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
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
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
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
77. If p : Every square is a rectangle q : Every rhombus is a kite then truth values of pq and pq are ______ and ________ respectively.
(A) F, F (B) T, F (C) F, T (D) T, T
Ans: D
78. Which of the following quantified statement is true ?
(A) The square of every real number is positive
(B) There exists a real number whose square is negative
(C) There exists a real number whose square is not positive
(D) Every real number is rational
Ans: A
79. Direction ratios of the line which is perpendicular to the lines with direction ratios –1, 2, 2 and 0, 2, 1 are
(A) 1, 1, 2
(B) 2, -1, 2
(C) -2, 1, 2
(D) 2, 1, -2
Ans: B
80. How many positive integers are there less than or equal to 150 which are relatively prime to 150 ?
(A) 40 (B) 42 (C) 38 (D) 44
Ans: A
81. The non—homogeneous system of linear equations in matrix form AX = B in ‘n’ unknowns has a unique solution if
(A) rank A = n
(B) rank [AB] = n
(C) rank A = rank [AB]
(D) rank A = rank [AB] = n
Ans: D
82. The H C F of two numbers is 15 and their L C M is 900. If one of number is 60, then the other is :
(A) 135 (B) 225 (C) 125 (D) 175
Ans: B
83. Time in a clock is 10.25. What is the angle between hour hand and minute hand ?
(A) 95° (B) 105° (C) 100° (D) 110°
Ans: B
84. A train 250 m long is moving at a speed of 86 km/hr. In how much time will it take to cross a man coming from the opposite direction at a speed of 4 km/hr ?
(A) 12 seconds (B) 14 seconds (C) 10 seconds (D) 16 seconds
Ans: C
85. If 7 men or 12 women can complete a work in 25 days. How many days take to finish same work with 21 men and 24 women ?
(A) 10 days (B) 5 days (C) 12 days (D) 15 days
Ans: B
86. Anil and Rahim deposited same amount of money for three years in a Bank. Anil deposited at 10% simple interest and Rahim deposited at 10% compound interest. After 3 years Rahim got ? 1550 more than that of Anil. How much amount they deposited ?
(A) ? 50,000 (B) ? 25,000 (C) ? 30,000 (D) ? 40,000
Ans: A
87. If 11th July 2013 is Thursday, then December 2016 is :
(A) Sunday (B) Saturday (C) Monday (D) Tuesday
Ans: B
88. If A:B=4:3,B:C=6:10thenA:B:Cis:
(A) 8:6:10 (B) 4:6:10 (C) 4:3:10 (D) 8:3:10
Ans: A
89. A man eat 28 kg fruits in a week. Find out his average :
(A) 5 (B) 7 (C) 3 (D) 4
Ans: D
90. A man sold two mobile phones at Rs. 4,500 each. He sold one at a loss of 15% and the other at a gain of 15%. His loss or gain is
(A) 15% gain (B) 15%loss
(C) 2.25% gain (D) 2.25% loss
Ans: D
91. John started from his home and walked 12 km. Then he took a right turn and walked 4 km. Then again, he took a right turn and walked 8 km and finally took another right turn and walked 1 km. How far is he from his home now ?
(A) 25km (B) 9km
(C) 5km (D) 3km
Ans: C
92. The angle between the minute hand and the hour hand of a clock when the time is 4:20 is
(A) 10° (B) 5°
(C) 0° (D) 8°
Ans: A
93. The L.C.M. of squares of two numbers is 12544 and the H.C.F. of the squares is 4. If one of the numbers is 14, what is the other number ? (A) 13 (B) 16 (C) 256 (D) 196
Ans: B
94. The ratio of number of men and women in a committee is 5:6. If the percentage increase in the number of men and women by 20% and 10% respectively, what will be the new ratio ?
(A) 6:7 (B) 10:1 1
(C) 9:10 (D) Cannot be determined.
Ans: B
95. Machines A and B working together can do a piece of work in 6 days. Only A can do it in 8 days. In how many days B alone could finish the work ?
(A) 24 (B) 12
(C) 16 (D) 20
Ans: A
96. A train 110 m long is running with a speed of 90 km/hr. In what time will it pass a boy who is running at 9 km/hr in the direction opposite to that in which the train is going ?
(A) 6560 (B) 8sec
(C) 5 sec (D) 4sec
Ans: D
97. Let A be the set of points in the interval (0, 1) such that the decimal expansion of x does not contain the digit 7. Then the lebesgue measure of E is
(A) 1 (B) 0.9 (C) 0.7 (D) 0
Ans: D
98. The order of Quaternion group is
(A) 2 (B) 4 (C) 6 (D) 8
Ans: D
99. The order of smallest non-abelian group is
(A) 4 (B) 6 (C) 8 (D) 2
Ans: B
100. Let G be a group of order 81. Then
(A) Center of G has order 9. (B) G is non-abelian (C) G is cyclic (D) G is abelian
Ans: D
(A) F, F (B) T, F (C) F, T (D) T, T
Ans: D
78. Which of the following quantified statement is true ?
(A) The square of every real number is positive
(B) There exists a real number whose square is negative
(C) There exists a real number whose square is not positive
(D) Every real number is rational
Ans: A
79. Direction ratios of the line which is perpendicular to the lines with direction ratios –1, 2, 2 and 0, 2, 1 are
(A) 1, 1, 2
(B) 2, -1, 2
(C) -2, 1, 2
(D) 2, 1, -2
Ans: B
80. How many positive integers are there less than or equal to 150 which are relatively prime to 150 ?
(A) 40 (B) 42 (C) 38 (D) 44
Ans: A
81. The non—homogeneous system of linear equations in matrix form AX = B in ‘n’ unknowns has a unique solution if
(A) rank A = n
(B) rank [AB] = n
(C) rank A = rank [AB]
(D) rank A = rank [AB] = n
Ans: D
82. The H C F of two numbers is 15 and their L C M is 900. If one of number is 60, then the other is :
(A) 135 (B) 225 (C) 125 (D) 175
Ans: B
83. Time in a clock is 10.25. What is the angle between hour hand and minute hand ?
(A) 95° (B) 105° (C) 100° (D) 110°
Ans: B
84. A train 250 m long is moving at a speed of 86 km/hr. In how much time will it take to cross a man coming from the opposite direction at a speed of 4 km/hr ?
(A) 12 seconds (B) 14 seconds (C) 10 seconds (D) 16 seconds
Ans: C
85. If 7 men or 12 women can complete a work in 25 days. How many days take to finish same work with 21 men and 24 women ?
(A) 10 days (B) 5 days (C) 12 days (D) 15 days
Ans: B
86. Anil and Rahim deposited same amount of money for three years in a Bank. Anil deposited at 10% simple interest and Rahim deposited at 10% compound interest. After 3 years Rahim got ? 1550 more than that of Anil. How much amount they deposited ?
(A) ? 50,000 (B) ? 25,000 (C) ? 30,000 (D) ? 40,000
Ans: A
87. If 11th July 2013 is Thursday, then December 2016 is :
(A) Sunday (B) Saturday (C) Monday (D) Tuesday
Ans: B
88. If A:B=4:3,B:C=6:10thenA:B:Cis:
(A) 8:6:10 (B) 4:6:10 (C) 4:3:10 (D) 8:3:10
Ans: A
89. A man eat 28 kg fruits in a week. Find out his average :
(A) 5 (B) 7 (C) 3 (D) 4
Ans: D
90. A man sold two mobile phones at Rs. 4,500 each. He sold one at a loss of 15% and the other at a gain of 15%. His loss or gain is
(A) 15% gain (B) 15%loss
(C) 2.25% gain (D) 2.25% loss
Ans: D
91. John started from his home and walked 12 km. Then he took a right turn and walked 4 km. Then again, he took a right turn and walked 8 km and finally took another right turn and walked 1 km. How far is he from his home now ?
(A) 25km (B) 9km
(C) 5km (D) 3km
Ans: C
92. The angle between the minute hand and the hour hand of a clock when the time is 4:20 is
(A) 10° (B) 5°
(C) 0° (D) 8°
Ans: A
93. The L.C.M. of squares of two numbers is 12544 and the H.C.F. of the squares is 4. If one of the numbers is 14, what is the other number ? (A) 13 (B) 16 (C) 256 (D) 196
Ans: B
94. The ratio of number of men and women in a committee is 5:6. If the percentage increase in the number of men and women by 20% and 10% respectively, what will be the new ratio ?
(A) 6:7 (B) 10:1 1
(C) 9:10 (D) Cannot be determined.
Ans: B
95. Machines A and B working together can do a piece of work in 6 days. Only A can do it in 8 days. In how many days B alone could finish the work ?
(A) 24 (B) 12
(C) 16 (D) 20
Ans: A
96. A train 110 m long is running with a speed of 90 km/hr. In what time will it pass a boy who is running at 9 km/hr in the direction opposite to that in which the train is going ?
(A) 6560 (B) 8sec
(C) 5 sec (D) 4sec
Ans: D
97. Let A be the set of points in the interval (0, 1) such that the decimal expansion of x does not contain the digit 7. Then the lebesgue measure of E is
(A) 1 (B) 0.9 (C) 0.7 (D) 0
Ans: D
98. The order of Quaternion group is
(A) 2 (B) 4 (C) 6 (D) 8
Ans: D
99. The order of smallest non-abelian group is
(A) 4 (B) 6 (C) 8 (D) 2
Ans: B
100. Let G be a group of order 81. Then
(A) Center of G has order 9. (B) G is non-abelian (C) G is cyclic (D) G is abelian
Ans: D