12/10/24, 1:33 PM 2024_UG03_231MA101_Question Bank

S.NO UNIT CHAP. PART Q.TYPE QUESTION CO KL QL

1 1 1 A OBJ CO1 R E

The matrix

A. identity matrix B. symmetric matrix

C. skew symmetric matrix D. none of these

Answer is : B
2 1 1 A OBJ CO1 R E
If A = [aij] is a square matrix of order 2 such that ,aij =1, when i j and aij =0 , when i = j, then A2 is

A. B.

C. D.

Answer is : D
3 1 1 A OBJ Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is CO1 R E

A. 9 B. 27

C. 81 D. 512

Answer is : D
4 1 1 A OBJ CO1 R E

If A is a square matrix such that A2 = A, then (I – A)3 + A is equal to

A. I B. 0

C. I-A D. I+A

Answer is : A
5 1 1 A OBJ The matrix which follows the conditions m = n is called? CO1 R E

Square matrix
A. B. Rectangular matrix

Diagonal matrix
C. Scalar matrix D.

Answer is : A
6 1 1 A OBJ CO1 R E

Which of the following is a scalar matrix?

A. B.

C. D.

Answer is : A
7 1 1 A OBJ Which of the following expression is incorrect for matrix multiplication? CO1 R E

A. A (BC ) = (AB ) C B. A ( B+ C) = AB + AC

C. AB = 0 if either A or B is 0 D. AB = BA

Answer is : D
8 1 1 A OBJ CO1 U M
If = 0 then the value of x is

A. 23/2 B. 13/2

C. =13/2 D. -23/2

Answer is : D
9 1 1 A OBJ CO1 R E

if A = then A-1 = ?

A. A B. -A

C. I D. -I

Answer is : A
10 1 2 A OBJ CO1 U E
If A =

A. -6 ,-12,-8 B. -6,-4,-9

C. -6,4,9 D. -6,12,8

Answer is : B

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11 1 2 A OBJ CO1 R E
Find

A. cos 2 B. - cos 2

C. cos 2 D. cos

Answer is : A
12 1 2 B DESC CO1 Ap E

Find the eigen values and eigen vectors of the matrix A =

13 1 2 B DESC CO1 Ap M

Find the eigen values and eigen vectors of the matrix A =

14 1 2 B DESC CO1 Ap E

Find the eigen values and eigen vectors of the matrix A =

15 1 2 B DESC CO1 Ap E

Find the eigen values and eigen vectors of the matrix A =

16 1 3 A OBJ Which of the following is not a property of determinant? CO1 R E

The value of determinant changes if all of its rows and columns are
A. B. The value of determinant changes if any two rows or columns are
interchanged
interchanged

The value of determinant gets multiplied by k, if each element of row or

C. D. column is multiplied by k
The value of determinant is zero if any two rows and columns are identical

Answer is : A
17 1 3 A OBJ Which of the following expression holds true for a symmetric matrix? CO1 R E

A. A =- A' B. A = A'

C. A = I D. A = | A |

Answer is : B
18 1 3 A OBJ CO1 Ap E
Find the value of if

A. x = 1 , - 1/3 B. x =-1, -1/3

C. x = 1, 1/3 D. x = -1 ,1/3

Answer is : A
19 1 3 A OBJ CO1 R E
A square matrix A is called orthogonal if ----------- where A' is the transpose of A

A. A = A2 B. A' = A-1

C. A = A -1 D. A = A'

Answer is : B
20 1 3 A OBJ If A is a square matrix of order 3 | A '| = -3 then |AA'| = CO1 U E

A. 9 B. -9

C. 3 D. -3

Answer is : A
21 1 3 A OBJ If is the Eigen value of a square matrix A then 1/ is the Eigen value of -------- CO1 R E

A. A B. A2

C. A -1 D. AT

Answer is : C
22 1 3 A OBJ CO1 R E
The Eigen values of a diagonal matrix are ------------

Elements of the second row

A. Elements of the first row B.

C. Elements of main diagonals D. None of these

Answer is : C
23 1 3 A OBJ CO1 R E
3
If is the Eigen value of a square matrix A then is the Eigen value of --------

A. A3 B. A-1

C. A2 D. AT

Answer is : A
24 1 3 B DESC CO1 U E
Write any four properties of Eigen values.

