1. If
z=x+iy then |z|=1 is the equation of ?
a)circle
b)parabola
c)ellipse
a)circle
b)parabola
c)ellipse
d)hyperbola
(A)
2.the number of finite sets which are closed under addition?
(A)
2.the number of finite sets which are closed under addition?
a)0
b)1
c)2
d)n
(B)
(B)
3. If
A.M = 5 and H.M = 4 of two values a & b, then
G.M ?
a. ±2√5
b. ±2√4
c. +√20
d. -√20 (A)
:4. For two no’s : a and b, If a>0 , b>0 then,
a. A.M < G.M < H.M
b. A.M < G.M > H.M
c. A.M > G.M < H.M
d. A.M > G.M > H.M (
D)
5.A triangle has 20 balls on it’s
base how many overall balls triangle has ?
a. 100
b. 200
c. 110
d. 210 ( D)
6.the sum of all
coefficients in expansion of (3+2x)^4 is
?
a) 16
B)625
c)30
d)32
(B)
7)
If B is square
matrix and B^t = - B , then B is called
A)
Symmetric
B)
Skew symmetric
C)
Singular
D)
Non-singular
Ans
: B
8)imaginary
roots of ax^2+bx+c=0 are always ?
a)equal
b)unequal
c)unequal
and conjugate
d)conjugate
9.if
H.M:G.M =4:5 then a:b is equal to ?
a)5:4
b)4:2
c)2:1
d)3:1 (A)
10. the slope of tangent of any point of
the curve is dy/dx = 2x-2 , and y(-1)=0 then the curve is
a) 4x+y+4=0
b) y=x^2 -2x – 3
c) y = x^2 – 2x
d) none of these (B)
a) 4x+y+4=0
b) y=x^2 -2x – 3
c) y = x^2 – 2x
d) none of these (B)
11. the curve f(x,y)=0 has a central symmetry
if
a) f(-x,-y)= f(x,y)
b) f(x,-y)= f(x,y)
c) f(-x,y)= f(x,y)
d) f(x,y)≠ f(x,y)
a) f(-x,-y)= f(x,y)
b) f(x,-y)= f(x,y)
c) f(-x,y)= f(x,y)
d) f(x,y)≠ f(x,y)
(A)
12. number of solutions of 3sinӨ + 4cosӨ=125 is
a) two solutions
b) finite solutions
c) infinite solutions
d) solution does not exist
a) two solutions
b) finite solutions
c) infinite solutions
d) solution does not exist
(D)
13. If y=3cos(ln2x)+4sin(ln2x) then,
A)x^2y2-xy1+y=0
B)x^2y2+xy1-y=0
c)x^2y2+xy1+y=0
D)y2+y1+y=0
y1 is first derivative and y2 is second derivative.
A)x^2y2-xy1+y=0
B)x^2y2+xy1-y=0
c)x^2y2+xy1+y=0
D)y2+y1+y=0
y1 is first derivative and y2 is second derivative.
(C)
14. a conic with unit eccentricity has the
relation
a) a>b
b) a=b
c) a<b
d) a=0 or b=0
a) a>b
b) a=b
c) a<b
d) a=0 or b=0
(D)
15. a polygon of n sides has number of diagonals
equal to
a) nC2
b) n(n-3)/2
c) nP2
d) nC2 – n
a) nC2
b) n(n-3)/2
c) nP2
d) nC2 – n
(D)
16.the sum of all odd numbers between 100 and
200 is
a) 6200
b) 7500
c) 6500
d) 3750(B)
a) 6200
b) 7500
c) 6500
d) 3750(B)
17. the set of all values of x for which
the p(x) is true called
a) tautology
b) contingency
c) absurdity
d) truth set (A)
a) tautology
b) contingency
c) absurdity
d) truth set (A)
18. cos 11 + sin 11 / cos 11 – sin 11 = ?
a) tan 56
b) sin 56
c) cos 56
d) none (A)
a) tan 56
b) sin 56
c) cos 56
d) none (A)
19. sin(180+@) =
a) –sin@
b) –cos@
c) sin@
d) none (A)
a) –sin@
b) –cos@
c) sin@
d) none (A)
20. if ‘a’ is the first term and ‘r’ is common
ratio , then (n+1)th term of the series is
a) ar^n
b) ar^(n-1)
c) ar
d) none (A)
a) ar^n
b) ar^(n-1)
c) ar
d) none (A)
21.
Two dices are rolled simultaneously . What is
the probability of obtaining 6 on both dices?
a)1\12
b)1\6
c)2\6
d)1\36 (D)
a)1\12
b)1\6
c)2\6
d)1\36 (D)
22.
