Question # 1

If a_n= 2n -3, write the first four terms

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-3, -1, 1, 3

1, 3, 5, 7

-1, 1, 3, 5

None of these

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Range of sin x is ______

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[-1, 1]

R

Negative real numbers

None of these

The set {{a,b}} is

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Infinite set

Singleton set

Two points set

None

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The middle term(s) of (a+x)11 is

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6th term

6thor 7th

7th term

6thand7th

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Through how many radians does the minute hand of a clock turn in one hour

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√2 +√3 +√5) = (√2 +√3 +√5: this property is called

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associative property w.r.t addition

commutative property

Closure property w.r.t addition

Additive identity

The distance of the point (-2 , -3) from x-axis is

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2

-3

3

5

if a_{9 =19,a9=31 are the 6th and 9th term of an A.P. and d=4 is the common difference, then 18th term of the sequence is}

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65

67

71

75

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

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2π

π

4π

π / 2

If A = [aij]mxpand B =[aij]pxnthen order of BA is

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m x n

p x n

n x m

None of these

The condition for polynomial equation ax²+ bx + c = 0 to be quadratic is

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For three consecutive terms in A.P middle term is called

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A.M

nth term

Central term

None of these

No term of a harmonic sequence can be

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0

1

2

3

The number of triplets (x, y, z) satisfying sin^-1x +cos^-1y + sin^-1z = 2π is

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0

2

1

Infinite

If circumference of circle is divided into 360 congruent parts the angle subtended by one part at the centre of circle is

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1 degree

1 second

1 minute

1 radian

n(n - 1) (n - 2) .... (n - r + 1) = ______

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The synthetic division method is only used to divide a polynomial by

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quadratic equation

binomial

linear equation

monomial

If a set S contains n elements then P (S) has ........ number of elements

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2ⁿ

2ⁿ²

2.n

n²

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A

-A

A^t

A^-

The graph of the linear equation of the form ax =by = c is a line which divided the plane into:

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Two similar regions

Two disjoint regions

Four equal parts

One region

Which shape of the following objects are approximately parabolic ares?

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Light reflectors

Force

Weight of the pendul

None of these

1⁰= ______

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360'

60"

60'

3600'

If f(x) = x²then f(-2) is

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-2

2

4

-4

H₁, H₂, H₃, .... H_nare called n harmonic means between a and b if a, H₁, H₂, H₃, ... H_nb are in

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H.P.

G.P.

A.P.

None of these

The number of real tangents that can be drawn to the ellipse 3x²+ 5y²= 32 passing thro. (3, 5) is

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0

1

2

Infinite

Unit vector in the positive direction of x-axis is

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sin(a-90°)=______;

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sina

cosa

-sinθ

-cosa

If the domain of sequence is finite set then the sequence is called

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geometric sequence

infinite sequence

finite sequence

arithmetic sequence

Associative law of multiplication

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ab = ba

a(bc) = (ab) c

a(b+c) = ab + ac

(a + b)c = ac + bc

A relation in which the equality is true only for some values of the known is called ______

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An identity

An equation

A polynomial

None of these

If a (p + q)²+ bpq +c = 0 and a (p + r)²+ 2 bpr + c = 0, then qr equals

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p²+ c/a

p²+ a/c

p²+ c/a

p²- c/a

A number A is called the arithmetic mean between a and b if a, A, b is ______

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Arithmetic sequence

Geometric sequence

Harmonic sequence

Arithmetic sequence

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16 / 7

6 / 17

7 / 16

None of these

Which of the following represents a vector

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(x, y)

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A

0

Unit vector

None

If b²- 4ac is positive then the roots of the equation are

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Real

Imaginary

Positive

Negative

A rule or correspondence that assigns to each element x in X a unique element y in Y is called a function from

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X to X

X to Y

Y to X

none of these

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

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4

8ab

9cos

4(a,b)

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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all are correct

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A disjunction of two statement p and q is true

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p is false

q is false

Both p and q are false

One of p and q is true

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The sum of first 60 natural numbers is

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1830

3660

1640

1770

The direction cosines of y-axis are

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1, 0, 0

0, 1, 0

0, 0, 1

1, 1, 1

A diagonal matrix is always

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Identity

Triangular

Scalar

Non-singular

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0

1

The proposition S(n) is true∀n∈N,S(k+1) true when ______is true

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S(1)

Both a & c

S(k)

None

The period of tan x/7 is

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3π

7π

15π

5π

The solution set of the equation |3x + 2| = 5 is

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The number of subsets of B = {1,2,3,4,5}

