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Questions |
Answers |
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1. |
If (1-x+x2)=a0+a1x+a2x2
+.....+a2nx2n then a0+a2+a4+&
+a2nequals. |
a) 3n
+½
b) 3n -½
c) (3n -1)/2
d) (3n +1)/2 |
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2. |
The fourth,
seventh and tenth terms of a G.P are p, q and r respectively the
|
a) q2
=pr
b) r2 =p2+q2
c) p2=q2+r2
d) p2=qr |
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3. |
cos10
cos20 cos30 . . . . . cos1790= |
a) 0
b) 2
c) 1/2
d) 1 |
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4. |
The sum of
the slopes of the lines represented by 4x2+2hxy-7y2
=0 is equal to the product of the slopes then h is |
a) -6
b) -2
c) -4
d) 4 |
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5. |
If f(9) =9
and f'(9)=4 then |
a) 1/2
b) 2
c) 3
d) 4 |
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6. |
The value of
sin250 + sin2100+ sin2150+....
+ sin2850 + sin2900 =
|
a) 9
b) 9(½)
c) 7
d) 8 |
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7. |
If the
equation x2 +y2 +2gx +2fy +1 =0 represents a pair
of lines then |
a) g2-f2
=1
b) f2 +g2 =½
c) f2 -g2 =1
d) f2+g2=1 |
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8. |
DABC is right angle at C, then tanA +tanB= |
a) c2/ab
b) b2/ac
c) a+b
d) a2/bc |
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9. |
If the sum
of the distances of a point from two perpendicular lines in a plane is 1
then its locus is. |
a) straight
line
b) intersecting line
c) circle
d) square |
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10. |
The value of
{(cot540/tan360) + (tan200+cot700)}
= |
a) 2
b) 3
c) 1
d) 0 |
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11. |
The vectors
6i^-2j^+3k^, 2i^-3j^+6k^
and 3i^-6j^+2k^ form a triangle which
is. |
a) Right
angled
b) Obtuse angled
c) Equilateral
d) Isosceles |
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12. |
12. If
 then |
a)
=(1/2) 
b) angle between and
is
p /3
c) is parallel to
d) is
perpendicular to
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|
13. |
The value of
is |
a)
b) 
c) 0
d)  |
|
14 |
If
q is the angle between the vectors
and
, then
equals |
a) tanq
b) -tanq
c) cotq
d) -cotq |
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15. |
If A and B
are square matrices of order n x n then (A-B)2 is equal to |
a) A2
-2BA+B2
b) A2-AB -BA+B2
c) A2 -2AB+B2
d) A2-B2 |
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16. |
Choose the
correct answer |
a) Every
diagonal matrix is an identity matrix
b) A square matrix whose each element is 1 is an identity matrix
c) Every scalar matrix is an identity matrix
d) Every identity matrix is a scalar matrix |
| |
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17. |
If f(a)=2, f'(a)=1,
g(a)=-1, g'(a)=2 then
 |
a) 5
b) 0
c) -5
d)1/5 |
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18. |
The function
f(x)={loge(1+ax)-loge(1-bx)}/x is undefined at
x=0. The value which
should be assigned to f at x=0, so that it is continuous at x=0 is |
a) a+b
b)loge(ab)
c) a-b
d)(a+b)/2 |
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19. |
If f(x)=cos(logx)
then f(x)f(y)-1/2[f(y/x)+f(xy)]has
the value |
a) 1/2
b) -2
c) 0
d) 1 |
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20. |
The area of
a circle centred at (1,2) and passing through (4,6) is |
a) 25p
sq.units
b) 30p sq.units
c) 5p sq.units
d) 15p sq.units |
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|
21. |
The
eccentricity of the hyperbola {Ö1999/3} *
(x2 -y2)=1 is |
a)
Ö 3
b) Ö 2
c) 2
d) 2Ö 2 |
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22. |
In the
coaxial system of circles x2+y2 +2gx+c=0 where g is a parameter, if C>0
then the circles are of |
a)
intersecting type
b) orthogonal
c) non-intersecting type
d) touching type |
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23. |
If the set A
has p elements, B has q elements, then the number of elements in AxB
|
a) p+q
b) p+q+1
c) pq
d) p2 |
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24. |
if
w is the nth root of unity then 1+
w+ w2+w3+
...+ wn-1 is |
a)-1
b) 2
c) 0
d) 1 |
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25. |
The
contrapositive of (p v q) ® r is |
a) ~r
® ~(p v p)
b) ~r ® (~p ^-q)
c) p ® (q v r)
d) r ® (p v q) |
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26. |
For the
circuit shown below.
