Question # 1

The set of real roots of the equation log_{(5x + 4)}(2x +3)³- log_{(2x + 3)}(10x²+ 23x + 12) = 1 is

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{-1}

{-3/5}

Empty set

{-1/3}

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(1,7/3)

(1, 7/5)

(1, 11/7)

(1, 3/5)

The points A(3,1),B(-2,-3),C(2,2) are vertices of an (an)

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Right triangle

Equilateral triangle

Isosceles triangle

Scalene triangle

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3 x 2

2 x 3

3 x 3

2 x 2

Range of cosecθis

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W - {y | -1 < y < 1}

R - {y | -1 < y < 1}

O - {y | -1 < y < 1}

R

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

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A finite non-empty set

Null set

Both a and b

None of these

sin (α +β)=

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sinαcosβ- cosαsinβ

sinαcosα- cosβsinβ

sinαcosα+ cosβsinβ

Which of the following is a scalar

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weight

force

speed

momentum

O (0,0)is called:

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Position vector

Free vector

Unite vector

Null vector

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tan(3π/2 +θ)=______;

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tanθ

cotθ

-tanθ

-cotθ

Equation of the chord of contact to the tangents drawn from (-3,4) to the circle x2 + y2 = 21

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-3x + 4y =21

4x - 3x = 0

-3x + 4y = 25

None of these

The set {1,-1,i,-i}

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Form a group w.r.t addition

Form a group w.r.t multiplication

Does not form a group w.r.t multiplication

Not closed under multiplication

The value of n, when ⁿP₂= 20 is

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3

4

6

5

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trigonometric equation

conditional equation

identity

None

Union of the sets of rational and irrational numbers is called 6th set of

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Natural numbers

Real numbers

Whole numbers

Prime numbers

If f(x) = x²then f(-2) is

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-2

2

4

-4

Which of the following function form 1 to itself are bi-jective

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F(x) = x + 3

F(x) = x⁵

F(x) = 3x + 2

F(x) = x²+ x

System of linear equations is inconsistent if

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System has no solution

System has one solution

System has two solution

None of above

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If (1+x-2x³)⁶= 1+a₁x + a₂x²+ a₃x³+ ..... the the value of a₂+ a₄+ a₆+ .....+a₁₂will be

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32

31

64

1024

The coefficient of xn in the expansion of (1-x)-1 is

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(-1)n2n

1

(-1)n(n+1)

(n+1)

To each element of a group there corresponds ............. inverse element

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Two

One

No

Three

sn (2sin-10.8)

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0.56

0.69

-0.16

0.96

If x + y + 1 = 0 touches the parabola y²=λx, thenλis equal to

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2

4

6

8

We also the system of non-homogeneous linear equations by

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a and b

b and c

c and a

a, b and c

Cofactor of an element a_ijis defined by

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(-1)^i+j|A|

(-1)^i+jM_ij

(-1)^i+jM^-1

None of these

The law of cosines reduces to a2 +c2 =b2 for

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α = 90°

β = 90°

γ = 90°

α +β +γ =180°

The solution set of the equation 4 cos²x - 3 + 0 is

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none of these

(x + 3) (x + 4) = x²+ 7x + 12 is ______

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Quadratic equation

Linear equation

Cubic equation

Identity

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