Question # 1

d/dx [cos x²] =________

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-2x cos x²

-2x² sin x²

x² sin x

-2x² sin x²

Cos 315° =

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0.707

0.5

1

0

Which of the following is not defined?

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Arcsin 1/9

ArcCos (-4/3)

Arctan 11/12

Arccot (-4)

The set of all positive even integers is

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Φ

{1,2,3}

{Φ}

{0}

Sin x + Cos x=1 x=

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π

π/2

π/3

π/4

In the figure angle A is =

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15

60

90

20

Which is in the solution set of 4x - 3y <2

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(3,0)

(4,1)

(1,3)

None

If ab > 0 and a < 0, which of the following is negative?

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b

-b

-a

(a - b)²

The direction cosines of y-axis are

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1,0,0

0,1,0

0,0,1

1,1,1

An angle of one radian is equivalent to

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90^o

60^o

67^o

57^o, 18^o

How many elements are in the sample space of two rolling dies

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6

12

18

36

If a line passes through origin then the equation of the line is

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y = m/x

y = mx

x = my

None

If you looking a high point from the ground then the angle formed is

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Angle of elevation

Angle of depression

Right angle

Horizon

The length of rectangle is twice as much as its breadth. If the perimeter is 120 cm, the length of the rectangle is

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Same as the original determinant

Additive inverse of the original determinant

Both A and B

Adj of the original matrix

How many different arrangements of the letters in the word QABABA are Possible?

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720

40

60

30

If 2 Sin x Cos 2 x = Sin x then?

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X = nπ+ π/6

X = nπ +π/3

X = nπ +1

X = nπ + π/2

The cube roots of unity ω = -------------------------

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1-i √-3 / 2

-1+i √-3 / 2i

-1+i √3 / 2

1+i √3 / 2

The equation of two polynomials P(x)/Q(x) where Q(x) ≠ 0 with no common factor is called

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12

1

10

-10

If θ= 60° then

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sin θ = 1/2

tan θ = cot 30°

θ = π/4

Sec θ =4

The equation of the normal to the circle x² + 2² = 25 at (4,3) is

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3x -4y =0

3x -4y= 5

4x + 3y=5

4x - 3y =25

The sum of the interior angles for a 16 sided polygon is

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0

ω

1

1 / ω

The difference of two consecutive terms of an A.P is called

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Zero

One

Four

Infinite

If α and β be irrational roots of a quadratic equation, then

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α = b/a and β = ca

α = a/b and β = -c/a

α² + β² = 1

α = -b/a and β= c/a

8 > t then

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(s -t) ²>(t -8)²

(s -t) ²<(t -8)²

(s -t) ²=(t -8)²

None

If f(x) : A → B and g (x) : A → B then Dom [f(x) + g(x)] is

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Dom f(x) ∩ Dom g (x)

Dom f(x) ∪ Dom g(x)

[Domf(x)]² - [Dom g(x)]²

[Dom g(x)]²-[Domf(x)]²

Partial fraction of 1/x³-1 will be of the form

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Conjugate pair

ordered pair

reciprocal pair

quadratic function

Cos^-1 x =

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∏ = sin^-1 x

∏ + sin^-1 x

∏/2 - sin^-1 x

∏/2 +sin^-1 x

If y = (ax)^m + b^m, then dy/dx equals

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m (ax)^m x^m-1

ma^m x^m-1

m a^m x^m-1

m a^m x^m-2

If A and B are two events then P(A∪B) =? (when A and B are disjoint)

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P(A) - P(B)

P(A) x P(B)

P(A) + P(B)

P(A) + P(B) -P(A∩B)

Domain of Y = csc x is

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R - nπ, n ε I

R

R -nπ/2,nεI

All negative Integers

If the order of A is n x m. Then order of kA is

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Forms a group

Does not form a group

Contains no additive identity

Contains no additive inverse

A fraction in which the degree of the numerator is less than the degree of the denominator is called

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1-i √-3 / 2

-1+i √-3 / 2i

-1+i √3 / 2

1+i √3 / 2

If the diagonal of a square has coordinates (1,2) and(5,6) the length of a side is

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3

4

1

5

If any two rows (or any two columns) of a square matrix are inter changed, the determinant of the resultant matrix is

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True

False

Fallacious

Some times true

If in isosceles right angled triangle one side is a then hypotenuse is

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a√2

a/2

a

Cannot be determined by given

If x < y, 2x = A and 2y = B then

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A =B

A < B

A< X

B < y

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

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Major axis

Minor axis

Focal axis

Conjugate axis

The radius of the circle (x- 1)² + (y + 3)² =64 is

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8

2√2

4

64

The area of circle of unit radius=

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0

1

4

π

Sin-1 (√2/2)=?