 The boolean polynomial is |
a) (~p^p)
^(~q^q)
b) (~p^q)^(q^p)
c) (~p^q) v (p^~q)
d) (~pv q) v(p v-q) |
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27. |
If
 |
a)
¥
b) 1
c) x
d) y |
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28. |
If Z=I+i
then the multiplicative inverse of Z2 is |
a) -i/2
b) i
c) 1-i
d) i/2
where i Ö -1 |
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29. |
 |
a) 0
b) loge4
c) loge3
d) loge2 |
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30. |
let
 tsint dt then f'(x)= |
a) x cosx
b) x2/2
c) sinx +cosx
d) x sin x |
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31. |
The value of
is |
a)
p /4
b) p /2
c) 2
d) p |
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32. |
 |
a) loge2/2
b) 2loge2
c) 2
d) loge2 |
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33. |
If f(x)=cos-1
then f'(e)= |
a) 1
b) Does not exist
c) 2/e
d) 1/e |
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34. |
 |
a)
b) 
c) 
d) |
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35. |
 |
a)
p ab
b) p 2 ab
c) p /ab
d) p /2ab |
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36. |
If x+iy =
 then (x2 +y2)2= |
a) (a2+b2)/(c2+d2)
b) (c2+d2)/(a2+b2)
c) (a2-b2)/(c2-d2)
d) Ö{(a2+b2)/(c2+d2)} |
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37. |
 The matrix is known as |
a) Upper
triangular matrix
b) Skew symmetric matrix
c) Symmetric matrix
d) Diagonal matrix |
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38. |
The number
of improper subgroups of G={1,-1, i,-i} w.r.t multiplication is
|
a) 3
b) 4
c) 1
d) 2 |
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39. |
In the group
G={ 0,1,2,3,4,5} under addition modulo 6,the value of (3*5-1)-1
is |
a) 4
b) 2
c) 3
d) 5 |
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40. |
An ellipse
has its centre at (1,-1) and semi major axis=8, which passes through the
point (1,3).Then the equation of the ellipse is |
a) {(x-1)2/16}+{(y+1)2/64}
=1
b) {(x+1)2/64}+{(y-1)2/16} =1
c) {(x+1)2/64}+{(y+1)2/16} =1
d) {(x-1)2/64}+{(y+1)2/16} =1 |
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41. |
In the
multiplicative group of 2 x 2 matrices of the form
 and a Î
R the inverse of is |
a)
b) does not exist
c) 
d)  |
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42. |
The circle x2+y2-8x+4y+4=0
touches |
a) 9 I and 3
I
b) 9 I and I
c) 5 I and 3 I
d) 5 I and I |
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43. |
Focus of the
parabola(y-2)2 =20(x+3) is |
a) (3,-2)
b) (2, -3)
c) (2,2)
d)(-3,2) |
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44. |
The locus of
the centre of a circle which touches externally the given two circles is |
a) Ellipse
b) Hyperbola
c) Circle
d) Parabola |
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45. |
The line p=x
cosa +y sina
becomes tangent to (x2/a2)-(y2/b2)=1
if |
a) p2=a2
cos2a +b2 sin2a
b) p2=a2 cos2a
-b2 sin2a
c) p2=a cosa -b sina
d) p2=a2 cosa +b2
sina |
|
46. |
Equation of
the normal to the hyperbola (x2/a2)-(y2/b2)=1
at the point (aSecq, b tanq
)is |
a){(ax/Secq
) +(by/tanq )}=a2-b2
b){(ax/Secq ) -(by/tanq
)}=a-b
c){(ax/Secq ) -(by/tanq
)}=a2-b2
d){(ax/Secq ) +(by/tanq
)}=a2+b2 |
|
47. |
If tan-1(x)+
2cot-1(x) = 2p /3 then x= |
a) (Ö
3-1)/(Ö3+1)
b) 3
c) Ö 3
d) Ö 2 |
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48. |
The angle
between the curve y2=4x and x2+y2=5 at
(1,2) is |
a) tan-1(3)
b) tan-1(2)
c) p /2
d) p /4 |
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49. |
For the
curve yn=an-1 x the subnormal at any point is
constant. The value of n must be |
a) 2
b) 3
c) 0
d) 1 |
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50. |
The maximum
value of the function f(x)=x1/x is |
a) 1/e
b) 2/e
c) e
d)e1/e |
51.
|
51.
= |
a)1/Ö
2 log
tan ( x/2 + p/8
) + C
b) log tan ( x/2 + p/8
) + C
c) 1/2 log tan ( x/2
+ p/8 ) + C
d) none of the above |
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52. |
 (1+tanx+tan2x) dx= |
a) ex
sin x+c
b) ex cos x+c
c) ex tan x+c
d) ex sec x+c |
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53. |
 |
a) (a+b)p
b) (a+b)p /4
c) p /4
d)(a+b)p /2 |
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54. |
 log(tan x)dx= |
a) 0
b) 1
c) p /4
d) p /2 |
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55. |
The area
enclosed between the parabola y2=4x and x2=4y is |
a)14/3
sq.units
b) 3/4 sq.units
c)3/16 sq.units
d)16/3 sq.units |
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56. |
Solutions of
the differential equation tan y sec2 x dx + tan x sec2
y dy=0 is |
a)(tan x /
tan y)=K
b)tan x tan y=K
c) tan x + tan y=K
d)tna x -tan y=K |
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57. |
The area
bounded by the curve y=loge x, the x axis, and the straight
line x=e is
|
a) 1-(1/e)
sq.units
b) 1+(1/e) sq.units
c) e sq.units
d) 1 sq.units |
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58. |
Let f be a
polynomial. Then the second derivative of f(ex) is |
a) f"(ex)
b) f(ex)e2x+f(ex)ex
c) f"(ex)ex+f'(ex)
d) f"(ex)e2x+f'(ex)ex |
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59. |
If m and n
are the order and degree of the differential equation
 then |
a) m=3, n=5
b) m=3,n=1
c) m=3,n=3
d) m=3,n=2 |
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60. |
The value of
 is |
a) 4abc
b) abc
c) 0
d) a+b+c
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