Question # 1

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Any recurring decimal represents a

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Irrational no

Integer

Rational no

None of these

π is ______

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A complex number

A rational number

A natural number

An irrational number

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1

2

3

None of these

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8

1/56

56

None of these

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

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

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With usual notations b2 = a2 + c2 -2ac cos is called______;

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None of these

Law of sines

Law of consines

Law of tangents

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

The curve f(x,y) = 0 has a central symmetry if

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f(-x,-y)=f(x,y)

f(x,-y)=f(x,y)

f(-x,y)=f(x,y)

f(-x,-y)≠f(x,y)

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A

B

U

None of these

The physical quantity which can be specified by a number alongwith unit is called a

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scalar

vector

constant

none of these

An A.P. consists of n(odd terms) and its middle term is m. then the sum of the A.P. is

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2 mn

1/2 mn

mn

mn²

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If x - 2 is a factor of ax2- 12x + a = 2a, then a = ______

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-5

5

0

1

Every identity matrix is

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Row-vector

Scalar

Column-vector

All

The conic ax2+2hxy+by2+2gx+2fy+c= 0 never represent a circle if

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a≠ b,h≠0

a=b

h≠0

h=0

Cos (cos4π/3)=

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π/2

π/3

2π/3

-π/3

The parametric equations of a circle are

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Each complex cube root of unity is square of

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itself

1

-1

the other

In the expansion of (x+y)n the coefficient of 5th and 12th terms are equal then n=

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12

n=14

17

n=15

The feasible region which can be enclosed within a circle is called

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Bounded region

Convex region

Unbounded region

None

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none of these

Ifα,βare the roots of ax²+ bx + c = 0 andα+ h,β+ h are the roots of px²+ qx + r=0, then h =

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An equation containing at least one derivative of a depends variable with respect to independent variable is a (an)

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Implicit equation

Differential equation

General equation

None of these

Parametric equation of circle : x²+y²+r², are

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r1 = x cos𝜽 r² = y sin𝜽

x = r cos𝜽 y = r sin𝜽

x = r sin𝜽1 y = r sin𝜽2

x = r₁ cos𝜽 y = r_{2 sin𝜽}

The set of months in a year beginning with S.

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{September, October, November}

Singleton set

Null set

Empty set

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The set {x|x∈N∧x-4=0} in tabular form is

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{-4}

{0}

{}

None of these

A function which is to be maximized or minimized is called an

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Explicit function

Implicit function

Objective function

None

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A variable

A constant

0

None of these

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(a,0) x (c, 0) =

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(0,ac)

(ac, 0)

(0,0)

(a, c)

sin^-1 x =

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tan^-1 x

Cosec^-1 x

Cosec x

cosec^-1(1/x)

The additive identity of real number is

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1

2

1/2

0

If #n = (n-5)2 + 5, then find #3 x #4.

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54

12

4

9

If Z₁= 1 + i, Z₂= 2+3i, then |Z₁- Z₂| = ?

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The set {1,2,3,4......} is called

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Set of natural numbers

Set of whole numbers

Set of rational number

Set of irrational numbers

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

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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Which of the following integrals can be evaluated

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Z is a group under

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Subtraction

Multiplication

Addition

None of these

(2, 1) is in the solution of the inequality

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2x + y > 7

x - y > 2

3x + 5y < 6

2x + y < 6

A = B if

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A is equivalent to B

Four cards are drawn at random from a pack of 52 playing cards. The probability of getting all the four cars of the same suit is

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44/4165

22/4165

11/4165

None of these

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A function f is said to be an even if f(-x) =

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0

1

f(x)

-f(x)

The period of cosec 10x is _______

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The first three terms in the expansion of (1 - x)^-1are

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1 + x + x²

1 - x - x²

-1 -x +x²

1 - x + x²

To express a single rational fraction as a sum of two or more single rational fractions which are called

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improper fractions

Partial fractions

mixed form

Polynomials

The value of n, when ⁿP₂= 20 is

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3

4

6

5

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none of these

√11 is

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an irrational number

Rational number

odd number

Negative number

Period of cos x is _____

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1

0

-1

2

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

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-2

-3

2

3

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A

-A

A^t

A^-

If the angle between two vectors with magnitude 6 and 2 is 60° when their scalar product is

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12

6

3

0

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

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Polynomial

Equation

Proper fraction

Improper fraction

If you are looking someone on the ground from the top of a hill the angle formed is called angle of _______;

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Elevation

Depression

Right angle

None off these

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Proper fraction

Improper fraction

Rational fraction

None of these

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sec x tan x

cos²x

sin²x

sec²x

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If for the matrix A,A5 = 1,then A-1=

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A2

A3

A

None of above

The set of integer is

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Finite group

A group w.r.t addition

A group w.r.t multiplication

Not a group

Period of cot x is ______

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(2x+a+b+c)

(a+b+c)

(a+b+c+x)

0

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sin[cot^-1{cos(tan^-1x)}]=

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Period of Sine and Cosine function is

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π

2π

-π

-2π

The vector k = [0,0,1] is called unit vector along:

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x -axis

y - axis

z- axis

None of these

If sin (πcosθ) = cos (πsinθ), then which of the following is correct?

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The matrix A = [aij]1xn is a

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Vector

Rectangular matrix

Column vector

Square matrix

If #n = (n-5)²+ 5, then find #3 x #4.

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54

12

4

9

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If S is a sample space and event set E = S then P(E) is

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>0

1

<1

0

Which one is a pair of allied angles

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(180° -θ)

(180° -θ,180° +θ)

(180° +θ)

None of these

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none of these

If cos 20°=K and cos x=2 k²-1, then the possible values of x between 0° and 360° are

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140°

50° and 140°

50° and 130°

40° and 320°

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a sec(ax + b) + c

- a sec(ax + b) + c

The period of the function f(x) = sin⁴x + cos⁴x is

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π

π/2

2π

None of these

Decimal part of irrational number is

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Terminating

Repeating only

Neither repeating nor terminating

Repeating and terminating

The trigonometric function are continuous whenever

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They are defined

their limit exist

Their period is given

All are incorrect

Range of 2 tan x is ______

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[-2, 2]

-1 < x < 1

R

None of these

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If f(x) = -x²then f(-2) is

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-2

2

-4

4

A set having only one element is called

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An empty set

Universal set

A singleton set

A power set

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(-6,4)

(-3,2)

(6,-4)

(3, -2)

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A diagonal matrix in which the diagonal elements are equal is called a

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Null matrix

Identity matrix

Scalar matrix

Row matrix

How many types of an equation

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1

3

2

None

The eccentricity e of an ellipse is always

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Rational

Real

Irrational

Integer

sin(π/2+θ) = _______;

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sinθ

cosθ

-sinθ

-cosθ

Cofactor of an element aij denoted by Aij is

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(-2)i+j

Mij

(-1)i+j Mij

None of above