Merit Students
Time: 1 Hr.
BITSAT - MATHEMATICS
Total Marks: 50
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Q 1:
, where z is non real, can be the angle of
)
a triangle if
b
a Re( z) = 1
)
) Im( z) = 2
c
b
)
)
d
c Re( z) +
)
) Im( z) = 0
d
)
,
,
, admit of nontrivial
solutions then
is
b
)
b
)
c
)
d
)
, H2 } are two arithmetic
a
)
b
d
)
a2 + b2
none of these
Q 6: Let
upto 50 terms, then
none of these
a
is
)
1
)
1
Q 3: The number of irrational terms in the expansion of
a
a = 60, b = 64
c
)
)
a = 60, b = 100
numbers a and b, then value of
)
2
c
d
a = 60, b = 25
means ( geometric) ( harmonic) between two positive real
none of these
y) = z, where
)
a = 30, b = 25
Q 5: If A1 , A2 ( G1 , G2 ) , {H
Q 2: If the equation a ( y + z) = x, b( z + x) = y and c ( x +
a
a
)
b
)
97
E is divisible by exactly 2 primes
E is even
c
)
98
d
)
96
Q 7: A natural number x is chosen at random from the first one
hundred natural numbers. The probability that
99
is
Q 4: The value of a and b so that x4 + 12x3 + 46x2 + ax + b is
square of quadratic expression is
a
)
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b
d
)
)
c
Q 11: The roots of
)
and a and b which can be real or complex. Then the value of k
d
such that a2 + b2 is as small as possible is
)
a
Q 8: The value of the expression
)
none of these
, where k is a real number,
k=2
b
)
a
)
b
)
c
)
d
)
c
1648
)
d
1646
)
Q 12: If
1645
a
)
zero
)
one of their digits repeated is
c
a
)
b
)
c
)
d
)
90000
)
10000
Q 13: If cos A + cos B + 2 cos C = 2 then the sides of the
are in
30240
a
)
69760
b
is
)
b
x<0
d
Q 10: The number of distinct terms in the expansion of
a
then
b
Q 9: The number of five-digit telephone numbers having at least
)
none of these
)
c
)
d
)
AP
BP
HP
none of these
)
Q 14: In a triangle ABC, cos A + cos B + cos C
c
triangle is
)
, then the
a isosceles
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Contact No. 9766616435
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)
b
)
c
)
d
)
)
Q 18: If sinx + cos y = a and cos x + sin y = b, then
right angled
equal to
equilateral
a
)
none of these
a+b
b
)
Q 15:
is equal to
c
a
)
)
d
b
)
)
Q 19: If
then x =
c
a
)
)
d
b
)
)
Q 16: The value of
is
c
tan 3
3 tan
tan
a
)
)
d
b
)
)
Q 20: Which of the following functions is an odd function.
c
a
)
)
d
)
b
none of these
)
Q 17: The smallest angle of the triangle whose sides are
is
c
)
a
d
)
)
b
3 cot
none of these
Q 21: If
)
c
a
)
)
d none of these
b
is
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Contact No. 9766616435
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is
)
d
c
)
)
Q 25: The value of
d
)
function
none of these
, where [.]
represents greatest integral function is
)
b
)
c
)
d
)
)
b
199
)
c
200
)
)
Q 26: If the line aX + bY + c = 0 is a normal to the curve xy = 1.
none of these
then
)
Is differentiable at x = 1, then
b
a
)
a = 1, b = 1
c
b
)
)
d
c
)
d
)
b
)
c
)
a > 0, b < 0
a < 0, b > 0
a < 0, b < 0
Q 27:
none of these
is equal to
a
( where [x] denotes the greatest integer
x) is
)
a > 0, b > 0
a = 1,
Q 24:
a
2
d
198
a
)
becomes continuous, is equal
a
Q 23: If
)
so that the
to
Q 22: The value of
a
none of these
)
b
)
1
c
left hand limit is 1, right hand limit non existent
d
right hand limit 1 and left hand limit
Q 28:
)
)
, then
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Contact No. 9766616435
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a
a
)
)
b
b
)
)
c
c
)
)
d
)
d
none of these
Q 29: Let
)
where [] denotes the integral part.