In a 3-dimensional (x, y, z) space, the set of
all points
5 units from the x-axis is:
a) a line.
b) 2 parallel lines.
c) a circle.
d) a sphere.(D)
5 units from the x-axis is:
a) a line.
b) 2 parallel lines.
c) a circle.
d) a sphere.(D)
23. For what nonzero whole number k does the
quadratic equation y^2+2ky+4k = 0 have exactly one real solution for y?
a)8
b)4
c)2
d)−4
e)−8
(B)
a)8
b)4
c)2
d)−4
e)−8
(B)
24. Which of the following is NOT a solution of
(x − 5)(x − 3)(x + 3)(x + 9) = 0?
a) 5
b) 3
c) −3
d) −5
(x − 5)(x − 3)(x + 3)(x + 9) = 0?
a) 5
b) 3
c) −3
d) −5
(D)
25. 1,2,3,4,5 h0w many 4
digit odd numbers can be made with out repeating
a)16
b)48
c)72
d)98
a)16
b)48
c)72
d)98
26. f the stay of six men for 14 days in a hotel
costs Rs.3360 , find the cost for the stay of 4 men for 7 days in the same
hotel?
a)823
b)1120
c)1372
d)2520 (B)
a)823
b)1120
c)1372
d)2520 (B)
27. Which is vector v if v.i=o,v.j=o,v.k=0
A(000)
B(111)
C(-101)
D(-1-1-1) (A)
A(000)
B(111)
C(-101)
D(-1-1-1) (A)
28.
D/dx of
(lnsin^2x)
A. 2sin x
b: 2cotx
c. 2(cosecx - tan x/2)
d. 2(tan x/2 -cosec x) (B)
A. 2sin x
b: 2cotx
c. 2(cosecx - tan x/2)
d. 2(tan x/2 -cosec x) (B)
29. the
ellipse 4x^2 + 8y^2 = 64 and circle x^2 + y^2 = 9 intersect a points where the
y coordinate is
a) + - √2
b) + - √5
c) + - √7
d) + - 10 ©
a) + - √2
b) + - √5
c) + - √7
d) + - 10 ©
30. if
the vertices of a triangle are (u,0), (v,8) and (0,0) then the area of the
triangle is
a) 4u
b) 2v
c) uv
d) 2uv
e) 1/2 uv (A)
a) 4u
b) 2v
c) uv
d) 2uv
e) 1/2 uv (A)
31. If
(A+iB)= 2+i / 2-3i, then the value of A^2 +B^2 is:
A. 13/5
B. 5/13
C. 13/9
D. None.
A. 13/5
B. 5/13
C. 13/9
D. None.
(B)
32. if
f(x)= √ (2x+3) and g(x) = x^2 +1 , then f(g(2))=
a) 2.24
b) 9
c) 3.61
d) 6 ©
a) 2.24
b) 9
c) 3.61
d) 6 ©
33. What
is the range of 2sinx + 7
a. [-1,+1]
b. R
c. [5,9]
d. [9,5]
a. [-1,+1]
b. R
c. [5,9]
d. [9,5]
©
34. The
quadratic equation with roots thrice the roots of equation 3x^2 + 10x +25=0 is
:
a) 3x^2 - 10x +25=0
b) x^2 + 10x +25=0
c) x^2 + 10x +75=0
d) x^2 10x -25=0 ©
a) 3x^2 - 10x +25=0
b) x^2 + 10x +25=0
c) x^2 + 10x +75=0
d) x^2 10x -25=0 ©
35.
what is
the derivative of e^ln sinx
a) e^ln sinx * tanx
b) tanx
c) e^ln sinx * cosecx
d) cosx
e) none of these (D)
a) e^ln sinx * tanx
b) tanx
c) e^ln sinx * cosecx
d) cosx
e) none of these (D)
36.which one is modulus of 2+i ?
a) sq root 2
b) 2
c) sq root 3
d) sq root 5 (D)
a) sq root 2
b) 2
c) sq root 3
d) sq root 5 (D)
37. which
of the following is a negative number?
a) i^25
b) i^50
c) i^75
d) i^100
a) i^25
b) i^50
c) i^75
d) i^100
(B)
38.
the line which is parallel to the latus rectum and lies at an equal
distance from the vertex as that of focus is called
a) vertex
b) axis of conic
c) focus
d) directrix (D)
a) vertex
b) axis of conic
c) focus
d) directrix (D)
39.
