## MATHEMATICS- PAGE 3

1. A person deposited Rs. 4000 in simple interest rate for 2 months. If he gets Rs. 60 as interest, what is the rate of interest ?

(A) 15% (B) 9% (C) 7.5% (D) 18%

Ans: B

2. Which is not a prime number ?

(A) 61 (B) 47 (C) 51 (D) 59

Ans: C

3. If 2a=3b=4c then a : b : c = __________.

(A) 6 : 4 : 3 (B) 2 : 3 : 4 (C) 3 : 4 : 6 (D) 4 : 3 : 2

Ans: A

4. Sum of two consecutive natural numbers is 31. What is the difference of their squares ?

(A) 961 (B) 31 (C) 1 (D) 62

Ans: B

5. If 13, X, 22 are three consecutive terms of an AP. What is the value of X ?

(A) 17.5 (B) 17 (C) 35 (D) 4.5

Ans: A

6. If the cost price of 15 books is equal to the selling price of 12 books. What is the profit percentage ?

(A) 20% (B) 50% (C) 30% (D) 25%

Ans: D

7. 15 members can complete a work in 12 days. How many more members are needed to complete this work in 9 days ?

(A) 18 (B) 3 (C) 5 (D) 20

Ans: C

(A) 15% (B) 9% (C) 7.5% (D) 18%

Ans: B

2. Which is not a prime number ?

(A) 61 (B) 47 (C) 51 (D) 59

Ans: C

3. If 2a=3b=4c then a : b : c = __________.

(A) 6 : 4 : 3 (B) 2 : 3 : 4 (C) 3 : 4 : 6 (D) 4 : 3 : 2

Ans: A

4. Sum of two consecutive natural numbers is 31. What is the difference of their squares ?

(A) 961 (B) 31 (C) 1 (D) 62

Ans: B

5. If 13, X, 22 are three consecutive terms of an AP. What is the value of X ?

(A) 17.5 (B) 17 (C) 35 (D) 4.5

Ans: A

6. If the cost price of 15 books is equal to the selling price of 12 books. What is the profit percentage ?

(A) 20% (B) 50% (C) 30% (D) 25%

Ans: D

7. 15 members can complete a work in 12 days. How many more members are needed to complete this work in 9 days ?

(A) 18 (B) 3 (C) 5 (D) 20

Ans: C

8:-The complete bipartite graph `K_(7,5)` has

A:-2 edges

B:-12 edges

C:-35 edges

D:-`7^(5)` edges

Ans: C

9:-Perimeter of the cardioid r = 1 – cos`Theta` is

A:-1

B:-2

C:-4

D:-8

Ans: D

10:-Area of the surface generated by revolving the curve y = x about the x-axis from x = 0 to x = 1 is

A:-2`pi`

B:-`2sqrt(2)pi`

C:-`sqrt(2)pi`

D:-`4pi`

Ans: B

11:-In Boolean algebra the law a+(a*b)=a is known as

A:-idempotent law

B:-distributive law

C:-boundedness law

D:-absorption law

Ans: D

12:-Transcendence of e was proved by

A:-Euler

B:-Cauchy

C:-Euclid

D:-Hermite

Ans: D

13:-Which of the following is false ?

A:-`2^(13)-=1(mod3)`

B:-`3^(13)-=1(mod2)`

C:-`13^(2)-=1(mod3)`

D:-`13^(3)-=1(mod2)`

Ans: A

14:-Degree of the field extension `Q(sqrt(3)+sqrt(2))` over `Q(sqrt(3))` is

A:-1

B:-2

C:-3

D:-4

Ans: B

15:-Number of subgroups of `ZZ_(18)` is

A:-2

B:-3

C:-6

D:-18

Ans: C

16:-Set of all integers `ZZ` is

A:-an integral domain but not a field

B:-a division ring but not a field

C:-a strictly skew field but not a field

D:-a division ring but not an integral domain

Ans: A

17:-Number of generators of `ZZ_(20)` is

A:-1

B:-2

C:-4

D:-8

Ans: D

18:-Let `RR` be the ring of real numbers. Units of `RR` are

A:-0

B:-elements of `RR-{0} `

C:-1

D:-elements of `RR-{1}`

Ans: B

19:-Which of the following is false ?

