maths

1 if is the complex cube first of unity then (1- +2) (1-2
12
14
16
None of these
2
/3
/4
/2
/6
3
log2
1/2 log2
None of above
4 The logical equivalence of ~(P-->~Q) is
P^ ~ Q
P ^ Q
~ P --> Q
~ P ^ Q
5 d/dx[ sin -1(3x/2 - x3/2) ]
6
1
0
3
1/2
7 (X+1/X-1)x-1
1
0
2
1/2
8 If y = 1+ x / |_1 + x2 / |_2 + -- - - then dy/dx =
ex
1/1+x
cotx
None of the these
9 Area included between the curves y2 = 4ax and x2 =4by is
32ab/3
16ab/3
16ab
None of the above
10 tan-1[3x-x3 / 1-3x2]dx=
4 - 1/2log 2
34 - 3/2log 2
34 - 1/2log 2
None of these above
11 If (2+i) (2+2i) (2+3i) … (2+ni) = x + iy then 5.8.13… (4+n2) =
x2 + y2
x2 - y2
x4 - y4
x4 + y4
12 Let A=then
AT=A
AT=-A
AT=2A
None of these above
13 The set of matrices M= from a group under multiplication operation with the identity element
14 G = { 1, 2, 3, 4, 5, 6 } is a group under multiplication mod 7. then (3 x 5-1) -1 =
2
4
6
5
15 The parabola (y + 1) 2 = a(x-2) passes through the point (1, -2). The equation of its directrix is
4x+1 = 0
4x-1 = 0
4x+q = 0
4x-q = 0
16 If (G, ·) is a group and a2 = e,aG then
abelian
non-abelian
finite
none of these
17 The equation of the circle passing through (2, 1) and touching the co-ordinate axes is
x2 + y2 - 2x - 2y + 1 = 0
x2 + y2 + 2x + 2y + 1 = 0
x2 + y2 - 2x - 2y - 1 = 0
x2 + y2 - 2x + 2y - 1 = 0
18 The inverse of is
none of these
19 The locus of a point such that the ratio of its distances from two fixed points is a constant is
a circle
a parabola
an ellipse
none of these
20 If the latusrectum of the ellipse x2 tan2 + y2 sec2= 1 is ½ then is
/12
/6
5/12
none of these
21 Equation of the normal to the ellipse x2 /a2 + y2 /b2 = 1 at the point (a cos,bsin)is
( ax /cos) + (by / sin) = a2 + b2
( ax /cos) - (by / sin)=a2 - b2
( ax /cos)- (by / sin)=a2 +b 2
( ax /cos)- (by / sin)=a-b
22 The amplitude of (-1) 5 is
/2
/4
3/2
23 The angle between the curves y2 = x and x2 = y at (1, 1) is
tan -1 3/4
tan -1 4/3
90 °
45 °
24 Subnormal to xy = c2 at any point varies directly as
cube of the ordinate
square of the ordinate
ordinate
none of these
25 The absolute maximum of y = x3 - 3x + 2 in [0, 2] is
2
4
6
0
26 ( 1 / 1 + e -x ) dx =
log (1 + e-x )
log (1 - e-x )
log (1 + e x )
none of these
27 elogx sin x dx =
x cos x + sin x
-xcos x + sin x
-x cos x - sin x
none of these
28 ( a sec x + b cosec ) / ( sec x + cosec x ) dx =
/2
/4
(a+b)/2
(a+b)/4
29 ex ( 1 + tan x + tan2 x) dx =
e/4 - 1
e/4
e/4 + 1
none of these
30 [ ( sin-1 x - cos -1 x ) / ( sin-1 x + cos -1 x ) ] dx =
log ( sin-1 x + cos-1 x )
none of these
31 The radius of the circle 9x2 + 9y2 + 18 x - 36y + 44 = 0 is
3
1/2
1/3
2
32 Area bounded by x = 4 - y2 and y-axis is
8/3
32/3
12
none of these
33 tan -1 x dx =
/4
/4+log2
4-1/2log 2
/2+log 2
34 The order and degree of the differential equation 1 + ( dy / dx) 2 ] 2/3 = d2y / dx2 are respectively
1,2
2,2
2,3
3,2
35 If = k (a-b) (b-c)(c-a) then k =
-1
1
2
abc
36 nco- nc1 + nc2 - nc3+ …….+ (-1) n nc n is equal to
2n
2n-1
0
2n +1
37 If o< a < b < c and a,b,c are in HP then log (a+c)+log(a-2b+c) is equal to
2 log (c-b)
2 log (a+c)
2 log (c-a)
none of these
38 If s = 4t3 - 18 t2 - 15. Find the velocity when the acceleration vanishes
-27
25
24
none of these
39 If the slopes of one of the lines represented by 4x2+ 2hxy + 3y2 = 0 three times the slope of the other than the
4
16
2
none of the above
40
-
0
none
41 The angle between the lines x2 - y2 - 2y - 1 = 0 is
600
900
750
00
42 The value of cot 82 1/20 =
43 In a triangle ABC if cos B = sin A / 2 sin C then the triangle is
equilateral
isosceles
right angled
none
44 A point moves such that the sum of the squares of the distances from the three verticles of a triangle is constant the locus of the point to
a pair of lines
a circle
parabola
ellipse
45 The value of ( tan 800 - tan 100 ) / tan 700 =
2
-2
4
-4
46 if are unit vectors and s the angle between them, then is a unit vector when =
/4
/3
2 /3
/2
47 If the vectors are coplanar then x =
2
-2
3
0
48 If | a | = 3, | b | = 4 and | a - b | = 5 then | a + b | =
6
4
5
3
49 [ a + b b + c c + a ]
2 [a b c ]
2 | a | | b | | c |
0
none
50 A then A + =
A + A
A - A
A A
none
51 Adjoint of a matrix exists when
A is non singular
A is a square matrix
A is singular
A is any other matrix
52 If (f o g) (1) = 3, g(1) = 2, g'(1) = 1 then f '(2) =
3
2
1/8
1/2
53 let f(x) be a continuous function and g(x) be a discontinuous function. Then f(x) + g(x)
continuous function
discontinuous function
any thing can't be said
none of these
54 If f(x) = cos (log x) then d/dx f(x) =
log x
- cos (log x)
- sin( log x) / x
none
55 The equation of the tangent to the circle x2 + y2 + 2gx + 2fy = 0 at (0, 0) is
gx + fy = 0
fx + gy = 0
gx = 0
fy = 0
56 The parametric equations of rectangular hyperbola xy = c2 are
x = t , y = 1/t
x = ct , y = c/t
x = t2, y = 1/t2
x = c / t , y = t
57 The limiting points of the co-axial system of circles x2 + y2 + 2gx + 4 = 0 are
( 2,0)
(02)
58 Set A has n elements. Its power set P(a) has
n2 elements
2n elements
22n elements
2n-1
59 The multiplicative inverse of (1-i) / (1+i) is
i
-i
1+i
1-i
60 The converse of the inverse of the conditional of a proposition p--> q is
converse itself
contra positive
inverse
none of these