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25 1 3 B DESC CO1 U E
n
Prove that if is the Eigen value of A then is the Eigen value of An .

26 1 3 B DESC CO1 E E

Find the Eigen Values of A4, A-I , A-1 if A =

27 1 4 A OBJ CO1 U E

If A =

then A -1 =

A. B. 6

C. 1/6 D. 1/6

Answer is : C
28 1 4 A OBJ If A,B are non- singular square matrices of the same order, then (AB-1)-1 = CO1 R E

A. BA-1 B. A-1 B-1

C. AB-1 D. AB

Answer is : A
29 1 4 A OBJ CO1 E E

If A= then the value of A4 is

A. B.

C. D.

Answer is : A
30 1 4 A OBJ CO1 E E

Which of the following is the inverse of the matrix A= ?

A. B.

C. D.

Answer is : C
31 1 4 A OBJ CO1 R E
Inverse of a square matrix A is obtained by -------- theorem.

A. Cayley Hamilton’s B. Rolles

C. Euler D. Greens.

Answer is : A
32 1 4 A OBJ CO1 R E
” Every square matrix satisfies its own characteristic equation “is the statement of

A. Cayley Hamilton’s theorem B. Rolles theorem

C. Euler theorem D. Greens theorem

Answer is : A
33 1 4 B DESC CO1 Ap E

Verify Cayley - Hamilton theorem for the matrix A =

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34 1 4 B DESC CO1 Ap E

Verify Cayley - Hamilton theorem for the matrix A =

35 1 4 B DESC CO1 R E
Write the statement and applications of Cayley –Hamilton theorem

36 1 4 C DESC CO1 Ap E

4 -1,
Use Cayley – Hamilton theorem find A and A if A =

37 1 4 C DESC CO1 Ap E

8 7 6 5 4 3 2
Use Cayley – Hamilton theorem to find the value of the matrix given by f(A) = A -5A +7A -3A +A -5A +8A -2A+i IF a =

38 1 4 C DESC CO1 Ap E

Use Cayley – Hamilton theorem to find A4and A-1 IF A =

39 1 4 C DESC CO1 Ap E

Use Cayley – Hamilton theorem to find A4and A-1 IF A =

40 1 5 A OBJ Every Identity matrix is an orthogonal matrix. CO1 R E

A. TRUE B. FALSE

C. Option3 D. Option4

Answer is : A
41 1 5 A OBJ Which of the following is not a condition for a given real nonsingular quadratic form, Q = XTAX , to be a negative definite quadratic form? CO1 R E

The rank of the matrix A is equal to the number of variables in the quadratic
A. The number of positive square terms in the quadratic form is equal to zero B. form (index)

C. All the eigen values of A are negative D. The rank and index are equal

Answer is : B
42 1 5 C DESC CO1 Ap E

Diagonalize the Matrix A =

43 1 6 A OBJ CO1 R E
A symmetric matrix is ----------- if all its eigenvalues are positive

A. positive definite B. positive semi definite

C. negative definite D. None of these

Answer is : A
44 1 6 A OBJ CO1 R E
A symmetric matrix is semidefinite if all its eigenvalues are -----------

A. Non negative B. positive and negative

all values are zero

C. D. none of these

Answer is : A
45 1 6 A OBJ CO1 R E
A symmetric matrix is -----------if some eigen vaues are positive and some are negative.

A. indefinite B. definite

C. semi definite D. semi-indefinite

Answer is : A
46 1 6 B DESC CO1 E E
Determine the nature of the folllowing quadratic form f(x1,x2,x3) = x12 +2x22

47 1 6 C DESC CO1 Ap E
Reduce the quadratic form 3x12+3x22 + 3x32 +2x1x2 + 2x1x2 - 2x2x3 to canonical form through an orthogonal transformation

48 1 6 C DESC CO1 Ap E
Reduce the quadratic form Q =6x2+3y2+3z2-4xy-2yz+4xz to canonical form by an orthogonal reduction. Hence find its nature.