A:-Every integral domain is a field

B:-Every field is an integral domain

C:-It p is a prime, then `ZZ_(p)` is a field

D:-Every finite integral domain is a field

Ans: A

20:-The remainder of `3^(50)` when divided by 13 is

A:-6

B:-9

C:-3

D:-0

Ans: B

21:-Bolzano-Weierstrass theorem

A:-Every convergent sequence of real numbers is bounded

B:-A bounded sequence of real numbers has a convergent subsequence

C:-Every sequence of real numbers has a convergent subsequence

D:-A sequence of non-negative real numbers is bounded if and only if it is convergent

Ans: B

22:-|z+3i| + |z–3i| = 8 represents

A:-a straight line

B:-a circle

C:-a hyperbola

D:-an ellipse

Ans: D

A:-2 edges

B:-12 edges

C:-35 edges

D:-`7^(5)` edges

Ans: C

9:-Perimeter of the cardioid r = 1 – cos`Theta` is

A:-1

B:-2

C:-4

D:-8

Ans: D

10:-Area of the surface generated by revolving the curve y = x about the x-axis from x = 0 to x = 1 is

A:-2`pi`

B:-`2sqrt(2)pi`

C:-`sqrt(2)pi`

D:-`4pi`

Ans: B

11:-In Boolean algebra the law a+(a*b)=a is known as

A:-idempotent law

B:-distributive law

C:-boundedness law

D:-absorption law

Ans: D

12:-Transcendence of e was proved by

A:-Euler

B:-Cauchy

C:-Euclid

D:-Hermite

Ans: D

13:-Which of the following is false ?

A:-`2^(13)-=1(mod3)`

B:-`3^(13)-=1(mod2)`

C:-`13^(2)-=1(mod3)`

D:-`13^(3)-=1(mod2)`

Ans: A

14:-Degree of the field extension `Q(sqrt(3)+sqrt(2))` over `Q(sqrt(3))` is

A:-1

B:-2

C:-3

D:-4

Ans: B

15:-Number of subgroups of `ZZ_(18)` is

A:-2

B:-3

C:-6

D:-18

Ans: C

16:-Set of all integers `ZZ` is

A:-an integral domain but not a field

B:-a division ring but not a field

C:-a strictly skew field but not a field

D:-a division ring but not an integral domain

Ans: A

17:-Number of generators of `ZZ_(20)` is

A:-1

B:-2

C:-4

D:-8

Ans: D

18:-Let `RR` be the ring of real numbers. Units of `RR` are

A:-0

B:-elements of `RR-{0} `

C:-1

D:-elements of `RR-{1}`

Ans: B

19:-Which of the following is false ?

A:-Every integral domain is a field

B:-Every field is an integral domain

C:-It p is a prime, then `ZZ_(p)` is a field

D:-Every finite integral domain is a field

Ans: A

20:-The remainder of `3^(50)` when divided by 13 is

A:-6

B:-9

C:-3

D:-0

Ans: B

21:-Bolzano-Weierstrass theorem

A:-Every convergent sequence of real numbers is bounded

B:-A bounded sequence of real numbers has a convergent subsequence

C:-Every sequence of real numbers has a convergent subsequence

D:-A sequence of non-negative real numbers is bounded if and only if it is convergent

Ans: B

22:-|z+3i| + |z–3i| = 8 represents

A:-a straight line

B:-a circle

C:-a hyperbola

D:-an ellipse

Ans: D

23:-If f(z) is continuous in a simply connected domain D and if `oint_(C)f(z)dz=0` for every closed path in D, then

f(z) is analytic in D

A:-Liouville's theorem

B:-Morera's theorem

C:-Cauchy's integral theorem

D:-Cauchy's integral formula

Ans: B

24:-At z = 0, the function `f(z)=e^((1)/(z))` has

A:-a removable singularity

B:-a simple pole

C:-an essential singularity

D:-no singular point

Ans: C

25:-Let `f(z)=(1-cosz)/(z^(5))` . Then f(z) has

A:-a pole of order 3 and residue `(-1)/(24)` at z = 0

B:-a pole of order 5 and residue `(-1)/(24)` at z = 0

C:-a pole of order 3 and residue `(1)/(5)` at z = 0

D:-a pole of order 5 and residue `(1)/(5)` at z = 0

Ans: A

26:-Which of the following is false ?

