SLIET SET 2025 Question Paper with Answer Key M.Sc Maths SET-VI

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SLIET SET 2025
Question Paper · M.Sc
Maths SET-VI
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SLIET SET 2025 Question Paper M.Sc Maths SET-VI Answer Key

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PaperCode: 2010 Paper Name: 2010-M.Sc. (SET-VI) M.SC(MATHS) Set Name: Original

Q-1

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A -20
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B 0
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C 20

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D -10

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Q-2 ag

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A m=4 B m≠4

C n≠5
l as D None of these

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Q-3

A 3 B 4

C 2 D 1

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Q-4 c. o
Cayley – Hamilton theorem states that every square matrix satisfies…
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A
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Its determinant B
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Its simultaneous equation

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C Its own characteristic equation D None of these

Q-5

A 2n B n²/2

C (n(n+1))/2
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D (n(n-1))/2
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Page 1 of 12

Q-6

A 1 B 2

C 3 D 4

Q-7 The number of generators in the cyclic group of order 10 are

A 1 B 2

C 3 D 4

Q-8 The number of homomorphism from Z₁₂ to Z₃₀ are

A 4 B 6

C 20 D 120

Q-9 Which of the following statement is false ?

A Every integral domain is a field B Every finite integral domain is a field

C Every field is an integral domain D Every field is a ring

Q-10 Which of the following is prime ideal of Z

A 4Z B 6Z

C 9Z D 3Z

Q-11

A 0 B 1

C 1/2 D does not exist

Q-12 The function f(z)=|z|² is

A everywhere analytic B nowhere analytic

C analytic at z=0 D None of these

Q-13 Which of the following is not harmonic function?

A u=sinhx cosy B

C u=x²+y² D u=x²-y²
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⁡

⁡

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a Q-14 The mapping w=z²-2z is
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A conformal at z=1 B not conformal at z=1

C not conformal at z=-1 D everywhere conformal

Q-15

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A
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monotonically increasing and is convergent to B monotonically decreasing and is convergent
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1
e m to 1
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C
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neither monotonically increasing nor
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D divergent
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convergent to 1ag
monotonically decreasing but is

Q-16

A diverges B
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converges to 3S-u₁-u₂

C converges to 3S-u₁-2u₂ D c. oconverges to 3S-2u₁-u₂

e m Correct Answer : D

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Q-17 ag

A B

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C D
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s e g la Correct Answer : A

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a Q-18

A B

C
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D
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Q-19

A convergent to 1.5 B divergent

C bounded D monotonically decreasing

Q-20

A 2 B 1/2

C 4 D 1/4

Q-21

A 0 B 1

C -1 D None of these

Q-22

A 0 B 1

C -1 D None of these

Q-23

A 1,3 B 1,2

C 2,3 D 3,5

Q-24

A 1 B

C e+1 D e-1

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Q-25

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a A 9/25 B 3/5
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C 5/9 D None of these

Q-26

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A

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B
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C
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Q-27 The maximum value of f(x)=sin x+cos2x is

A 9/8 B 1

C 5/4 D 0

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Q-28

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A f_x (0,0)=f(0,0) B f(x,y) is differentiable at origin

C D f(x,y) is continuous at origin

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Q-29
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Rolle’s theorem is applicable to the

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A
s e functions differentiable in [a,b] and B
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functions continuous in [a,b]only and having
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continuous in (a,b) only and having same same value at point ‘a’ and ‘b’

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value at point ‘a’ and ‘b’

functions continuous in [a,b] and D monotonically Increasing functions
differentiable in (a,b) only and having
same value at point ‘a’ and ‘b’

Q-30

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c. o e m
⁡

A 0 B

em as
s
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C 2m D SLIET SET 2025 Question Paper with Answer Key M.Sc Maths SET-VI

Q-31

A B

C D

Q-32 Which of the following is false?