49 1 6 C DESC CO1 An E
Reduce the quadratic form 2xy - 2yz +2xz to canonical form by orthogonal reduction. Also find its nature, index, rank and signature

50 1 6 C DESC CO1 An E
Reduce the quadratic form x12 + 5x22 + x32 +2x1x2 +6 x1 x3 + 2 x2 x3 to canonical form through an orthogonal transformation. Also find its nature, index, rank
and signature

51 1 6 C DESC CO1 Ap E
Reduce the quadratic form 3x12 + 3x22 +3x32 +2 x1x2 +2 x1x3 -2 x2x3 to canonical form through an orthogonal transformation

52 1 7 B DESC CO1 R E
Mention any four applications of Eigen values and Eigen vectors .

53 2 1 A OBJ Find range of function . CO2 R E

A. Set of real numbers B. Set of positive real numbers

C. Set of integers D. Set of natural numbers

Answer is : B

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54 2 1 A OBJ In a function from set A to set B, every element of set A has___________ image in set B. CO2 R E

A. one and only one B. different

C. same D. many

Answer is : A
55 2 1 A OBJ Which of the following is not a function? CO2 R E

A. B.

C. D.

Answer is : C
56 2 1 A OBJ CO2 R E
. Find the domain of the function.

A. B.

C. D.

Answer is : C
57 2 1 A OBJ CO2 R E
is equal to

A. B.

C. D.

Answer is : D
58 2 1 A OBJ CO2 R E

the value is

A. B.

C. D.

Answer is : B
59 2 1 A OBJ CO2 R E
is equal to

A. B.

C. D.

Answer is : B
60 2 1 A OBJ CO2 R E
is

A. B.

C. D. None of these

Answer is : D
61 2 1 A OBJ CO2 R E

Solve

A. B.

C. D.

Answer is : B
62 2 1 C DESC CO2 U M
Evaluate the limit and justify each step by indicating the appropriate limit law,

63 2 2 A OBJ CO2 R E
is

A. B.

C. D.

Answer is : D
64 2 2 A OBJ What is the mathematical expression for the definition of continuity? CO2 R E

A. B.

C. D.

Answer is : B
65 2 2 A OBJ is continuous on for a fixed . CO2 R E

A. B.

C. D.

Answer is : A
66 2 2 B DESC CO2 U E
Show that the function is continuous on the interval

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67 2 2 C DESC CO2 U M

Discuss the continuity of the function

68 2 3 A OBJ CO2 U M
What is/are conditions for a function to be continuous on ?

A. The function is continuous at each point of B. The function is right continuous

C. The function is left continuous D. Right continuous, left continuous, continuous at each point of

Answer is : D
69 2 3 A OBJ CO2 U M

Is a continuous function?

A. Only in some cases B. Cannot be determined

C. Continuous D. Not continuous

Answer is : D
70 2 3 B DESC CO2 U M
Evaluate the limit

71 2 3 B DESC CO2 U M

Evaluate

72 2 3 C DESC CO2 Ap D

Find the values of a and b that make continuous everywhere

73 2 4 A OBJ First derivative of the natural logarithm is CO2 R E

A. B.

C. D.

Answer is : A
74 2 4 B DESC CO2 R E
If f(x) = then find .Also find

75 2 4 B DESC CO2 U M
Find the derivative of

76 2 4 B DESC CO2 U M
Find the derivative of

77 2 4 C DESC CO2 U M
Find the derivative (i) (ii)

78 2 5 A OBJ An expression for the derivative of the exponential function using the definition of derivative. CO2 R E

A. B.

C. D. 1

Answer is : C
79 2 5 A OBJ First derivative of the sine function CO2 R E

A. B.

C. D.

Answer is : A
80 2 5 A OBJ CO2 R E
Find the derivative of

A. B.

C. D.

Answer is : A
81 2 5 A OBJ Calculate the derivative of the function CO2 R E

A. B.

C. D.

Answer is : D
82 2 5 B DESC CO2 U M
using by implicit method of first derivative.