A:-Every order topology is Hausdorff

B:-Subspace of a Hausdorff space is Hausdorff

C:-Every Hausdorff space is normal

D:-Product of two Hausdorff space is Hausdorff

Ans: C

27:-Deleted comb space is

A:-connected and path connected

B:-connected but not path connected

C:-not connected but path connected

D:-neither connected nor path connected

Ans: B

28:-Which of the following need not be a normal space ?

A:-product of two normal spaces

B:-a metrizable space

C:-a compact Hausdorff space

D:-a regular space with a countable basis

Ans: A

29:-Which of the following is false ?

A:-the one point compactification of the real line `RR` is homeomorphic to an ellipse

B:-the one point compactification of the open interval (0, 1) is homeomorphic to closed interval [0, 1]

C:-the one point compactification of the open interval (0, 1) is homeomorphic to the circle `S^(1)`

D:-the one point compactification of `RR^(2)` is homeomorphic to the sphere `S^(2)`

Ans: B

30:-Which of the following is not a topological property ?

A:-length and area

B:-connectedness

C:-continuity

D:-compactness

Ans: A

31:-The area included between one arch of the curve y=sin x and the x-axis is

A:--2

B:-2

C:-0

D:--1

Ans: B

f(z) is analytic in D

A:-Liouville's theorem

B:-Morera's theorem

C:-Cauchy's integral theorem

D:-Cauchy's integral formula

Ans: B

24:-At z = 0, the function `f(z)=e^((1)/(z))` has

A:-a removable singularity

B:-a simple pole

C:-an essential singularity

D:-no singular point

Ans: C

25:-Let `f(z)=(1-cosz)/(z^(5))` . Then f(z) has

A:-a pole of order 3 and residue `(-1)/(24)` at z = 0

B:-a pole of order 5 and residue `(-1)/(24)` at z = 0

C:-a pole of order 3 and residue `(1)/(5)` at z = 0

D:-a pole of order 5 and residue `(1)/(5)` at z = 0

Ans: A

26:-Which of the following is false ?

A:-Every order topology is Hausdorff

B:-Subspace of a Hausdorff space is Hausdorff

C:-Every Hausdorff space is normal

D:-Product of two Hausdorff space is Hausdorff

Ans: C

27:-Deleted comb space is

A:-connected and path connected

B:-connected but not path connected

C:-not connected but path connected

D:-neither connected nor path connected

Ans: B

28:-Which of the following need not be a normal space ?

A:-product of two normal spaces

B:-a metrizable space

C:-a compact Hausdorff space

D:-a regular space with a countable basis

Ans: A

29:-Which of the following is false ?

A:-the one point compactification of the real line `RR` is homeomorphic to an ellipse

B:-the one point compactification of the open interval (0, 1) is homeomorphic to closed interval [0, 1]

C:-the one point compactification of the open interval (0, 1) is homeomorphic to the circle `S^(1)`

D:-the one point compactification of `RR^(2)` is homeomorphic to the sphere `S^(2)`

Ans: B

30:-Which of the following is not a topological property ?

A:-length and area

B:-connectedness

C:-continuity

D:-compactness

Ans: A

31:-The area included between one arch of the curve y=sin x and the x-axis is

A:--2

B:-2

C:-0

D:--1

Ans: B

32. If f is measurable, then |f| is

(a) not measurable (b) discontinuous

(c) measurable (d) not uniformly continuous

Ans: C

33. Every closed subset of a compact metric space is

(a) Compact (b) Bounded

(c) Complete (d) None of these

Ans: A

34. The dimension of a vector space V of all scalar matrices of type n × n is

(a) 0 (b) n

(c) n × n (d) 1

Ans: D

35. If f and g be bounded functions defined on [a, b] and let p be any partition of [a, b], then which of the following is true ?

(a) U(p, f + g) ≤ U(p, f) + U(p, g)

(b) U(p, f + g) ≥ U(p, f) + U(p, g)

(c) U(p, f + g) ≤ L(p, f) + L(p, g)

(d) None of the above

Ans: A

36. A division ring is

(a) a field

(b) an integral domain

(c) a ring with division as one operation

(d) None of the above

Ans: D

37. If H is a normal subgroup of a finite group G and O(G/H) = 3, O(G) = 12 then O(H) is

(a) 4 (b) 3

(c) 2 (d) 1

Ans: A

38. Every finite group is isomorphic to which of the following ?

(a) an abelian group (b) a permutation group

(c) a cyclic group (d) the group (Z, +)

Ans: B

39. The theorem :

“A bounded entire function is constant”.

is named after which of the following mathematician ?

