Question # 1

The statement that a group can have more than one identity elements is

Question # 2

The set of the first elements of the orders pairs forming a relations is called its

Question # 6

Given X,Y are any two sets such that number of elements in set X = 28, number of elements in set Y = 28, and number of elements in set X∪Y = 54, then number of elements in set X ∩ Y =

Question # 7

The sum of the focal distance from any point on the ellipse 9x^{2} +16y2 =144 is

Question # 13

Every term of a G.P. is positive and also every term is the sum of two preceding terms. Then the common ratio of the G.P. is

Question # 17

The coefficient of the third term of (8a-b)^{1/3}, after simplification is

Question # 23

The exterior angle of the interior angle C of he quadrilateral whose vertices are A(5,2),B(-2,3),C(-3,-4),D(4,-5) is

Question # 24

The probability to get an odd number in a dice thrown once is

Question # 25

A matrix in which the number of rows is not equal to the number of columns is called a

Question # 27

Digit in the unit place of the number 183! + 3^{183}

Question # 28

The standard parabolic form of the equation f(x) = x^{2} +4 x +1 is

Question # 30

How many necklaces can be made from 6 beads of different colours?

Question # 31

Optimize means ______ a quantity under certain constraints

Question # 32

If p, q, r and in A.P., a is G.M. between p and q and b is G.M. between q and r, then a^{2}, q^{2}, b^{2}are in

Question # 34

The direction cosines of a line equally inclined with co-ordinate axes are

Question # 38

The total cost of 2 apples and 3 oranges is $1.70, which of the following is true

Question # 40

The slope of the tangent of the circle x^{3} + y^{3} =25 at (4,3) is:

Question # 47

Number of combination of zero or more things out of n different things

Question # 48

The general solution of the differential equation x dy / dx = 1 + y is:

Question # 49

If the sum of two unit vectors is a unit vector the the magnitude of their difference is

Question # 50

The line through the centre and perpendicular to the transverse axis is called the

Question # 51

If cos (2 sin-1 x) = 1/9 , then what is the value of x?

Question # 52

√2 +√3 +√5) = (√2 +√3 +√5: this property is called

Question # 56

The number of the diagonals of a 6 sided figure is

Question # 60

The st. lines whose direction cosines satisfy al + bm + cn = 0, fmn + gnl + hlm=0 are perpendicular if

Question # 63

The approximate increase in the area of a circular disc if its diameter increased form 44cm to 44.4cm is

Question # 66

The line y = 4x + c touches the hyperbola x^{2}- y^{2}= 1 if

Question # 70

Two matrices A and B are conformable for the product AB if

Question # 72

The set {-1,1} is closed under the binary operation of

Question # 75

If x-2 and x-1 both are factors of x^{3}-3x^{3}+2x-4p, then P must equal to

Question # 84

Every relation, which can be represented by a linear equation in two variables, represents a

Question # 87

Power set of X i.e P(X)..........under the binary operation of union U

Question # 89

In set builder notation the set {0,1,2,........100} can be written as

Question # 90

Which shape of the following objects are approximately parabolic ares?

Question # 95

Write the first four terms of the arithmetic sequence 5, 2, -1, ... is

Question # 96

Area bounded between the curve xy=2 and the lines x=1 and x=2

Question # 104

Sand falls from a tube in such a way that it forms a cone whose height is always 4/3 times the radius of its base and radius of the base increases at the rate of 1/8 cm/sec. When this radius is 1 meter, the rate at which the amount of sand increases is

Question # 108

If y = sin (ax + b), then fourth derivative of y with respect to x =

Question # 116

If there is one-one correspondence between A and B, then we write.

Question # 117

The area enclosed between the graph y = x^{2 }-4x and the x- axis is:

Question # 120

If x is an image of y under the function f. This can be written as

Question # 124

If the angle between two vectors__ u__ and __v__ is 0 orπ, then the vectors __u__ and __v__ are:

Question # 127

The set {x +iy / x, y ∈ Q} forms a group under the binary operation of

Question # 129

If a,β are the roots of the equation x^{2} + kx +12 = 0 such that a - β = 1, the value of k is

Question # 141

If the st. line 3x + 4y = K touches the circle x^{2}+ y^{2}- 10x = 0 then the value of K is

Question # 143

The equation of the normal to the circle x^{2}+ y^{2}= 25 at (4, 3) is

Question # 146

A non-terminating non_recurring decimal represents an

Question # 147

How many arrangements of the letters of the word MATHEMATICS can be made

Question # 148

The remove the term involving xy, from 7x^{2} -6√3xy+ 13y^{2} -16 =0 the angel of rotation is

Question # 150

The solution set of the equation 4 cos^{2}x - 3 + 0 is

Question # 155

If one end of the diameter of the circle x^{2} + y^{2}- 5x = 3y -22 = 0 is (3,4) the other end is:

Question # 159

The slope of the tangent at the point (h,h) of the circle x^{2} +y^{2} =a^{2} is

Question # 164

The points (5, 2, 4)(6, -1, 2) and (8, -7, k) are collinear if k is equal to

Question # 168

p(x) = 2x^{4}- 3x^{3}+ 2x - 1 is polynomial of degree

Question # 172

A subset of set of complex number whose elements are of the form (a,0) is called

Question # 173

The series obtained by adding the terms of a geometric sequence is called

Question # 179

The law of cosines reduces to a^{2} +c^{2} =b^{2 }for

Question # 180

Two balanced dice are tossed once, the sample space when the integers on the faces of two dice are the same is

Question # 185

Out of 10, 000 families with 4 children each, the number of families all of whose children are daughters is

Question # 186

The line y =mx +1 is tangent to the parabola y^{2} =4x if

Question # 190

The sum of the roots of the equation x^{2} -6x +2 = 0 is

Question # 193

If the intersecting plane is parallel to a generator of the cone, but intersects its one nappe only, the curve obtained is

Question # 195

The points (5, 0, 2), (2, -6, 0), (4, -9, 6) and (7, -3, 8) are vertices of a

Question # 197

If 2 tan^{1}(cos x) = tan^{-1}(cosec^{2}x), then x is equal to

Question # 201

An observer on the top of a cliff 200 m above the sea level, observes the angles of depression of two ships on opposite sides of the cliff to be 45° and 30°, respectively. The distance between the ships if the line joining them points to the base of cliff is

Question # 202

The area of the circle centred at (1,2) and passing through (4,6) is

Question # 204

In order of A is m x n and order of B is n x p then order of AB is

Question # 205

If a polynomial p(x) is divided by x-c, then the remainder is

Question # 207

The set of the first elements of the ordered pairs forming a relation is called its

Question # 209

AB is a vertical pole and C is its middle point. The end A is on the level ground and P is any point on the level ground other than A. the portion CB subtends and angle*β*at P. If AP : AB = 2 : 1 then*β*=

Question # 215

Equation of normal to the circle x^{2} + y^{2} =25 at (5cosθ,5sinθ)

Question # 216

The degree of differential equation is the power of the