83 2 5 B DESC CO2 U M
If , using by implicit method of first derivative.

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84 2 5 C DESC CO2 Ap D

Use implicit differentiation to Find in terms of and .

(i) (ii)

85 2 6 A OBJ Find the derivative of a linear function using the definition of derivative CO2 R E

A. B.

C. D.

Answer is : C
86 2 6 A OBJ Find the derivative of the function CO2 R E

A. B.

C. D.

Answer is : C
87 2 6 A OBJ CO2 R E
If , then is

A. B.

C. D. None of these

Answer is : A
88 2 6 A OBJ CO2 R E
If then is

A. B.

C. D.

Answer is : B
89 2 6 A OBJ CO2 R E
Find the differentiation of

A. B.

C. D.

Answer is : C
90 2 6 A OBJ CO2 R E
Find the derivative of .

A. B.

C. D.

Answer is : C
91 2 6 A OBJ CO2 R E

If , then is

A. B.

C. D.

Answer is : A
92 2 6 A OBJ Differentiate with respect to . CO2 R E

A. B.

C. D.

Answer is : C
93 2 6 B DESC CO2 U M
Find the first derivative of

94 2 6 B DESC CO2 U M
Find the first derivatice of

95 2 7 A OBJ For which value of will have its maximum? CO2 R E

A. B.

C. D.

Answer is : C
96 2 7 A OBJ What will be the point of maximum of the function ? CO2 R E

A. B.

C. D.

Answer is : C

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97 2 7 A OBJ What will be the point of minimum of the function CO2 R E

A. B.

C. D.

Answer is : B
98 2 7 A OBJ CO2 R E
The function has

A. one minima and two maxima B. two minima and one maxima

C. two minima and two maxima D. one minima and one maxima

Answer is : D
99 2 7 C DESC CO2 U M
(i) Find the maximum and minimum value of

on

(ii) in , solve by maxima and minima method.

100 2 7 C DESC CO2 U M

Find the local maximum and minimum of using the second derivative test

(i)

(ii)

101 2 7 C DESC CO2 Ap D

Find the absolute maximum and absolute minimum value of

on

102 2 7 C DESC CO2 Ap D

Find the critical points of the following functions

(i)

(ii)

103 3 1 A OBJ CO3 R E

If u is a homogeneous functions of degree n in x and y then

A. 0 B.

C. n(n-1) D. nu

Answer is : D
104 3 1 A OBJ CO3 R E
Given the function what is fyyy(1,1)=

A. e B.

C. -e D.

Answer is : A
105 3 1 A OBJ CO3 R E

If

A. 1 B.

C. 2 D.

Answer is : C
106 3 1 A OBJ CO3 R E

Consider the function find fx(1,1) is

A. B.

C. D. 0

Answer is : C
107 3 1 A OBJ CO3 R E

If then find

A. B.

C. D.

Answer is : D

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108 3 1 A OBJ CO3 R E
Given the function what is at

A. 0 B. 1

C. 3 D. 1

Answer is : C
109 3 1 A OBJ CO3 R E

If then

A. B.

C. D.

Answer is : A
110 3 1 A OBJ CO3 R E

If and then

A. B.

C. D.

Answer is : C
111 3 1 A OBJ CO3 R E
The given function is then the first derivative of x=

A. B.

C. D.

Answer is : A
112 3 1 A OBJ CO3 R E

Consider the function find

A. B.

C. 1 D.

Answer is : A
113 3 1 A OBJ CO3 R E

If then

A. u+v B. 1+v+uv

C. 1-uv D. 1+u+v

Answer is : D
114 3 1 A OBJ CO3 R E

If then

A. -r B.

C. 1 D. 0

Answer is : B
115 3 1 A OBJ CO3 R E

If f(x,y)= then find at

A. 33 B. 0

C. 3 D. 1

Answer is : B
116 3 1 A OBJ CO3 R E
Give the function f(x,y) = find fxx at (1,1) is =

A. B. e

C. 1 D. 0

Answer is : B
117 3 1 A OBJ CO3 R E
If what is the value of

A. B.

C. D.

Answer is : A

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118 3 1 A OBJ CO3 R E

What is the value of for the

A. 3xy B. 6x

C. 3x+5 D. 6xy

Answer is : B
119 3 1 A OBJ CO3 R E
Number of third order partial derivatives of function of two independent variables is _____.