(a) Cauchy (b) Schwarz

(c) Liouville (d) Morera

Ans: C

40. Let m be a positive integer and x, y be integers then which of the following is not true :

(a) (x + y) mod m = (x mod m + y mod m) mod m

(b) (x – y) mod m = (x mod m + (–y mod m)) mod m

(c) (x ⋅ y) mod m = ((x mod m) (y mod m)) mod m

(d) (x – y) mod m = (x mod m – (–y mod m)) mod m

Ans: D

41. In solving a system of non-homogeneous linear equations AX = B by Gauss-elimination method the co-efficient matrix A is reduced to

(a) a diagonal matrix (b) a lower triangular matrix

(c) an upper triangular matrix (d) a scalar matrix

Ans: C

42. The order of convergence in Newton-Raphson method for solving f(x) = 0 is

(a) 1 (b) 2

(c) 3 (d) 4

Ans: B

43. Mean and standard deviation of 200 items were 60 and 20, respectively. At the time of checking it was found that two values were wrongly recorded as 3 and 67 instead of 13 and 17. The correct mean and standard deviation, respectively, are

(a) 49.8, 20.09 (b) 51.8, 12.09

(c) 59.8, 20.09 (d) 61.8, 31.09

Ans: C

44. If for a series the arithmetic mean is 25 and harmonic mean is 9 then the geometric mean of the series is

(a) 12 (b) 13

(c) 14 (d) 15

Ans: D

45. Rejecting a true hypothesis is

(a) Type II error (b) Type I error

(c) Type I and II error (d) None of the above

Ans: B

46. The arithmetic mean of two numbers is 10 and their geometric mean is 8. Then the numbers are

(a) 16, 14 (b) 10, 10

(c) 16, 4 (d) 4, 8

Ans: C

47. In a binomial distribution p =1/4, q =3/4, n = 12 then the ratio Arithmetic mean : Standard deviation is :

(a) 3 : 1 (b) 1 : 3

(c) 1 : 2 (d) 2 : 1

Ans: D

48. For a normal distribution mode = 20, then it’s A. mean is

(a) 20 (b) 40

(c) 15 (d) None of these

Ans: A

49. For a certain normal distribution, the first moment about the value 8 is 22 and the fourth moment about the value 30 is 243. Then co-efficient of variation of the distribution is

(a) 5% (b) 10%

(c) 15% (d) 20%

Ans: B

50. The economic order quantity for the inventory problem :

Annual demand = 36000 units

Cost per unit = ` 1

Ordering cost = ` 25

Cost of capital = 15%

Store charge = 5%

is :

(a) 300 units (b) 30 units

(c) 130 units (d) 3000 units

Ans: D

51. The re-order level from the following data :

Annual Demand = 2400 units,

Lead Time =1/2 month,

is

(a) 10 units (b) 15 units

(c) 100 units (d) 1200 units

Ans: C

52. If m is the number of rows and n is the number of columns in a contingency table then degree of freedom is

(a) (m – 1) (b) mn – 1

(c) (m – 1) (n – 1) (d) mn

Ans: C

53. Solution of the linear programming problem :

Min : x + y,

Subject to 2x + y ≥ 8

2x + 5y ≥ 10

x, y ≥ 0

is :

(a) 4.25 (b) 8.0 (c) 4.5 (d) 5.0

Ans: A

54. The MODI method to solve transportation problem uses the stepping stones path

(a) to calculate the marginal cost of unused cells.

(b) to determine how many times to allocate to the selected unused cell.

(c) to determine the values of the row and column index numbers.

(d) to none of the above.

Ans: B

(a) not measurable (b) discontinuous

(c) measurable (d) not uniformly continuous

Ans: C

33. Every closed subset of a compact metric space is

(a) Compact (b) Bounded

(c) Complete (d) None of these

Ans: A

34. The dimension of a vector space V of all scalar matrices of type n × n is

(a) 0 (b) n

(c) n × n (d) 1

Ans: D

35. If f and g be bounded functions defined on [a, b] and let p be any partition of [a, b], then which of the following is true ?