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π/2

π/3

3π/4

2π

Sin^-1 (-x) =

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Cos^-1 1/x

-Sin^-1 X

1/sin-1x

Sin^-1 1/x

Which is an explicit function

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y = x² +2x -1

x² +xy +y² =2

xy² -y +9/xy =1

All are

If the 9^th tern of A.P is 8 and the 4^th term is 20. then the first term is

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1

2

-2

-1

Ab > 0 and a > 0 then

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a > b

a < b

a = b

None

Tan^-1 1/x =______

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Sin x

Sec^-1 X

Cot^-1 X

Sin Ix/cos- Ix

120° degrees are equal to how many radians?

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π/3 radians

2π/3 radians

π/4 radians

π/2 radians

The range of inequality x + 2 > 4 is

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(-1,2)

(-2,2)

(1,∞)

None

Tan (π + Tan^-1 x) =?

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Tan x

X

-x

Cot^-1 x

Cos^-1 (-x) =_______.

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π +cos^-1 x

π -sin^-1 x

π +sin^-1 x

π -cos^-1 x

d/dx (√x) =

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2√x

1/√x

1/2√x

None of these

The line joining (1,3) to (a,b) has unit gradient then

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a-b =-2

a+b = 0

A-b =5

2a + 3b =1

Sin (2π -θ) =______.

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Cosθ

-Sinθ

-cosθ

The mid point of the line joining (=1,-3) to(3,-5) is

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(1, 1)

(1,-1)

(2, -8)

(1, -4)

Corola available in 5 models 8 colours and 3 sizes how many Corola must a local dealer have no hand in order to have one of each kind avialable?

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24

120

16

39

The parametric equation of a curve are x = t², y = t²then

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dy/dx =3t/2

dy/dx =t⁵

dy/dx =5t⁴

None

r + 3 > 5 then which is true

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r + 2 > 4

r + 2 < 4

r + 2 + 4

None

x is a member of the set {-1,0,3,5} y is a member of the set {-2,1,2,4} which is possible?

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x- y =-6

x -y < -6

x -y > 6

None

The set { {a,b} } is

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{X/X∈ A∧x ∈ U}

{X/X∉ A∧x ∈ U}

{X/X∈ A and x ∉ U}

A-U

Sin 720° = ________

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1

0

2

1/2

The Domain of f(x) = log x is

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[0,∞]

(0, ∞)

[0,∞[

[∞ ,∞]

P(x) = 2x⁴ -3x³ +2x-1 is polynomial of degree

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1

2

3

4

∫sec (ax + b) tan(ax + b) dx=_______

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sec(ax + b)/a

sec² (ax + b)/2

sec(ax + b)/x

1/2

If A and B are matrices such that AB=BA=I then

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A and B are multiplicative inverse of each other

A and B are additive inverses of each other

A and B are singular matrices

A and B are equal

Second derivative of y = x⁹ + 10x² + 2x -1 at x = 0 is

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10

20

12

1

What is the domain of y = Cot^-1 x?

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Set of irrational numbers only

Set of all real numbers

Set of integers only

Set of complex numbers only

The nth term in G.P 3,-6,12,............ is

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25, 20

20, 10

20, 5

15, 10

The point (-5,3) is the center of a circle and P(7,-2) lies on the circle the radius of the circle is

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2

13

7

8

The number of ways in which 5 distinct toys can be distributed among 3 children is

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3⁵

5³

C⁵₃

P⁵₃

If Z₁ = √-36, Z₂=√-25, Z₃= √-16, then what is the sum of Z₁, Z₂ and Z₃ ?

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√3 I

√7

-2-1

√5

The principal value of sin^-1 [√3/2] is

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π/3

-π/3

2π/3

5π/3

Which of the following is the equation of a line with slope 0 and passing through the point (4,3)

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X =4

X = -4

Y = 3

Y = -6