A. 9 B. 4

C. 8 D. 2

Answer is : C
120 3 1 A OBJ CO3 R E

If f(x,y)= then the value of fy at (0,1) is

A. 101 B. -96

C. 210 D. 0

Answer is : B
121 3 1 A OBJ CO3 R E

If f(x,y)= then find fxy at

A. B.

C. D.

Answer is : A
122 3 1 A OBJ CO3 R E

If f(x,y)= then find fxy at

A. B.

C. D. None of the above

Answer is : C
123 3 1 A OBJ Stationary point is a point where function f (x,y) have CO3 R E

A. B.

and
C. D. and

Answer is : C
124 3 1 A OBJ CO3 R E
Evaluate the minimum value of f(x,y)=

A. 3 B. -3

C. 9 D. -9

Answer is : A
125 3 1 A OBJ CO3 R E
What is the saddle point?

A. Point where function has maximum value B. Point where function has minimum value

C. Point where function has zero value D. Point where function has neither has maximum value nor minimum value

Answer is : D
126 3 1 A OBJ CO3 R E
Divide 120 into three parts so that the sum of their products taken two at a time is maximum. If x, y, z are two parts, find value of x, y and z.

A. x=40, y=40, z=40 B. x=38, y=50, z=32

C. x=50, y=40, z=30 D. x=80, y=30, z=50

Answer is : A
127 3 1 A OBJ CO3 R E
The staionary points of are

A. (-3,0) B. (0,3)

C. (0,-3) D. None of the above

Answer is : A

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128 3 1 A OBJ Maximize the function x + y – z = 1 with respect to the constraint xy=36. CO3 R E

A. 0 B. -8

C. 8 D. no maxima exists

Answer is : D
129 3 1 A OBJ CO3 R E
Find the points on the plane x + y + z = 9 which are closest to origin.

A. (3,3,3) B. (2,1,3)

C. (2,2,2) D. (3,4,1)

Answer is : A
130 3 1 A OBJ The span of a Astroid is increased along both the x and y axes equally. Then the maximum value of: z = x + y along the Astroid is? CO3 R E

A. Increases B. Decreases

C. Invariant D. The scaling of asteroid is irrelevant

Answer is : A
131 3 1 A OBJ CO3 R E

The extreme value of the function f(X1,X2,,.....,Xn) = with respect to the constraint where m always

stays lesser than n and as m,n tends to infinity is?

A. 1 B.

C. 2 D.

Answer is : B
132 3 1 A OBJ CO3 R E
The staionary points of are

A. B.

C. D. None of the above

Answer is : A
133 3 1 B DESC CO3 R E
State and prove Euler’s theorem for homogeneous functions.

134 3 1 B DESC CO3 R E

If u = tan-1 then prove that .

135 3 1 B DESC CO3 R E

If w=f(y-z,z-x, x-y) then show that .

136 3 1 B DESC CO3 R E

If u = x log(xy) where find .

137 3 1 B DESC CO3 R E

Find the Jacobian of with respect to if

138 3 1 B DESC CO3 R E

If prove that

139 3 1 B DESC CO3 R E

Find the Taylor’s series expansion of in powers of (x-1) and (y-2) upto 2rd degree terms.

140 3 1 B DESC CO3 R E

Write necessary and sufficient conditions for maximum and minimum.

141 3 1 B DESC CO3 R E

A flat circular plate is heated so that the temperature at any point is . Find the coldest point on the plate.