(a) U(p, f + g) ≤ U(p, f) + U(p, g)

(b) U(p, f + g) ≥ U(p, f) + U(p, g)

(c) U(p, f + g) ≤ L(p, f) + L(p, g)

(d) None of the above

Ans: A

36. A division ring is

(a) a field

(b) an integral domain

(c) a ring with division as one operation

(d) None of the above

Ans: D

37. If H is a normal subgroup of a finite group G and O(G/H) = 3, O(G) = 12 then O(H) is

(a) 4 (b) 3

(c) 2 (d) 1

Ans: A

38. Every finite group is isomorphic to which of the following ?

(a) an abelian group (b) a permutation group

(c) a cyclic group (d) the group (Z, +)

Ans: B

39. The theorem :

“A bounded entire function is constant”.

is named after which of the following mathematician ?

(a) Cauchy (b) Schwarz

(c) Liouville (d) Morera

Ans: C

40. Let m be a positive integer and x, y be integers then which of the following is not true :

(a) (x + y) mod m = (x mod m + y mod m) mod m

(b) (x – y) mod m = (x mod m + (–y mod m)) mod m

(c) (x ⋅ y) mod m = ((x mod m) (y mod m)) mod m

(d) (x – y) mod m = (x mod m – (–y mod m)) mod m

Ans: D

41. In solving a system of non-homogeneous linear equations AX = B by Gauss-elimination method the co-efficient matrix A is reduced to

(a) a diagonal matrix (b) a lower triangular matrix

(c) an upper triangular matrix (d) a scalar matrix

Ans: C

42. The order of convergence in Newton-Raphson method for solving f(x) = 0 is

(a) 1 (b) 2

(c) 3 (d) 4

Ans: B

43. Mean and standard deviation of 200 items were 60 and 20, respectively. At the time of checking it was found that two values were wrongly recorded as 3 and 67 instead of 13 and 17. The correct mean and standard deviation, respectively, are

(a) 49.8, 20.09 (b) 51.8, 12.09

(c) 59.8, 20.09 (d) 61.8, 31.09

Ans: C

44. If for a series the arithmetic mean is 25 and harmonic mean is 9 then the geometric mean of the series is

(a) 12 (b) 13

(c) 14 (d) 15

Ans: D

45. Rejecting a true hypothesis is

(a) Type II error (b) Type I error

(c) Type I and II error (d) None of the above

Ans: B

46. The arithmetic mean of two numbers is 10 and their geometric mean is 8. Then the numbers are

(a) 16, 14 (b) 10, 10

(c) 16, 4 (d) 4, 8

Ans: C

47. In a binomial distribution p =1/4, q =3/4, n = 12 then the ratio Arithmetic mean : Standard deviation is :

(a) 3 : 1 (b) 1 : 3

(c) 1 : 2 (d) 2 : 1

Ans: D

48. For a normal distribution mode = 20, then it’s A. mean is

(a) 20 (b) 40

(c) 15 (d) None of these

Ans: A

49. For a certain normal distribution, the first moment about the value 8 is 22 and the fourth moment about the value 30 is 243. Then co-efficient of variation of the distribution is

(a) 5% (b) 10%

(c) 15% (d) 20%

Ans: B

50. The economic order quantity for the inventory problem :

Annual demand = 36000 units

Cost per unit = ` 1

Ordering cost = ` 25

Cost of capital = 15%

Store charge = 5%

is :

(a) 300 units (b) 30 units

(c) 130 units (d) 3000 units

Ans: D

51. The re-order level from the following data :

Annual Demand = 2400 units,

Lead Time =1/2 month,

is

(a) 10 units (b) 15 units

(c) 100 units (d) 1200 units

Ans: C

52. If m is the number of rows and n is the number of columns in a contingency table then degree of freedom is

(a) (m – 1) (b) mn – 1

(c) (m – 1) (n – 1) (d) mn

Ans: C

53. Solution of the linear programming problem :

Min : x + y,

Subject to 2x + y ≥ 8

2x + 5y ≥ 10

x, y ≥ 0

is :

(a) 4.25 (b) 8.0 (c) 4.5 (d) 5.0

Ans: A

54. The MODI method to solve transportation problem uses the stepping stones path

(a) to calculate the marginal cost of unused cells.

(b) to determine how many times to allocate to the selected unused cell.

(c) to determine the values of the row and column index numbers.