dy/dx of 1/x^2 is
a.-2/x^3
b.2x^ -3/(x^2)^2
c.both
d.none (A)
a.-2/x^3
b.2x^ -3/(x^2)^2
c.both
d.none (A)
40. log x is undefined at
a.0
b.infinity
c.>10
d.<10 (A)
a.0
b.infinity
c.>10
d.<10 (A)
41. in which function we can not determine dependent and independent
variables
a.explicit
b.implicit
c.parametric
d.onto (B)
a.explicit
b.implicit
c.parametric
d.onto (B)
42. something^infinity=
a.infinity
b.zero
c.undefined
d.none (A)
a.infinity
b.zero
c.undefined
d.none (A)
43. an acute angle is
a.>90
b.<90
c.=180
d.>180 (A)
a.>90
b.<90
c.=180
d.>180 (A)
44. in sandwitch theorem angle is measured in
a.radian
b.steradian
c.degree
d.none (A)
a.radian
b.steradian
c.degree
d.none (A)
45. Sum of first 100 consective powers of iota is (LUMS)
a).0
b)-i
c)1
d)i_1 (A)
a).0
b)-i
c)1
d)i_1 (A)
46. derivative of xsina
w.r.t x
a- cosa
b- xcosa+sina
c- -xcosa+sina
d- sina (D)
a- cosa
b- xcosa+sina
c- -xcosa+sina
d- sina (D)
47.the number of ways in which 6 different
beads can be made in to a necklace is ?
a)60
b)48
c)72
d)120
(A)
48.if polygon has 20 diagonals.the number of
its sides are ?
a)6
b)5
c)8
d)7 ©
49.the total number of terms in the expression
of (1-x+x^2)^4 is ?
a)5
b)15
c)10
d)8
(B)
50.the middle term of (a+x)500 is ___ term
a) 501th
b)499th
c)250th
d)251th
(D)
51.the sum of binomial coeeficient of (a+x)^n
is?
a)2^n-1
b)2^n+1
c)2^n
d)n^2
©
52.if tan theta=-1/3 then 3cos 2theta-sin
2theta is
a)4
b)-2
c)-1
d)3
(D)
53.sin75 cos 75 is a/an ?
a)integer
b)rational
c)irrational
d)real
(B)
54.3/4 rotation in anti clock wise direction
a)270 degree
b)-270 degree
c)+270 degree
d)90 degree
(A)
55.the angle coterminal with -71 pi/6 is ?
a)5 pi/6
b)pi/6
c)-5pi/6
d)-pi/6
(B)
56.1+tan^2 theta= ?
a)sin ^2 theta
b)sec^2 theta
c)tan ^2 theta
d)cos ^2 theta
(B)
57.the number of solution points of y=cos x
and y=cos 2x over their period is ?
a)0
b)1
c)2
d)3
(B)
58.in equilateral triangle each angle is ?
a)pi /6
b)pi/3
c)pi/2
d)pi
(A)
59.the ratio of sides of triangle ABC is 1: √3:2 then angles are in the ratio ?
a)3:5:2
b)3:2:1
c) 1: √3:2
d)1:2:3
©
60.cos (2cos^-1 x )is equal ?
a)pi /4
b)pi
c)2 pi
d)2pi/3
(A)
61.tan ^-1 (1/4) + tan^-1 (2/9) is equal to ?
a)a/2 cos ^-1 3/5
b)1/2 sin ^-1 (3/2)
c)1/2 tan^-1 (3/5)
d)tan^-1 (1/2) (D)
62. sec 4x =1/2 can be solved over the interval whose length
is ?
a)8 pi
b)pi
c)pi/2
d)4pi ©
63.if sin 2x- cos 3x =0 then x =?
a)0
b=pi/10
c)pi/2
d)3 pi/2 (B)
64.a trigonometric equation has infinitely many solutions due
to ?
a)continuity
b)discontinuity
c)periodicity
d)smooth curves ©
65.f(x) = |2x-1|
a)f(x) is continuous
a)f(x) is continuous
b)f(x) is discontinuous
c)f(x) undergoes a sudden change in gradient at x=1/2
d)f^-1 exists
©
66.function for which f(x) +f^-1(x) =2f(x)
a)even function
b)odd function
c)f(x)y=1-x
d)f(x)y=1/x
(D)
67.The range of f(x)=x/x^2-9 is ?
a)R-{+-3 }
b)R-{9}
c)R-{0}
d)R (D)
68.d/dx (sin x)=?
a)cos x
b)-sinx
c)cosec x
d)sec ^2 x (A)
69.d/dx (tanhx )=?
a)sechx
b)cosec hx
c)sech^2 x
d)sinhx
©
70.the function y=ax^2 + bx+c has a minimum value if ?