142 3 1 B DESC CO3 R E

A rectangular box open at the top and have a volume of 32cc. Find the dimensions of the box, that requires the least material for its construction.

143 3 1 B DESC CO3 R E

Find the dimensions of the rectangular box without top of maximum capacity with surface area 432 square metre.

144 3 1 C DESC CO3 R E

(i)If u is a homogeneous function of degree n in x and y, show that .

(ii) If then show that

145 3 1 C DESC CO3 R E

If where then prove that

146 3 1 C DESC CO3 R E

If then prove that

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147 3 1 C DESC CO3 R E

(i) Find the Jacobian of the transformation

(ii) Find the Taylor’s series expansion of in powers of and upto 3rd degree terms.

148 3 1 C DESC CO3 R E

Expand about upto the third term using Taylor’s series and in powers of x and y as far as the terms of the third degree.

149 3 1 C DESC CO3 R E

Find the extreme values of the function f(x, y) = x3+y3-3x -12y+20.

150 3 1 C DESC CO3 R E

Examine f(x,y) = x3 y2 ( 1 – x –y ) for its extreme values.

151 3 1 C DESC CO3 R E

A rectangular box open at the top is to have a given capacity K. Find the dimensions of the box requiring least material for its construction.

152 3 1 C DESC CO3 R E

The temperature u( x , y , z ) at any point in space is u = 400 xyz2. Find the highest temperature on surface of the sphere, x2+ y2+ z2 = 1.

153 3 1 C DESC CO3 R E

Find the volume of the greatest rectangular parallelepiped inscribed in the ellipsoid

154 4 1 A OBJ CO4 R E

The value of is

A. 1 B. 2

C. 3 D. 4

Answer is : B
155 4 1 A OBJ CO1 R E

The value of is

A. log 2 B. 0

C. log 4 D. log 8

Answer is : A
156 4 1 A OBJ CO1 R E

Find the integral value of is

A. 0 B. 1

C. 2 D. 1/2

Answer is : D
157 4 1 A OBJ CO1 R E

Evaluate the value of is

A. 0 B. 2

C. 1 D. 4

Answer is : B
158 4 1 A OBJ CO1 R E

Find the integration of is

Answer is : A
159 4 1 A OBJ CO1 R E

The value of

A. 1 B. 0

C. -1 D. 5/2

Answer is : D

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160 4 1 A OBJ CO1 R E
The indefinite integration of value is

A. B.

C. D.

Answer is : B
161 4 1 A OBJ CO1 R E
The value of is

A. B.

C. D.

Answer is : B
162 4 1 A OBJ CO1 R E
Integrate is

A. B.

C. D.

Answer is : A
163 4 1 A OBJ CO1 R E
Integrate is

A. B.

C. D.

Answer is : C
164 4 1 A OBJ CO1 R E
Integrate the following with respect to

A. B.

C. D.

Answer is : A
165 4 1 A OBJ CO1 R E
Integrate the following with respect to =

A. B.

C. D.

Answer is : A
166 4 1 A OBJ CO1 R E
The definite integration of value is

A. B.

C. D.

Answer is : A
167 4 1 A OBJ CO1 R E
The definite integration of value is

A. B.

C. D.

Answer is : C
168 4 1 A OBJ CO1 R E
The definite integration value is

A. B.

C. D.

Answer is : A
169 4 1 A OBJ CO1 R E
The value of

A. B.

C. D.

Answer is : B
170 4 1 A OBJ CO1 R E
Evaluate the integral value of

A. B.

C. D.

Answer is : C

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171 4 1 A OBJ CO1 R E
Find the value of

A. B.

C. D.

Answer is : B
172 4 1 A OBJ CO1 R E
Integrate is

A. B. 0

C. D.

Answer is : A
173 4 1 A OBJ CO1 R E

Let which of the following true

A. is a rational number B.

C. D.

Answer is : C
174 4 1 A OBJ CO1 R E
Find the value of

A. B.

C. D. None of these

Answer is : B
175 4 1 A OBJ CO1 R E

Find the integral value of is

A. I = Convergent B. I = Divergent

C. I=0 D. I=1

Answer is : A
176 4 1 A OBJ CO1 R E

The integral is

A. Convergent B. divergent

C. 0 D. 1

Answer is : B
177 4 1 A OBJ CO1 R E

Consider the improper integral is

A. Convergent B. divergent

C. Can't determine D. none of these

Answer is : B
178 4 1 B DESC CO1 R E

Find the value of .