(d) to none of the above.

Ans: B

55. The sum of the first 10 terms common to the series 17, 21, 25 .......... and 16, 21, 26 .......... is :

(A) 1100 (B) 1010 (C) 1110 (D) 1200

Ans: C

56. The radius of the sphere through the points (4, 3, 0), (0, 4, 3), (0, 5, 0) and (4, 0, 3) is :

(A) 5 (B) 7 (C) 4 (D) 6

Ans: A

57. The maximum value of xy+5 subject to 2x+y=4 is :

(A) 4 (B) 3 (C) 8 (D) 7

Ans: D

58. If 3 distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is :

(A) 4/1155

(B) 4/1255

(C) 3/1155

(D) 3/1255

Ans: A

59. The number of triangles which can be formed by using the vertices of a regular polygon of (n+3) sides is 220. Then the value of n is :

(A) 10 (B) 8 (C) 11 (D) 9

Ans: D

60. Mean deviation of the data 3, 10, 10, 4, 7, 10, 5, 7 from mean is :

(A) 2 (B) 2.25 (C) 3 (D) 3.25

Ans: B

61. The number of 4 digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without repetition is :

(A) 420 (B) 300 (C) 120 (D) 320

Ans: A

62. If a matrix A is Symmetric as well as Skew Symmetric, then :

(A) A is a diagonal matrix (B) A is a unit matrix

(C) A is a triangular matrix (D) A is a null matrix

Ans: D

(A) 1100 (B) 1010 (C) 1110 (D) 1200

Ans: C

56. The radius of the sphere through the points (4, 3, 0), (0, 4, 3), (0, 5, 0) and (4, 0, 3) is :

(A) 5 (B) 7 (C) 4 (D) 6

Ans: A

57. The maximum value of xy+5 subject to 2x+y=4 is :

(A) 4 (B) 3 (C) 8 (D) 7

Ans: D

58. If 3 distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is :

(A) 4/1155

(B) 4/1255

(C) 3/1155

(D) 3/1255

Ans: A

59. The number of triangles which can be formed by using the vertices of a regular polygon of (n+3) sides is 220. Then the value of n is :

(A) 10 (B) 8 (C) 11 (D) 9

Ans: D

60. Mean deviation of the data 3, 10, 10, 4, 7, 10, 5, 7 from mean is :

(A) 2 (B) 2.25 (C) 3 (D) 3.25

Ans: B

61. The number of 4 digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without repetition is :

(A) 420 (B) 300 (C) 120 (D) 320

Ans: A

62. If a matrix A is Symmetric as well as Skew Symmetric, then :

(A) A is a diagonal matrix (B) A is a unit matrix

(C) A is a triangular matrix (D) A is a null matrix

Ans: D

63. Solutions of the system of equations 3x + y + 2z = 3, 2x – 3y – z = – 3, x + 2y + z = 4 are

A:-x = 1 y = 2 z = – 1

B:-x = 2, y = 3, z = 1

C:-x = 1, y = 2, z = 3

D:-x = 1, y = 4, z = 0

Correct Answer:- Option-A

64. The term independent of x in the expansion of `(x^(2)+1/x)^(6)` is

A:-0

B:-12

C:-10

D:-15

Correct Answer:- Option-D

65. If A + B = 45°, then (1 + tanA) (1 + tanB) is equal to` `

A:-2

B:-1

C:-4

D:-5

Correct Answer:- Option-A

66. Equation to the line passing through the point (– 3, 2) and perpendicular to the line 4x + 2y + 5 = 0 is

A:-x – 3y + 2 = 0

B:-x – 2y + 7 = 0

C:-x + y = 0

D:-x – y = 0

Correct Answer:- Option-B

67:-The maximum number of eigen values of an n `xx` n matrix is

A:-n B:-`n^(2)` C:-2n D:-`(1)/(2)n(n-1)`

Ans: A

68:-Which among the following is a mathematically incorrect operation ?

A:-grad div B:-div curl C:-grad curl D:-curl grad

Ans: C

69:-In cylindrical co-ordinates, where surface `rho` = 3 and z = 2 intersect is

A:-a finite plane B:-a semi infinite plane C:-a cylinder D:-a circle

Ans: D

70:-For a Fourier transform, which of the following statements is correct ``?