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10

32

16

5

Under multiplication, solution set of is

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Groupoid

Abelian group

Semi group

All of these

In set builder notation the set {0,1,2,........100} can be written as

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{x / xε B ∧ x ≤ 100}

{x / x ∈ W ∧ x < 101}

{x / x ∈ Z ∧ x < 101}

The set of first 100 whole numbers

The set of complex numbers forms

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Commutative group w.r.t addition

Commutative group w.r.t multiplication

Commutative group w.r.t division

Non commutative group w.r.t addition

If 3x4 +4x3+x5is divided by x+1 , which of the following is the remainder

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7

-2

6

1

The distance between the points (1, 2) and (2, 1) is

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3

6

Domain of sec x is ______

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1⁰= ______

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The differential equation representing the family of curves y = A cos (x + B), where A, B are parameters, is

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The range of the function f : x→ y is defined by

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{x| y = f (x) ∀x∈ X ∧y∈y}

{(x,y) |y = f (x)∀x∈ X}

{y|y = f (x) ∀x∈ X ∧y∈y}

Y

I f the focus is F ( 0,-a) and directrix is the line v=a, then equation of the parabola is:

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x² = 4ay

y² = 4ax

y² = -4ax

x² = 4ax

A relation in which the equality is true for all values of the unknown is called ______

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An identity

An equation

A polynomial

None of these

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0

2

4/3

5/3

The centroid of a triangle divides each median in the ratio

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2 : 1

3 : 1

3 : 2

1 : 1

An equation in which at least one term contains dy/dx, d² y /dx²etc, is called.

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Differential equation

Initial condition

General solution

Singular equation

______________ invented a symbolic way to write the statement "y is a function of x" as y= f(x)

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Leibniz

Newton

Euler

None of these

Intersection of two parabolas

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parabola

Two points

Four points

Hyperobla

If p and q are two statements then their biconditional 'p if q' is denoted by

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Which element is the additive inverse of (a,b) in Complex numbers

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(a,0)

(0,b)

(a,b)

(-a,-b)

The solution of differential equation:

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dy/dx+y/x = x²is :

4xy = x⁴+ c

4x = x⁴= c

4 y = x⁴+ c

4x=4x³ + c

What is the period of tan 4/3 x =?

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π/4

4π/3

7π/4

3π/4

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3 x 1

1 x 3

3 x 3

1 x 1

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Associative law of addition

Commutative law of addition

Additive identity

Closure law of addition

The ellipse and hyperbola are called

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Concentric conics

Central conics

Both a b

None

A tower subtends an angleαat a point on the same level as the root of the tower and at a second point, b meters above the first, the angle of depression of the foot of the tower isβ. The height of the tower is

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b cotαtanβ

b tanαtanβ

b tanαcotβ

None of these

For n€ N,2^n>2 > n is to only when

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n<2

n≤ 4

n≥ 4

The maximum value of sin x + cos x is

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If the points (a,2b):(c,a+b):(2c-a,h) lie on the same line then

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h=2a

h=a+b

h=ab

h=ac

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0

1

The domain of a finite sequence is a

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Set of natural numbers

R

Subset of N

Proper subset of N

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None of these

Matrices are represented by

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Natural numbers

Real numbers

Small letters

Capital letters

The multiplicative inverse of x such that x = 0 is

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-x

does not exist

1/x

0

The domain the function : f(x) = x² is given by

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R

Set of all non-negative Real numbers

R^-1

None of these

The domain of y = cos-1 x is

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-∞ < x < ∞

-1≤ x≤ 1

x≤ -1 or x ≥ 1

None of these

The key for opening a door is in a bunch of 10 keys. A man attempts to open the door by trying the keys at random discarding the wrong key. The probability that the door is opened in the 5th trial is

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1 / 10

2 / 10

3 / 10

4 / 10

For a square matrix A, if A = A^t, then A is called

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matrix

Transpose

Symmetric

Non-symmetric

A kite flying at a height of 67.2 m is attached to a fully stretched string inclined at an angle of 53 to the horizontal, the length of the string

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62m

82m

73m

57m

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a = a

a < a

a > a

a²= a

Φset is the ______ of all sets?

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Subset

Union

Universal

Intersection

The points (5, -4, 2),(4, -3, 1),(7, -6, 4),(8, -7, 5) are vertices of a

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Square

Parallelogram

Rectangle

Rhombus

If a statement S(n) is true for n = 1 and the truth of S(n) for n = k implies the truth of S(n) for = k + 1, then S(n) is true for all

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Real numbers n

Integers n

Positive integers n

None of these

2cos2 a/2 =______;

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1+sina

1-sina

1+cosa

1-cosa

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2s²

2s³

s³

3s³

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-3 -2i

3 +2i

1 + 2i

1 - 2i

Two unbiased dice are thrown. The probability that the total score is > 5 is

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1 / 18

7 / 18

13 / 18

11 / 18