Question # 1

A ________ divides the plane into left and right half planes.

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Vertical line

Horizontal line

Non vertical line

Inequality

The fifth term of (a+2x3)17 is

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4013 x3a13

2208a13 x12

223x7a18

38080a13 x12

∀a,b ε R, ab = be is a

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Commutative law of multiplication

Closure law of multiplication

Associative law of multiplication

Multiplicative identity

The point R dividing externally the line joining the points P(x₁, y₁) and Q(x₂, y₂) in the ratio k₁: k₂has the coordinates

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If f(√x)=sin x , then f′(x) =______;

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2xcosx2

cosx2

cos√x

None of these

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1/x

-x

2x

0.5 x

(1+w)(1+w2)(1+w4)(1+w8)....50 factors

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0

-1

1

2

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n if n is even

0 for any natural number n

1 if in odd

None of these

The 5th term of (3a-2b)^-1is

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

The area bounded by y = x (x2 - 4) and below x - axis is

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4

0

-4

8

Any point, where f is neither increasing nor decreasing and f(x) = 0 at that point, is called a

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Minimum

Maximum

Stationary point

Constant point

n different objects can be arranged taken all at a time in ______

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(n + 1)! ways

(n - 1)! ways

n! ways

n ways

Out of 10, 000 families with 4 children each, the number of families all of whose children are daughters is

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375

500

625

150

If n∈Z+ then(a+x)n is a/an

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Finite series

Convergent series

Infinite series

Divergent series

If sin 6θ+ sin 4θ+ sin 2θ, thenθ=

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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

If the focus lies on the y-axis with coordinates f(0,a) and directrix of the parabola is y = -a, the equation of parabola is:

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y² = -4 ax

x² = 4ay

x² = -4ay

y² = 4ax

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Less then 1

Equal to 1

Greater than 1 but less then 2

Greater then or equal to 2

Sine rule for a triangle states that

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a/sin A = b/sin B = c/sin C

sin A/a = sin B/b = sin C/c

a/sin A + b/sin B + c/sin C

2a/sin A = 2b/sin B = 2c/sin C

If a₁and r are the first term and the common ratio respectively then (n + 1)th term of the G.P. is

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0

a₁r^n-1

a₁rⁿ⁺¹

a₁rⁿ

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IfΔABC is right, law of cosine reduce to

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Law of sine

Law of tangent

Phthogorous theorem

Hero's formula

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Sin-1(-x)=

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x

-x

-sin-1 x

cos-1 x

If f(x) = -x³then f(-2) is

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-2

-4

-8

8

The probability to get an odd number in a dice thrown once is

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1/2

1/6

1/3

2

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3/4

-3/4

4/3

-4/3

i² =

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1

2

-1

0

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Addition

Subtraction

Multiplication

None of these

If a > 0,b > 0, c > 0 then the roots of the equation ax2+ bx + c =0 are

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Real and negative

Non-real with negative real parts

Real and positive

Nothing can be said

Which of the following is the subset of all sets

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Φ

{1,2,3}

{Φ}

{0}

How many types of an equation

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1

3

2

None

Associative law of multiplication

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ab - ba

a(bc) = (ab) c

a(b + c) = ab +ac

(a +b)c = ac + bc

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

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0

90°

180°

360°

The set of real numbers is a subset of

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The set of natural numbers

The set of rational numbers

The set of integers

The set of complex numbers

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Cosec 60° = ______

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The equation of the circle with centre (5, -2) and radius 4 is

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(x-5)²+ (y+2)²= 16

(x-5)²+ (y+2)²= 4

(x-5)²+ (y-2)²= 16

(x-5)²+ (y-2)²= 4

The set { 1 , -1} is closed w.r.t.

