Question # 1

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If f(x) = x³- 2x²+ 4x -1 then f(2) is

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7

-16

16

-9

r + 3 >5 then which is true

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r + 2 > 4

r + 2 < 4

r + 2 = 4

None

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sin x + c

-sin x + c

cos x + c

-cos x + c

The range of y = cot x = ______

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-∞> y > +∞

-∞> x > +∞

-∞ <y < +∞

None of above

Domain of tangent function is

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Additive property in R

Multiplication property in R

Cancellation property in R

Distribution property in R

The mid point of the line segment joining the points (3,-1) and (-3,1) is

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(3,-1)

(0,0)

(2,2)

(4,4)

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2

4

3

16

All letters of the word "AGAIN" are permuted in all possible ways and the words so formed (with or without meaning) are written as in dictionary, then the 50th word is

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NAAGI

NAAIG

IAANG

INAGA

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

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Infinite series

Arithmetic series

Geometric series

Harmonic series

A combination lock on a suitcase has 3 wheels each labeled with nine digits from 1 to 9. If an opening combination is a particular sequence of three digits with no repeats, the probability of a person guessing the right combination is

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1 / 500

1 / 504

1 / 252

1 / 250

A vector with magnitude one is called

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constant vector

unit vector

zero vector

null vector

The distance between the points A(-8,3) and B(2,-1) is

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116

none of these

0! = ______

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0

1

2

Not defined

If B ={x/x€ Z ^ - 3 < x < 6}, then n (B) =

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5

{-3,-2,-1,0,1,2,3,4,5,6}

8

9

If|a| =|b|=|a + b|=1, then|a+ b| = 5, then|a-b| =

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4

6

5

3

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(x³- 3x²)⁸+ c

3x²- 6x + c

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1

-1

-1/2

1/2

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Coordinates of the focus of the parabola x² - 4x -8y-4=0 are:

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(0,2)

(,0,1)

(2,0)

(1,2)

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If a^x= b^y= c^zand a, b, c are in G.P. then x, y, z are in

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A.P.

G.P.

H.P.

None of these

The number of values of x in the interval [0, 5π] satisfying the equation 3 sin²x - 7 sinx + 2 = 0 is

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0

5

6

10

sin (α+β) - sin (α -β) =

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4 cosαsinβ

2 cosαsinβ

4 cosαcosβ

4 sin αsinβ

The square of the distance between two points P(x₁, y₁) and Q(x₂, y₂) is

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Which element is the additive inverse of (a, b) in Complex numbers?

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(a, 0)

(0, b)

(a, b)

(-a, -b)

A circle which touches one side of a triangle extermally and the other two sides produced is called

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In-circle

Circumcircle

e-circle

Point circle

The straight line passing through the focus and perpendicular to the directrix of the conic is known as its

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Tangent

axis

Focal chord

major or manor axis

If ax²+ bx + x = 0 is satisfied by every value of x, then

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b = 0, c = 0

c = 0

b = 0

a = b = c = 0

∀ a ε R ∃ o ε R such that a + v = 0 + a = a is property of

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Commutative law of addition

Associative law of addition

Additive identity

Additive inverse

If A and B are skew-symmetric then (AB)t is

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At Bt

AB

-AB

BA

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cos x

sec x tan x

sec²x

-cosec²x

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Evert element of A is in B

Every element of B is in A

Every element of A is in B'

Every element of A is in A

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Rational fraction

Proper fraction

Improper rational fraction

None of these

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 angleβat P. If AP : AB = 2 : 1 thenβ=

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y=0 of the parabola y² = 4ax is the

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equation of directirx

Equatio of the tangent

Equation of axis

equation of latus rectum

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The mid point of the line joining the points P(x₁, y₁) and Q(x₂, y₂) is

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xy= 2 is:

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a constant function

an identity function

an improper function

implicit function

Cos 0° = ______

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-1

0

1

Undefined

______________ invented a symbolic way to write the statement "y is a function of x" as y= f(x)

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Leibniz

Newton

Euler

None of these

For which of the following ordered pairs (s, t) is s + t > 2 and s - t < -3?