A B

C D

Q-33

A 1 B 1/2

C 1/4 D 1/8

Q-34 The value of β(3,2) is

A 1/8 B 1/12

C 1/4 D 1/16

Q-35 The formula for Green’s theorem is

A B

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D SLIET SET 2025 Question Paper with Answer Key M.Sc Maths SET-VI
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Divergence and Curl of a vector field are
Q-36
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A Vector & Scalar
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C Vector & Vector
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Q-37

A 1, 2 B 2, 3

C 1, 3 D 2, 2

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Q-38
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The complementary function of differential equation (x² D²+xD)y=log(x) is
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A

C
c₁+c₂ log(x)

c₁+c₂ x²
ag B

D
c₁ x+c₂ log(x)

c₁+c₂ x

Q-39

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A B

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C D

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Q-40 The general solution of the linear partial differential equation yzp+zxq=xy is

A F(x²-y²,z-x)=0 B F(x²-y²,y²-z² )=0

C F(x²-z²,z²-x² )=0 D F(x²-y²,y-x)=0

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Q-41

A px=qy B py=qx

C px+qy=0 D

Q-42 For any function f(x,y) and r,s,t having their usual meaning then f will be minimum if

A rt-s²>0 B rt-s²<0

C rt-s²,r<0 D rt-s²,r>0

Q-43 Let f(x,y,z) be a function of three variables x ,y ,z which are connected by relation ϕ(x,y,z). Then new function
generated by Lagrange’s method of undetermined multipliers is

A B

C D All of the these

Q-44 Laplace transformation of unit step function
u(t-a) is

A 1 B

C D

Q-45

A B

C D

Q-46

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B SLIET SET 2025 Question Paper with Answer Key M.Sc Maths SET-VI
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Q-47

√(π/s) √π
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A B

C √s

. c om D √(s/π)

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Q-48
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Virtual work refers to
a
virtual work done by virtual forces virtual work done by actual forces
A B

C actual work done by virtual forces D actual work done by actual forces

Q-49 A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it
is actually a six.

1/8 B
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3/8

c. o
A

C 5/8 D 7/8

s em Correct Answer : B

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Q-50 ag
In a Binomial Distribution, if p=q, then P(X = x) is given by?

A B

C D

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A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph
Q-51

m s
and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train ise
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A 40 m B 45 m

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a C 50 m D 55 m

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Q-52

A ACB B ADB

C AEB D AFB

Q-53 Speed of a boat in still water is 9 km/hr. It goes 12 km down- stream and comes back to the starting point in three
hours. What is the speed of water in the stream?

A 3 km/hr B 3.5 km/hr

C 5 km/hr D 5.5 km/hr

Q-54 A bucket containing water is tied to one end of a rope of length 2.5 m and rotated about the other end in a vertical
circle. What should be the minimum velocity of the bucket at the highest point, so that the water in the bucket will not
spill? (g = 10 m/s²)?

A 2.5 m/s B 4 m/s

C 5 m/s D 7 m/s

Q-55 A, B, C, D, E, F and G are members of a family consisting of four adults and three children, two of whom, F and G are
girls. A and D are brothers and A is a doctor. E is an engineer married to one of the brothers and has two children. B is
married to D and G is their child. Who is C?

A E’s daughter B F’s father

C G’s Brother D A’s son

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Q-56

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A 8 B 9

C 10 D 11

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Q-57

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A 1 B 2

C 3 D 4

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Q-58 In covering a distance of 30 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less

as than B. A's speed is:
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A 5 km/h B 7 km/h

C 9 km/h D 10 km/h

Q-59 Which of the following parts of the sun is easily visible only during a total solar eclipse?

A Core B Photosphere

C Sunspots D Corona

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Q-60 Sickle Cell Anemia is a
se
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A Genetic Disorder Virus
B SLIET Disease
SET 2025 Question Paper with Answer Key M.Sc Maths SET-VI
C Bacterial Disease D None of these

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