1.

2.

3.

4.

Sol :

Required area =

Answer: (4)

Q. 18.

1. 1

2. 1

3. 2

4. 2


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Sol :

Answer: (2)

Q 19. The number of complex numbers z such that equals.

1. 1

2. 2

3.

4. 0

Sol :

Only one solution and that is circumcentre of triangle formed by (1, 0), (0, 1) and (1, 0).

Answer: (1)

Q. 20. A line AB in three-dimensional space makes angles 45and 120with the positive x-axis and the

positive y-axis respectively. If AB makes an acute angle with the positive z-axis, then equals

1.

2.

3.

4.

Sol :

Answer: (2)

Q. 21. Let and let , where Then

1.

2.

3.


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4.

Sol :

Q. 22. A person is to count 4500 currency notes. Let denote the number of notes he counts in the

minute. If and are in an AP with common difference2, then the time

taken by him to

count all notes is.

1. 34 minutes

2. 125 minutes

3. 135 minutes

4. 24 minutes

Sol :

Answer: (1)

Q. 23 . Let be a positive increasing function with

1.

2.

3. 3

4. 1


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Sol : Clearly

Answer: (4)

Q. 24. Let be a function defined on R such that

equals

1.

2.

3.

4.

Sol:

Answer: (1)

Q. 25. The line L given by passes through the point . The l ine K is parallel to L and has

the equation . Then the distance between L and K is

1.

2.

3.

4.

Sol :


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As L is passing through

Answer: (3)

Q. 26. Let S be a non-empty subset of R. Consider the following statement:

P : There is a rational number such that .Which of the following statements is the negation of the statement P?

1. There is no rational number such that .

2. Every rational number satisfies .

3. and is not rational.

4. There is a rational number such that .

Sol :Answer: (2)

Q. 27. Consider the system of linear equations:

The system has.

1. exactly 3 solutions

2. a unique solution

3. no solution

4. infinite number of solutions

Sol :

Clearly (iii) and (iv) are parallel planes. No solution.

Answer: (3)

Q. 28. Let

.

1.


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2.

3.

4.

Sol :

Q. 29. The equation of the tangent to the curve that is parallel to the x-axis, is.

1. Y =1

2. Y =2

3. Y =3

4. Y =0

Sol:

Q. 30. The circle intersects the line at two distinct points if.

1.

2.

3.

4.

Sol:

Centre of circle (2, 4) and radius is 5.


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Answer: (1)

aieee maths 2010

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