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(3, 2)

(2, 3)

(1, 8)

(0, 3)

x²+ x - 6 = 0 is a conditional equation and it is true for

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2, 3

2, -3

-2, -3

-2, 3

The point ________ is in the solution of the inequality 2x - 3y < 4

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(0, -2)

(1, -3)

(2, 2)

(3, 0)

A chord passing through the centre of the circle is called

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the secant of the circle

the tangent of the circle

the arc of the circle

the diameter of the circle

Geometrically the modulus of a complex number represents its distance from the

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Point (1,0)

Point (0,1)

Point (1,1)

Point (0,0)

The vertex of the equation y² = 4ax is:

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(2, -2)

(1,1)

(0 , 0)

(2 , 2)

The sum if 1,3,5,7,9........ up to 20 terms is

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400

472

563

264

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∀x, y ∈ R, either x = y or x > y or x < y is

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Transitive property

Reflexive property

Trichotomy property

None of these

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If a plane passes through the vertex of a cone then the intersection is

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an ellipse

a hyperbola

a point circle

a parabola

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none of these

If a, b, c, d, e, f are in A.P.,then e-c is equal to

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2(c - a)

2(f - d)

2(d - c)

d - c

If S is a sample space and event set E = S then P(E) is

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>0

1

<1

0

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a

2a

3a

4a

A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. Then CP²+ CQ²+ CR²+ CS²=

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r²

2 r²

3 r²

4 r²

The distance of a moving particle at any instant t is x = 3t2 +1 then velocity of particle at t = 10 is

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50 cm/sec

60 cm/sec

61 cm/sec

None of these

The equation of the directrix of the parabola x²= 4ay is

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x + a = 0

x - a = 0

y + a = 0

y - a = 0

If a 1-1 correspondence can be established b/w two sets A and B, then they are called

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Equal sets

Equivalent sets

Over lapping sets

None of these

A sequence of number whose reciprocals form an arithmetic sequence is called

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Geometric sequence

Arithmetic series

Harmonic sequence

Harmonic series

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none of these

i²=

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1

2

-1

0

The magnitude of vector a=i-3j+5k is:

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3

√35

√17

√35

The point of concurrency of the medians of the ΔABC is called its

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Orthocenter

Centriod

Circumcentre

Incentre

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π

2π

π/2

None of these

The period of sin x/2 = Cos x/3 is

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2p

12p

13p

7p

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2

6

There are ______ basic techniques for solving a quadratic equation

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Two

Three

Four

None of these

Total number of subsets that can be formed out of the set {a,b,c} is

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1

4

8

12

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0

abc

1/abc

None of these

The system of measurement in which the angle is measured in radians is called the

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circular system

CGS system

sexagesimal system

none of these

3x + 4 < 0 is

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not inequality

equation

identity

inequality

If for two events A and B , P(A∪B)=1,then events A and B are

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Certain events

Mutually exclusive

Complementary events

Independent

For two events A and B if P(A) = P (A/B) = 1/4 and P(B/A) = 1/2, then

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A is sub-event of B

A and B are mutually exclusive

A and B are independent and P(A/B) = 3/4

None of these

cos h²x + sin h² x

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an even function

an odd function

an even and implicit function

neither even nor a odd

The upper 3/4 the portion of a vertical pole subtends an angle tan^-13/5 at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is

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20 m

40 m

60 m

80 m

The additive inverse of 0 is

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1

-1

0

Does not exist

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(A ∩ B)c =

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A∩ B

(A ∪ B)c

Ac∪Bc

Φ

For any set X, X∪X is

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X

X'

Φ

Universal Set

The zero vector is

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[0, 0, 0]

[1, 1, 1]

[0, 1, 0]

[0, 0, 1]

(1,0) is in the solution of the inequality

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3x + 2y > 8

2x - 3y < 4

2x + 3y > 3

x - 2y < -5

The point lying on the terminal rat of -270° is

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(1,0)

(0,-1)

(0,1)

(-1,0)

If 0 = {1,3,5.......}, then n (0) =

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99

odd integers

Even numbers

Infinite

Cos (α+β) - cos (α-β) =

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-2 sinα sinβ

2 sinαcosβ

-2 sinαcosα

4 sinα cosβ

The solution set of x²- 5x + 6 = 0 is

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{1, 3}

{2, 3}

{1, 2}

None of these

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π

π / 2

π / 3

π / 4

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Conclusion

Implication

Antecedent

Hypothesis

(n + 2) (n + 1) n= ______

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If d₁is the distance between (0,0) and (1,2) and d₂is the distance between (0,0) and (2,1) then

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d₁= d₂

d₁<d₂

d_1>d₂

none of these

If we have a statement "if p then q" then q is called

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Conclusion

Implication

Unknown

Hypothesis

The eccentricity of the conic 9x²- 16y²= 144 is

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4/5

5/4

4/3

3/4

The point ________ is in the solution of the inequality 2x - 3y > 5

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(1, -1)

(2,2)

(0,0)

(3,0)