none of these
Q 32: Let
be three non-coplanar vectors such that
,
Then the function
a
)
b
)
c
)
,
. If
has a removable discontinuity at
,
, then
a
)
is differentiable at
b
)
is periodic having period
c
d
)
)
d
Q 30: Let
)
, when g is such that
Q 33: ABCD is a quadrilateral and E is the point of intersection
of the lines joining the mid-points of opposite sides. If
, then x =
Then
satisfies the inequality
a
a
)
)
b
b
)
)
c
c
)
)
d
)
d
)
none of these
Q 31: Let
and
be two vectors
to each other
in the x-plane. then a vector in the same plane having
projections 1 and 2 along
and
respectively, is
3
4
7
9
Q 34: The sides of a parallelogram are
and
.
The unit vector parallel to one of the diagonals is
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Contact No. 9766616435
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a
)
)
c
b
)
)
d
c
)
)
Q 38: If D, E, F are mid points of the sides BC, CA, AB
d
respectively of a triangle ABC, then
)
Q 35: A vector a has components 2p and 1 with respect to a
rectangular Cartesian system. The system is rotated through a
certain angle about the origin in the counterwise sense. If a has
components p + 1 and 1 with respect to the new system, then
a
)
b
)
c
)
d
)
)
b
)
c
)
d
)
)
p=0
)
)
d
p = 1 or p =
)
2
none of these
Q 39: If
p=
or p =
and
are the adjacent
sides of a parallelogram, then angle between the diagonals is
a
p = 1 or p =
)
is equal to
b
)
0
c
)
a
d
)
2a
Q 40: Let
and
. If
a unit vector
,
none of these
then the maximum value of the scalar triple product
Q 37: If a and b are non-perpendicular vector then a vector r
a
satisfying
)
by
0
b
c
Q 36: The vector
a
a
and
= 0, where c is any vector is given
b
a
)
)
c
b
)
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is
d
a
)
)
Q 41: Equation of the tangent to the parabola
makes an angle
a
)
which
b
)
with its axis is
c
y = x tan
)
b
d
)
)
c
Q 45: The equation
represents a sphere
)
d
if
is
)
a
Q 42: Triangle OAB ( O is origin) lies in XOY plane. OA = 3
)
units, OB = 4 units and area of the triangle is 6 sq. units. Locus
b
of D where D is foot of perpendicular from O onto AB is given by
)
a
c
)
)
b
d
)
)
c
Q 46: The equation of the sphere concentric with the sphere
zero or negative
negative
zero
positive
)
and which passes through
d
the origin is
)
a
Q 43: The centre of the circle
)
is
b
a ( 2,
)
) 3)
c
b
)
)
d
c
)
)
d
)
none of these
Q 47: If a line segment AM = a moves in the plane XOY
none of these
Q 44: The angle between the two planes
is
remaining parallel to OX so that the left end point A slides along
and
the circle
, the locus of M is
a
)
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b
b
)
)
c
c
)
)
d
d
)
)
2, 3
3, 4
4, 5
Q 48: Equation of the locus of the pole with respect to the
ellipse
, of any tangent line to the auxiliary circle is
the curve
where
a
)
b
)
c
)
d
)
Q 49: Point P is on the closed segment joining ( 2, 0) and ( 0,
1) and point Q is on the closed segment joining ( 6, 0) and
( 0, 6) .
Then length of the shortest possible segment
a
)
is
2
b
)
c
)
d
)
none of these
Q 50: The equation of the circle which touches the axes of the
co-ordinates and the line
the first quadrant of
a
)
and whose centre lies in
where c is
1, 6
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