Sanjay Gupta, Dev Samaj College For Women, Ferozepur City SAMPLE QUESTIONS FOR M.Sc. (HON'S ) MATHEMATICS_2017
1. Let G be a group of order 147. For any ¹
a
A) B) C) D)
a Î G ,
6. The integrating factor of ¶y differential + 2 xy = 4 x 3
, the number of solutions of x 2 = a is 49 one three zero
e
the is
¶x
given by (A) e y 2 2
2. In the ring Z [i ] , where Z is the ring of integers, the element 1 - i A) is both irreducible as well as prime B) is neither irreducible nor prime C) is irreducible but not prime D) is prime but not irreducible 3. The equation of the tangent to the curve at any point ( a , b ) is given by A)
(x - a)
B)
¶f ¶f (a ,b) + ( y - b ) (a ,b) = 0 ¶y ¶x
¶f ¶f (a ,b) - ( y - b) (a , b ) = 0 ¶y ¶x ¶f ¶f 6 (y - b) (a, b) + ( x - a ) (a ,b) = 0 ¶y ¶x ¶f ¶f (x - a) (a,b ) - ( y - b) (a,b) = 0 ¶x ¶y
(D)
4. Two spheres 2
x2 + y2 + z
+ 2u1 x + 2v1 y + 2 w1 z + d 1 = 0
(1, - 2 ,1) is
Ñ f at the point
(A) (B) (C) (D)
f ( x , y ) =0
(x - a)
C)
(B) e x (C) e x D) e y 7. If f ( x 1 y 1 z 1 = 3 x 2 y - y 3 z 2 , then Ù
Ù
Ù
- 12 i - 9 j - 16 k Ù
12
Ù
i + 9 j - 16
- 12
- 12
Ù
i
Ù
+ 9
i + 9
Ù
k
Ù
j + 16
Ù
j - 16
Ù
k Ù
k
8. If one root of the equation x 3 - 13 x 2 + 15 x + 189 = 0 exceeds the other by 2, then all the roots are (A) 7, 9 and 3 (B) -7, -9 and -3 (C) 7, 9 and –3 (D) -7, -9 and 3 9.
Two forces 13 kg.wt. and 3 3 kg.wt.
= 0
act on a particle at an angle q and equal to a resultant force of 14 kg.wt., then the angle between the forces is 0 (A) 45 0 (B) 30 0 (C) 60 (D) 900
(D) 2 ( u 1 - u 2 ) + 2 ( v 1 - v 2 ) + 2 ( w 1 - w 2 ) = ( d 1 - d 2 )
10. Let be subspaces of W 1 and W 2 dimensions 5 and 4 respectively of a vector space V of dimension 6.
x
2
+ y
2
+ z
2
+ 2u 2 x + 2v2 y + 2 w 2 z + d
cut each other orthogonally if (A) 2 u 1u 2 + 2 v1v 2 + 2 w 1 w 2 = d 1 + d (B) u 1u 2 + v1 v 2 + w 1 w 2 = 0 (C)
2
u1 v w1 d = 1 = = 1 u2 v2 w2 d2
5. The series (A) (B) (C) (D)
2
å
1 n (log n )
convergent convergent divergent if convergent
is p
if p > 0 if p > 1 p >1
if 0 < p < 1
Then dim ( W 1 Ç W 2 ) is (A) Zero (B) one (C) at most two (D) at least three
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