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Addition

Multiplications

Subtraction

None of these

The set of integers is a subset of

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The set of natural numbers

The set of whole numbers

The set of prime numbers

The set of rational numbers

The period of cot 8x is

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π/10

9π/7

π/9

π/8

sin2 π/6 + sin2 π/3 + tan2 π/4 =______;

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1

2

3

4

csc(-π/2) = __________;

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0

1

-1

Undefined

0 (zero) is

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An irrational number

A rational number

A negative integer

A positive number

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The point of contact of the circles x²+ y² - 6x -6y+10 = 0 and x² + y² =2 is

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(-3 ,2)

(1 , 3)

( -2 , -1)

None of these

The period of the trigonometric function y = sin x cos x is

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2π

π

4π

π / 2

Decimal part of irrational number is

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Terminating

Repeating only

Neither repeating nor terminating

Repeating and terminating

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0

1

2

4

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The slope of the normal at (4,3) to the circle x²+y²=25 is

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3/4

-3/4

4/3

-4/3

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perpendicular vectors

concurrent vectors

parallel vectors

none of these

If A and B are two matrices such that AB = B and BA =A, then A²+ B²=

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2 AB

2 BA

A + B

AB

If y=sin(ax+b) then y4=________:

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sin4(ax+b)

a4sin(ax+b)

a4cos(ax+b)

None of these

The sum of infinite numbers of terms of an arithmetic series is

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Finite

Infinite

May or may not finite

None of these

If a > b or a < b than a = b is a

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Additive property

Transitive property

Trichotomy property of inequality

The formula an = arn-1represents

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nth term of G.P

Sum of the first n terms

G.M between a and b

None of these

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-cosec²x

-sec²x

- cosec x cot x

cosec x

If one end of the diameter of the circle x² + y²- 5x = 3y -22 = 0 is (3,4) the other end is:

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(2,7)

(-2,-7)

(-2,7)

(2,-7)

If distance of (a,b) from origin is 5 then

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a²+ b²=5

a = 5

b = 5

sec h x = ________

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The set of rational numbers is subset of

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The set of natural numbers

The set of real numbers

The set of integers

The set of whole numbers

A matrix with a single row is called a

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Column matrix

Row matrix

Null matrix

Identity matrix

Domain of secθis

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For two vector a and b, a+b = _______

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a b

b+a

b-a

None

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A line segment whose end points lie on a circle is called

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The secant of the circle

The arc of the circle

The chord of the circle

The circumference of the circle

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(1,7/3)

(1, 7/5)

(1, 11/7)

(1, 3/5)

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A triangle which is not right angle is called ______ triangle

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acute

Obtuse

Right

Oblique

sin(3π/2 -θ)=_______;

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sinθ

cosθ

-sinθ

-cosθ

If the roots of ax²+ bx + c =0 are equal in magnitude but opposite in sign, then

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a = 0

b = 0

c = 0

None of these

The general equation of circle x³ + y³ + 2gx + 2fy + c = 0 , contains:

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Three independent variables

Two independent conntants

Three indepentent parameters

Three independent constants

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u,v,wand u x (v.w) are

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Equal

Parallel

Additive immense of each other

Meaningless

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A(α) - A(β)

A(α) + A(β)

A(α-β)

A(α+β)

3x + 4 < 0 is

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inequality

equation

identity

not inequality

How many arrangements of the letter of the word PAKPATTAN can be made

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f(x) = log x + 3 is a

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trigonometric function

algebraic function

exponential function

logarithmic function

Three dice are thrown together. The probability of getting a total of at least 6 is

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103 / 108

10 / 216

93 / 108

None of these

The magnitude of vector a 2i-7j is

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√23

√43

3

√53

(51)⁴is equal to

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7065201

8065201

6765201

6565201

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If the roots of x²+ ax + b = 0 are non-real, then for all real x, x²+ ax + b is

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Negative

Positive

Zero

Nothing can be said

If 2 tan¹(cos x) = tan^-1(cosec²x), then x is equal to

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π/ 3

π/ 2

π/ 6

π

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A

A'

U

xy= 2 is:

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a constant function

an identity function

an improper function

implicit function

The line 3x - 4y = 0

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Is a tangent to the circle x²+ y²= 25

Is a normal to the circle x²+ y²=25

Does not meet the circle x²+ y²= 25

Does not pass thro' the origin

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Rational

Irrational

Natural

Odd

The angles of elevation of the top of a tower at the top and the foot of a pole of height 10 m are 30° and 60° respectively. The height of the tower is

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10 m

15 m

20 m

None of these

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The area of a sector with central angle of 0.5 radians in a circular region whose radius is 2m is

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The three consecutive numbers a,√ab,b are in

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G.P

H.P

G.M

None of these

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none of these

If G is the centroid of the triangle, then GA +GB+GC=

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0

1

-1

3

In common logarithm the base is

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1

0

10

e