179 4 1 B DESC CO1 R E

Find

180 4 1 B DESC CO1 R E

Evaluate

181 4 1 B DESC CO1 U E

Find the intgral value of

182 4 1 B DESC CO1 R E

Evaluate the

183 4 1 B DESC CO1 R E

Find the value of

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184 4 1 B DESC CO1 R E

Determine the value of

185 4 1 B DESC CO1 R E

Find the value of

186 4 1 B DESC CO1 R E

Determine the integral value of

187 4 1 B DESC CO1 R E

Evaluate

188 4 1 B DESC CO1 R E

Examine the convergence if

189 4 1 C DESC CO1 R E

(i) Evaluate

(ii)Find the value of

190 4 1 C DESC CO1 R E

Evaluate

191 4 1 C DESC CO1 R E

Evaluate

192 4 1 C DESC CO1 R E

Find the reduction formula for

193 4 1 C DESC CO1 R E

Find the integral value of with respect to

194 4 1 C DESC CO1 R E

Evaluate

195 4 1 C DESC CO1 R E

Evaluate where

196 4 1 C DESC CO1 R E

(i)Evaluate the following integral

197 4 1 C DESC CO1 R E

Evaluate

198 4 1 C DESC CO1 R E

(i)Test the convergence of

(ii) Evaluate

199 4 3 B DESC CO1 R E

Evaluate

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200 5 1 A OBJ CO1 R E

The value of

A. (ab)/2 B. (a+b)/2

C. (ab(a+b))/(2) D. 2

Answer is : A
201 5 1 A OBJ CO1 R E

The result of

A. B.

C. D.

Answer is : A
202 5 1 A OBJ CO1 R E

Value of the integral

A. 0 B. 4

C. 8 D. 6

Answer is : A
203 5 1 A OBJ CO1 R E

Value of integral

A. 1 B.

C. D.

Answer is : A
204 5 1 A OBJ CO1 R E

Value of

A. 0 B. 1

C. D.

Answer is : A
205 5 1 A OBJ CO1 R E

The value of

A. 5 B. 15/6

C. 12 D. 8/7

Answer is : A
206 5 1 A OBJ Recall the circle of radius by double integration in polar coordinates CO1 R E

A. B.

C. D.

Answer is : A
207 5 1 A OBJ CO1 R E

Value of is

A. B.

C. D.

Answer is : A
208 5 1 A OBJ CO1 R E
Area of region between two circles and is

A. B.

C. D.

Answer is : A
209 5 1 A OBJ Area of region between two curves and is CO1 R E

A. B.

C. D.

Answer is : A
210 5 1 A OBJ CO1 R E
Answer is : A

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then after changing the order of integration

A. B.

C. D.

211 5 1 A OBJ The volume of cube bounded by the planes , , and co-ordinate plane is CO1 R E

A. B.

C. D.

Answer is : A
212 5 1 A OBJ CO1 R E
In polar co-ordinate system value of =

A. B.

C. D.

Answer is : A
213 5 1 A OBJ CO1 R E
The spherical polar co-ordinates system value of is

A. B.

C. D.

Answer is : A
214 5 1 A OBJ CO1 R E
The area bounded by the curve and to is

A. B.

C. D. None of these

Answer is : A
215 5 1 A OBJ The volume of solid curve is CO1 R E

A. B.

C. D.

Answer is : A
216 5 1 A OBJ CO1 R E
Area of the region bounded by complete region is