a)a is not zero
b)a>0
c)a<0
d)a=0
(B)
71.)the slope of tangent to the curve y=tab (2tan^-1 x/2) at
x=0
a)0
b)1
c)-1
d)1/4
(B)
72)f:x|à |x^2 -1| ,x belongs to R .f’(1) is?
a)2
b)-2
c)0
d)1
(A)
73) a quadrilateral whose diagonals are always perpendicular
to each other is ?
a)square
b)rectangle
c)rhombus
d)parallelogram
©
74.the distance between x+2y-5=0 and 2x+4y=1 is ?
a)2√6
b)4
c)9/2
d)9/2√5
(D)
75.the perpendicular distance of a line 12x+5y=7 from the
origin is ?
a)13/7
b)7/13
c)13
d)none
(B)
76.two straight lines represented by equation
ax^2+2hxy+by^2=0 are real and distinct if ?
a)h^2-ab>0
b)h^2-ab<0
c)h^2-ab=0
d)h^2-ab is not equal to zero
(A)
77.if x+6y+k=0 is the equation of altitude from A to BC of a
triangle ABC with vertices A(-3,2) ,B(5,4),C(2,-8) then k= ?
a)9
b)-29
c)45
d)-9 (D)
78.a function which is to be maximized or minimized is called
?
a)optimal function
b)maximized function
c)objective function
d)subjective function
©
79) the line y=mx+c intersects the circle x^2+y^2=a^2 in at
the most ?
a)one point
b)two points
c) three points
d)no point
(B)
80.the two circles x^2+y^2-2x-4y=0 and x^2+y^2-8y-4=0
a)touch internally
b)touch externally
c)intersect
d)do not touch
(A)
81.the value of k for which the line 4x+3y+k=0 touches the
circle 2x^2+2y^2-5x=0 is ?
a)15/4
b)-5/4
c)45/4
d)-45/4
(D)
82.the centre of the circle 5x^2+5y^2+14x+12y-10=0
a) (-7,-6)
b) (7,6)
c) (-7/5,-6/5)
d) (7/5,6/5)
©
83.the equation of directix of x^2-4x-3y+13=0
is ?
a)x=2
b)y=3
c)x=9/4
d)y=9/4
(D)
84.xy=c is the equation of ?
a)hyperbola
b)ellipse
c)rectangular hyperbola
d)none
©
85.y=mx+c will be common tangent to y^2=16x
and x^2=2y if ?
a)c=481
b)c=-2
c) c=1
d)c=0
(D)
86.section of right circular cone by a plane
parallel to its base is ?
a)circle
b)parabola
c)ellipse
d)hyperbola
(A)
87.the conic is called pair of straight lines
if ?
a)e=0
b)e= infinity
c)e=1
d)e<1
(B)
88.the points A(-3,5,-4) ,B(-1,1,1) ,C(-1,2,2)
and D(-3,4,-5) are ?
a)collinear
b)coplanar
c)vertices of parallelogram
d)vertices of tetrahedron
(B)
89.th vector u x v is perpendicular to ?
a)u
b)v
c)both u
and v
d)none
©
90.if for two vectors a and b , a.b=0
and a x b=0 then ?
a)a
is null vector
b)b
is null vector
c)a or
b is null vector
d)a
and b are null vectors
©
91)
For any
non zero scalar k,if a = kb , then a and b are ?
a)parallel
b)perpendicular
c)coplanar
d)none
(A)
92) coordinate unit vector i
is defined by ?
a)[1,0]
b) [1,1,0]
c) [0,1]
d) [1,1]
(A)
93)for the vector 3i-j+2k,cos @ is qual to ?
a)3/ √14
b)-1/ √14
c)1/ √14
d)4/√14
(A)
94.if e is the identity element of a group G then inverse of
e is ?
a)1/e
b)e
c)-e
d)none
(B)
95.)if A and B are non singular matrix with the same order
then (BA)^-1 is ?
a)B^-1 A^-1
b)A^-1 B^-1
c)BA
d)AB
(B)
96.diagonal matrix can never be ?
a)symmetric
b)skew- symmetric
c)scalar
d)all
(B)
97) the roots of x^2=4a (mx+c) are equal if ?
a)c=a/m
b)c= -am^2
c)-a/m
d)c=am^2
(B)
98.the number of complex cube roots of unity is ?
a)1
b)2
c)3
d)infinite
(B)
99)the numbers 1/a ,a+b/2ab ,1/b are in ?
a)H.p
b)A.P
c)G.P
d)none
(B)
100)if the 5th A.M between 4 and 8 is 13/2 then
number of A.Ms inserted between 4 and 8 is ?
a)5
b)7
c)6
d)4
(B)
No comments:
Post a Comment