A:-FT of an even function is even and that of an odd function is odd

B:-FT of an even function is odd and the of an odd function is even

C:-FT of an even function is even and that of an odd function is even

D:-FT of an even function is odd and that of an odd function is odd

Ans: A

71:-The complex function `Z^((1)/(2))` is

A:-single valued B:-double valued

C:-n-valued D:-2n-valued

Ans: B

72:-If `A_(ij)` and `B^(ik)` are two tensors and `A_(ij)B^(ik)=delta^(k)_j` the Kronecker Delta, then `A_(ij)` and `B^(ik)` are

A:-associate tensors B:-conjugate tensors

C:-symmetric tensors D:-fundamental tensors

Ans: B

73:-If `P_(n)(x)` represents the Legendre polynomials, the value of `int_-1^1[P_(2)(x)]^(2)dx` is

A:-`(2)/(3)` B:-`(1)/(3)` C:-`(2)/(5)` D:-`(3)/(5)`

Ans: C

74:-The value of `int_c(4-3z)/(z(z-1)(z-2)` dz where c is the circle |z| = `(1)/(2)` is

A:-2`Pii` B:-`8Pii` C:-`4Pii` D:-zero

Ans: C

75:-The value of a so that the vector is solenoidal is

A:-1 B:-4 C:--5 D:--7

Ans: D

76:-For a system in which the Lagrangian is not an explicit function of time, the Hamiltonian is

A:-constant B:-infinity C:-zero D:-none of these

Ans: A

A:-x = 1 y = 2 z = – 1

B:-x = 2, y = 3, z = 1

C:-x = 1, y = 2, z = 3

D:-x = 1, y = 4, z = 0

Correct Answer:- Option-A

64. The term independent of x in the expansion of `(x^(2)+1/x)^(6)` is

A:-0

B:-12

C:-10

D:-15

Correct Answer:- Option-D

65. If A + B = 45°, then (1 + tanA) (1 + tanB) is equal to` `

A:-2

B:-1

C:-4

D:-5

Correct Answer:- Option-A

66. Equation to the line passing through the point (– 3, 2) and perpendicular to the line 4x + 2y + 5 = 0 is

A:-x – 3y + 2 = 0

B:-x – 2y + 7 = 0

C:-x + y = 0

D:-x – y = 0

Correct Answer:- Option-B

67:-The maximum number of eigen values of an n `xx` n matrix is

A:-n B:-`n^(2)` C:-2n D:-`(1)/(2)n(n-1)`

Ans: A

68:-Which among the following is a mathematically incorrect operation ?

A:-grad div B:-div curl C:-grad curl D:-curl grad

Ans: C

69:-In cylindrical co-ordinates, where surface `rho` = 3 and z = 2 intersect is

A:-a finite plane B:-a semi infinite plane C:-a cylinder D:-a circle

Ans: D

70:-For a Fourier transform, which of the following statements is correct ``?

A:-FT of an even function is even and that of an odd function is odd

B:-FT of an even function is odd and the of an odd function is even

C:-FT of an even function is even and that of an odd function is even

D:-FT of an even function is odd and that of an odd function is odd

Ans: A

71:-The complex function `Z^((1)/(2))` is

A:-single valued B:-double valued

C:-n-valued D:-2n-valued

Ans: B

72:-If `A_(ij)` and `B^(ik)` are two tensors and `A_(ij)B^(ik)=delta^(k)_j` the Kronecker Delta, then `A_(ij)` and `B^(ik)` are

A:-associate tensors B:-conjugate tensors

C:-symmetric tensors D:-fundamental tensors

Ans: B

73:-If `P_(n)(x)` represents the Legendre polynomials, the value of `int_-1^1[P_(2)(x)]^(2)dx` is

A:-`(2)/(3)` B:-`(1)/(3)` C:-`(2)/(5)` D:-`(3)/(5)`

Ans: C

74:-The value of `int_c(4-3z)/(z(z-1)(z-2)` dz where c is the circle |z| = `(1)/(2)` is

A:-2`Pii` B:-`8Pii` C:-`4Pii` D:-zero

Ans: C

75:-The value of a so that the vector is solenoidal is

A:-1 B:-4 C:--5 D:--7

Ans: D

76:-For a system in which the Lagrangian is not an explicit function of time, the Hamiltonian is

A:-constant B:-infinity C:-zero D:-none of these

Ans: A