Question # 1

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

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Polynomial

Proper fraction

Rational fraction

None

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The point of concurrency of the angle bisectors of a triangle is called

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incentre

circumcentre

e-centre

centroid

In ladder leaning against a vertical well makes an angle of 24^𝜊with the wall, Its foot is 5m from the wall, its length is

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5.47m

2m

7m

6.29m

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

If l, m, n are the d.c.'s of a line, then

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l2+ m2+ n2= 0

l2+ m2+ n2= 1

l + m + n = 1

l = m = n = 1

A fraction in which the degree of the numerator is greater than or equal to the degree of the denominator is called

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A proper fraction

An improper fraction

An equation

An identity

Sand falls from a tube in such a way that it forms a cone whose height is always 4/3 times the radius of its base and radius of the base increases at the rate of 1/8 cm/sec. When this radius is 1 meter, the rate at which the amount of sand increases is

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Sequence also called..............

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Series

Function

progressions

Elements

The process of finding a function whose derivative is given is called a

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Differentiation

Integration

Differential

None

If uv= Projuv then

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Uandvare parallel

vis a unit vector

Uis a unit vector

Both b and c

The third term of a G.P. is 4, The product of first five terms is

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43

45

46

None of these

The A.M. of two numbers is 34 and G.M. is 16, the numbers are

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2 and 64

64 and 3

64 and 4

None of these

How many different 5-digit even numbers are possible form digit 1,2,4,6,8

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4 : 4!

4!

5!

4!+4!

The value of cos(cos-1 1/2) is

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1/2

√3/2

-1/2

1/√2

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The value of sin^-1 5/13 is equal to

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Cos 5/13

Tan^-1 5/12

cos^-15/12

2 cos^-14/5

i³ =

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-1

i

-i

1

Two circle s1: x2+ y2 +2x- 2y- 7= 0: s2: x2+ y2- 6x+ 4y+ 9= 0

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Touch externally

Touch internally

Intersects each other

Do not intersects

The axis of the parabola x² = 4ay is:

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y = 0

x = 0

x = -a

y = a

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The second degree equation of the form Ax2 +By2 +Gx +Fy +C =0 represent hyperbola if

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A = B≠ 0

A≠ B and both are of same sign

A≠ B both are of opposite sign

Either A = 0 or B =0

The slope of the normal at the point (at², 2at) of the parabola y²= 4ax is

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1/t

t

-t

-1/t

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Cosec 60° = ______

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i³=

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-1

i

-i

1

cos(a-β) = ______;

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sin a cosβ + cos a sinβ

sin a cos β - cos a sinβ

cos a cos β + sin a sinβ

cos a cosβ - sin a sinβ

(a,b) +(-a,-b) =

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(0,0)

(a,b)

(-a,-b)

(1,1)

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A function from X to X is denoted as

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f : X to Y

f : Y to Y

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a₁+ a₂

a²₁+ a²₂

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f(x) = x²

f(x²) = x

f(x) = x

none of these

What is the period of cos 6x =?

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π/2

π/3

π/4

π

If f (x) is defined and continuous then f (x) is always

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Rational function

Trigonometric function

Logarithmic function

All are correct

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If 6th term of a series in A.P, is -2 and 8th term is -8, the first term of the serie is

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13

-13

18

-10

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Evert element of A is in B

Every element of B is in A

Every element of A is in B'

Every element of A is in A

The ortho center of triangle whose vertices are (0,0)(3,0)(0,4) is

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(0,0)

(1,1)

(2,2)

(3,3)

The area of sector with central angle of 1 radian in a circular region whose radius is 2m is

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0.5m2

2m2

1m2

4m2

The sum of the coefficient in the expansion of (a + x)⁵is

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32

16

8

5

If the intersection of two sets is non-empty, but either is a subset of other are called

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Disjoint sets

Over lapping

Equal sets

None of these

There are 25 tickets bearing number from 1 to 25. One ticket is drawn at random. The probability that the number on it is a multiple of 5 or 6 is

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7 / 25

9 / 25

11 / 25

None of these

A man of height 6 ft observes the top of a tower and the foot of the tower at angles of 45° and 30° of elevation and depression respectively. The height of the tower is

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3x + 4 > 0 is

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equation

identity

inequality

none of these

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quadratic function

constant function

linear function

exponential function

Range of sin x is ______

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[-1, 1]

R

Negative real numbers

None of these

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The sum of all even numbers less than 100 is

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2450

2352

2272

2468

If 0 = {1,3,5.......}, then n (0) =

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99

odd integers

Even numbers

Infinite

How many term are there in the A.P, in which a₁ = 11 , a_n =68, d=3

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30

27

20

21

Multiplicative inverse of "1" is

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+- 1

0

1

None of these

Period of 3 sin x is ______

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If n is any positive integer ,t hen 2+4+6+......+2 n=

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2ⁿ-1

2ⁿ+1

n²+1

n(n+1)

The multiplicative inverse of -1 in the set {1-, 1} is

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1

-1

0

Does not exist

sin^-1[-1/2] = ______

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(A∪B)∪C= --------------------------

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A∩B(B∪C)

A∪(B∪C)

A∪(B∩C)

None of these

What is the 26th term of the sequence, if its general term is a_{n = (-1)}ⁿ⁺¹

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2

26

27

1

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2 and 9

3 and 2

2/3 and 9

3/2 and 6

The line through the intersection of the lines x+ 2y+ 3= 0 : 3x +4y +7 =0 and making equal intercepts on the axes is

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x+ y+ 1= 0

x+ y- 2= 0

x+ y+ 2= 0

2x +y +2 =0

Domain of 3 sin x is ______

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[-3, 3]

R

Positive real numbers

None of these

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

Vector additon is:

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Commutative

Associative

Commutative and Associative

None of these

All letters of the word "AGAIN" are permuted in all possible ways and the words so formed (with or without meaning) are written as in dictionary, then the 50th word is

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NAAGI

NAAIG

IAANG

INAGA

In following question, a number series is given with one term missing. choose the correct alternative that will same pattern and fill in the blank spaces.1 , 4, 9, 16, 25, x

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35

36

48

49

The third term of a G.P. is the square of first term. If the second term is 8, then the 6th term is

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120

124

128

132

Φset is the ______ of all sets?

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Subset

Union

Universal

Intersection

The eccentricity of the parabola y²= -8x is

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-2

2

-1

1

The angle between the vectors 3i + j - k and 2i - j + k is

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If P is a proposition then its negative is denoted by

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The sum of an infinite geometric series exist if

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| r | < 1

| r | > 1

r = 1

r = -1

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If a,b,c are unit vectors then |a + b|2 +|a - b|2

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4

8ab

9cos

4(a,b)

The minimum value of the quadratic function f(x) = x2 +6x -2, is

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11

6

-11

13

sin h x = ___________

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The many subset can be formed from the set {a,b,c,d}

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8

4

12

16

The expansion of (1 - 3x)^-1is valid if

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| x | < 1

| x | < 3

| x | < 1/3

None of these

A person standing on the bank of a river observes that the angle subtended by a tree of the opposite bank is 60°, when he retreats 40 m from the bank, he finds the angle to be 30°. The height of the tree and the breadth of the river are

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I f a =5i + 2j, then|a| =

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√13

√7

1/√13

√29

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First, the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangement is