Question # 1

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3

1

4

Cos (α+β) - cos (α-β) =

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-2 sinα sinβ

2 sinαcosβ

-2 sinαcosα

4 sinα cosβ

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

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True

False

Ambiguous

Some times true

If z=(x,y) then z has no multiplicative inverse when

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x ≠ 0, y = 0

x = 0, y = 0

x = 0, y ≠ 0

None of these

Two circle x² + y²+2x - 8 = 0 and x² + y² -6 + 6x -46 =0:

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touch internally

do not intersect

touch externally

None of these

If f(x) = x³- 2x²+ 4x -1 then f(0) is

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0

1

-1

none of these

If f(√x)=sin x , then f′(x) =______;

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2xcosx2

cosx2

cos√x

None of these

In R the right cancellation property w.r.t. addition is

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The sets {1, 2, 4} and {4, 6, 8, 10} are

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Equal sets

Equivalent sets

Disjoint sets

Over lapping sets

8 . 7 . 6. 5 in factorial form is

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Let A be a square matrix. Then, 1/2 (A-A') is

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Skew-symmetric

Symmetric

Null

None of the above

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5 / 12

3 / 8

5 / 8

7 / 4

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The maximum value of 12 sinθ-9 sin²θis x

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3

4

5

None of these

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none of these

Sin -1 x=

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sin(π/2-x)

Sin-1 (π/2-x)

π/2-cos-1x

π/2 + cos-1x

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quadratic function

constant function

linear function

exponential function

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0

1

undefined

An improper rational fraction can be reduced by division to a

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Proper fraction

Polynomial

mixed form

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I quadrant

II quadrant

III quadrant

IV quadrant

If w is a cube root of unity then 1 + w + w²= ______

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1

2

0

-1

If θ be angle between u,v and u,v determine the sides of a triangle then the third side opposite to angle θ has length

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|u+v|

|u|+|v|

|u-v|

|u|-|v|

The parabola y²= x is symmetric about

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x-axis

y-axis

Both x and y-axis

The line y = x

If sin (πcosθ) = cos (πsinθ), then which of the following is correct?

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Sum of two quantities is at least 20 is denoted by

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x +y =20

x +y≥ 20

x +y≠ 20

x +y≤20

x = sin^-13, then the value of sin x is

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√(3/2)

3

Not possible

-1

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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Tan(α-β)=

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