| 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, a G 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 |