A. 1 sq units B. sq units

C. sq units D. sq units

Answer is : A
217 5 1 A OBJ CO1 R E

The value of

A. 2 B. 6

C. 8 D. 4

Answer is : A
218 5 1 A OBJ CO1 R E

In double integral where is

A. Region of integration B. Order of integration

C. Area of integration D. Volume of integration

Answer is : A

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219 5 1 A OBJ CO1 R E

If then is

A. B.

C. D.

Answer is : A
220 5 1 A OBJ CO1 R E

The value of

A. 1 B. 1/4

C. 0 D. 1/2

Answer is : A
221 5 1 A OBJ CO1 R E

For evaluation of where A is the area of the rectangle

0≤x≤3,0≤y≤1

A. First with respect to then with respect to B. First with respect to then with respect to

C. Does not matter D. None of these

Answer is : A
222 5 1 A OBJ CO1 R E

The integral is solved by using change of order of integration. the strip for new limit is

A. Vertical strip B. Horizontal strip

C. Radial D. All of the above

Answer is : A
223 5 1 A OBJ CO1 R E
For ∬xy dxdy,where R is the region bounded by the circle , x≥0,y≥0 then the required region is

A. R1 B. R2

C. R3 D. R4

Answer is : A
224 5 1 A OBJ CO1 R E
For ∬xy dxdy,where R is the region bounded by axis, and ,then the required region is

A. R1 B. R2

C. R3 D. R4

Answer is : A
225 5 1 A OBJ CO1 R E

After changing into polar co-ordinates, the integrals taken the limits of is

A. 0 to B. 0 to r

C. 0 to D. none of these

Answer is : A
226 5 1 A OBJ CO1 R E

By changing the order of integrals the limits of integration becomes

A. x: y to a, y: 0 to a B. x: y to a, y: 0 to y

C. x: 0 to a, y: 0 to a D. x: 0 to a, y: 0 to x.

Answer is : A
227 5 1 A OBJ CO1 R E
If the equation of the circle is ,then radius of the circle is

A. a B. a/2

C. a/4 D. 2

Answer is : A
228 5 1 A OBJ Application of double integral for finding CO1 R E

A. Mass B. Area

C. Center of gravity D. All are correct

Answer is : A

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229 5 1 B DESC CO1 R E

Show that is

230 5 1 B DESC CO1 R E

Evaluate

231 5 1 B DESC CO1 R E

Evaluate over the region in the positive quadrant for which

x + y ≤1

232 5 1 B DESC CO1 R E

To show that , A is the area bounded between the circles and is

233 5 1 B DESC CO1 R E

Evaluate by changing the order of integration in .

234 5 1 B DESC CO1 R E

Evaluate

235 5 1 B DESC CO1 R E

Find the area of the region bounded by and

236 5 1 B DESC CO1 R E

Find the area of the region outside the inner circle and inside the outer
circle by double integration.

237 5 1 B DESC CO1 R E

Find the area of the circle of radius “a “ by double integration.

238 5 1 B DESC CO1 R E

Find the area of the ellipse

239 5 1 B DESC CO1 R E

Find the area of the cardioid

240 5 1 B DESC CO1 R E

Evaluate

241 5 1 C DESC CO1 R E

Find the area enclosed by the parabolas and .

242 5 1 C DESC CO1 R E

Evaluate , R is the region in the first quadrant bounded by the hyperbola x y=16 and the curve y=x, y=0,x=8.

243 5 1 C DESC CO1 R E

Change the order of integration in and hence evaluate the same.

244 5 1 C DESC CO1 R E

Change the order of integration in the integral and hence evaluate it.

245 5 1 C DESC CO1 R E

Find the area which is inside the circle and the outside the cardioid r=a(1+cosθ)

246 5 1 C DESC CO1 R E

Express in polar coordinates and then evaluate it.

247 5 1 C DESC CO1 R E

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By changing into polar coordinates show that . Hence

evaluate

248 5 1 C DESC CO1 R E

Show that

249 5 1 C DESC CO1 R E

Find the volume of the tetrahedron bounded by the plane and the

coordinateplane

250 5 1 C DESC CO1 R E

Find the volume bounded by the cylinder and the planes and

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