Question # 1

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 (Q, .)

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Infinite set

Singleton set

Two points set

None

∫cot (ax + b) dx =

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1/a log |sin (ax + b)| +c

1/a log |cos ax + b)

1/b |sin (ax + b)|

1/a log |sin (bx + a)|

The axis of the parabola y² = 4ax is

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x =0

Y =0

X = y

X = -y

In a school, there are 150 students. Out of these 80 students enrolled for mathematics class, 50 enrolled for English class, and 60 enrolled for Physics class. The student enrolled for English cannot attend any other class, but the students of mathematics and Physics can take two courses at a time. Find the number of students who have taken both physics and mathematics.

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40

30

50

20

In the function v = 4/3 π r³, V is a function of

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3/4

r

v

π

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 θ= 60° then

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sin θ = 1/2

tan θ = cot 30°

θ = π/4

Sec θ =4

F(x) = xx decreases in the interval

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(0,e)

(0.1)

(-∞.0)

None

The two consecutive positive integers whose product is 56 are

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7, 8

14, 4

28, 2

56, 1

The conic is a parabola if

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e <1

e > 1

e = 1

e = 0

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

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A =B

A < B

A< X

B < y

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

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720

40

60

30

Which of the following is not defined?

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Arcsin 1/9

ArcCos (-4/3)

Arctan 11/12

Arccot (-4)

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

Sin (2π -θ) =______.

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Cosθ

-Sinθ

-cosθ

If -1 < x < 0, which of the following statement must be true?

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x < x² < x²

x < x³ < x²

x² < x³ < x

x²< x < x³

If Cⁿ_r, Pⁿ_r = 24:1 then r = ?

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1

2

3

4

An angle 0 is such that tan θ = 1 and cos θ is negative then

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Sin θ is positive

Cos θ = √2/4

cosθ = -1

sec θ is negative

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

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Zero

One

Four

Infinite

The equation of the circle with center origin and radius 2√2 is

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x² + y² = 2√2

x² + y² = 8

x² - y² = 2√2

x² - y² = 8

The two different parts of the hyperbola are called is

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Vertices

Directrices

Nappes

Branches

If x lies in {0, 2π} and Cosec x = 2 then x =

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π/ 6 and 5π/6

π +2nπ

nπ

2π/3 and π/3

Sin^-1 x =?

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π/2- Sin^-1 x

π/2 -Cos^-1 x

-Sin^-1 x

-Cos^-1 x

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

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

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(3,0)

(4,1)

(1,3)

None

Which is not included in the domain of Cos^-1 x

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0

1

-1

2

If the sum of the roots of (a + 1)x² + (2a + 3)x + (3a + 4) = 0 is -1, then product of the roots is

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Commutative law w.r.t multiplication

Associative law w.r.t addition

Distributive law w.r.t addition

Multiplication of a scalar with the matrix

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

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π/3

-π/3

2π/3

5π/3

d/dx [cos x²] =________

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-2x cos x²

-2x² sin x²

x² sin x

-2x² sin x²

The degree of the polynomial 2x⁴ + 3x² + 16x + 28 = x⁴ + 2x² is

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[a_{ij -}b_ji]

[a_{ij -}b_ij]

[a_{ij] - [}b_ij]

AreCot √3 =?

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π/2

π

2π

π/6

Sin-1 (√2/2)=?

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π/2

π/3

3π/4

2π

In the triangle Δ ABC, where C is the right angle Tan A + Tan B=

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A +B

C² /AB

A²/BC

B²/AC

Given X, Y are any two sets such that number of elements in 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=

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-7 + 2i

7 + 2i

7-2i

√53

The perpendicular bisector of any chord of a circle

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Passes through the center of the circle

Does not pass through the center of the circle

May or may not pass through the center of the circle

None of these

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

d/dx a^x is

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xa^x-1

a^x

x in a

a^x in a

Ab > 0 and a > 0 then

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a > b

a < b

a = b

None

In the figure PS is perpendicular to QR, if PQ = PR 26 and P8 = 24,then QR=

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10

20

40

26

∫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

One of the roots of the equation 2x² + 3x + n = 0 is the reciprocal of the other, then n = --------------------

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Both A,B have the same number of columns

Both A,B do not have the same order

Number of col A is same as number of rows of B

Number of rows of A is same as number of col of B

The set (Z, +) forms a group

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Function on B

Range

Domain

A into B

Let A, B, and C be any sets such that A∪B=A∪C and A∩B=A∩C then

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A ≠ C

B = C

A = B

A ≠ B

If Cosα = 3/5, Cosβ = 5/13, then

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Cos(α +β) =33/65

Sin(α +β) =56/65

sin²(α +β/2) =1/65

Cos(α +β) =63/65

The set {1, -1, i, -i}, form a group under

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addition

multiplication

subtraction

None

Complex roots of real quadratic equation occur in

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Nilpotent matrix

Singular matrix

Non singular matrix

Diagonal matrix

d/dx (√x) =

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2√x

1/√x

1/2√x

None of these

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

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6

12

18

36

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

If sin θ= 3/5 Cos θ=

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1/2

3/5

4/5

1

Sin^-1 √3/2 =?

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2π/3

π/2

π/3

v/5

The angle a (0° < a< 180°) measured counterclockwise from positive x-axis to a non-horizontal straight line / is called the

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Rotation

Inclination

Radian

None

The center of a circle of radius 10 is on the origin which of the following points lies with in the circle

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(10,0)

(8,8)

(8,4)

(0,10)

If f (x) = x/x²- 4 then which is not included in the domain of f(x)

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0

-2

1

4

The magnitude of a vector can never be

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Zero

Negative

Positive

Absolute

The direction cosines of y-axis are

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1,0,0

0,1,0

0,0,1

1,1,1

A function F(x) is called even if

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F(x) = F(-x)

F(x) = -F(x)

2F(x) = 0

Which of the following is the subset of all sets ?

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A ≠ C

B = C

A = B

A ≠ B

A point of a solution region where two of its boundary lines intersect is called

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Boundary

Inequality

Half plane

Vertex

The set of all positive even integers is

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Φ

{1,2,3}

{Φ}

{0}

The nth term of A,P:1,5,9,15...........is given by

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4n - 3

4n + 1

3n -4

4n +3

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

d/dx ∫x¹ dx =________.

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1/4 x⁴

X³

3x³

x⁴/4

0 (zero) is

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A irrational number

A rational number

A negative integer

A positive number

Sin(a + b) + Sin(a- b) =

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Sin a Cos b

Sin a Sin b

Sin a + Cos b

Sin a - 2Cos b

The area of circle of unit radius=

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0

1

4

π

If Sin θ =Cosθ then θ=

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30°

45°

60°

90°

If f(x) = x³- 2x² +4x-1, then f(-2) =?

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0

-25

5

45