Question # 1

Number of ways of writing the letters of WORD taken all at a time is

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24

4

12

6

If 4 - x >5, then

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x > 1

x > -1

x < 1

x < -1

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Diagonal matrix

Scalar matrix

Triangular matrix

Identity matrix

Tan 3x tan 2x-tan x is equal to

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Tan x tan 2x tan 3x

-tan x tan 2x tan 3x

Tan x tan 2x - tan - tan x tan 3x - tan 2x tan 3x

None of these

sin(180° -θ)=

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cosθ

-cosθ

Tanθ

Sinθ

3x + 4 > 0 is

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equation

inequality

identity

none of these

A committee consists of 9 experts taken from three institutions A, B, and C, of which 2 are from, A, 3 form B and 4 from C. If three experts resign, then the probability that they belong to different institutions is

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1 / 729

1 / 24

1 / 21

2 / 7

If a force F = 2i + j +3k acts at point (1,-2,2) of a body then the moment of F about a pint lying on the line of action of the force is

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5

Equal to the moment of the force about origin

0

Cannot be found

The vertex of the graph of the quadratic function f(x) = x2 -10, is

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(0 , -10)

(-10,0)

(10,0)

(0,10)

Multiplicative inverse of "1" is

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+- 1

0

1

None of these

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For all points (x,y) in third quadrant

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x > 0 , y < 0

x > 0 , y > 0

x < 0 , y < 0

x < 0 , y > 0

The first three terms in the expansion of (1 + x)³are

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1 + 3x +6x²

1- 3x + 6x²\

-3 -3x -6x²

1- 3x -6x²

The sum of n terms of a series is denoted by

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d

n

S_n

a_n

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none of these

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Onto function is also called

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Binjective function

Injective function

Surjechive function

None of these

Multiplicative inverse of 0 is

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0

1

+-1

Does not exist

if A = (x/x€ Q˄ 0 < x < 1}, the A is

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Infinite set

Finite set

Set of rational numbers

Set of real numbers

The equation (cos p - 1)x²+ x (cos p) + sin p = 0 in the variable x, has real roots, then p can take any value in the interval

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(0, 2π)

(-π, -0)

(0,π)

None of these

The number of terms in the expansion of (a + b)⁹is

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10

11

9

12

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cos x + c

-sin x + c

-cos x + c

sin x + c

If (0, 0) and (0, -1) are end points of a diameter, then the equation of the circle is

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The perpendicular bisector of any chord of a circle

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Passes through the centre of the circle

Does not pass through the centre of the circle

May or may not pass through the centre of the circle

None of these

Geometrically the modulus of a complex number represents its distance from the

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Point (1,0)

Point (0,1)

Point (1,1)

Point (0,0)

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Hermitian matrix

Skew-hermitian matrix

Symmetric matrix

Identity matrix

A function of the form p(x)/Q(x) is called:

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Rational function

Logarithmic function

Exponential function

Hyperbolic function

If sin x + sin²x = 1, then the value of Cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x + 2 cos⁴x + cos²x-2 is equal to

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0

1

2

sin²x

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The quadratic equation 8 sec²θ- 6 secθ+1 = 0 has

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Infinitely many roots

Exactly two roots

Exactly four roots

No roots

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

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10

32

16

5

If n is odd then the middle terms in the expansion of (a + x)ⁿare

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I andII quadrants

II andIII quadrants

II andIVquadrants

none of these

Sin h^-1x = _________

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Domain of y = scs x is

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All real numbers except π/2 + n*π

R

All negative integers

None of these

The additive inverse of 1 is

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1

-1

0

Does not exist

sin(3π/2 -θ)=_______;

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sinθ

cosθ

-sinθ

-cosθ

Given X.Y are any two sets such that number of elements in X = 18, number of elements in set Y = 24,and number of elements in set X∪ Y =40,then number of elements in set x∩ Y =

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3

1

2

4

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20

10

0

None of these

AB is a vertical pole and C is its middle point. The end A is on the level ground and P is any point on the level ground other than A. the portion CB subtends and angleβat P. If AP : AB = 2 : 1 thenβ=

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Three points whose position vector a,b,c are collinear

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axb +b x c+ c x a = 0

a,b +b,c +c,a =0

a,|a xc| =0

a+b+c =0

ⁿC₂= exists when n is ______

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A class contains nine boys and three girls, in how many ways can the teacher choose a committee of four?

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460

495

272

60

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direction ratios

direction cosines

direction angles

none of these

The general term in the expansion of (a+x)n is

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(r-1)th term

(r+1)th term

rth term

none

The solution of the quadratic equation x2 -7x + 10=0, is

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2

5

2,5

7

The vertex of the standard position angles lies on

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(0,0)

(0,1)

(1,0)

(1,1)

If a^x= b^y= c^zand a, b, c are in G.P. then x, y, z are in

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A.P.

G.P.

H.P.

None of these

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The range of the tangent function is

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all real numbers

-1 ≤ x ≥ 1

natural number

z⁺

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(-6,4)

(-3,2)

(6,-4)

(3, -2)

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0

-1

1

not defined

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The mid point of the line segment joining the points (a,b) and (b,a) is

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Range of sin x is ______

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[-1, 1]

R

Negative real numbers

None of these

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

In one hour, the hour hand of a clock turns through

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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 = B

B = C

A≠ C

A ≠ B

The equation of the plane which bisects the line joining (2, 3, 4) and (6, 7, 8) is

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x + y + z - 15 = 0

x - y + z - 15 = 0

x - y - z - 15 = 0

x + y + z + 15 = 0

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

Every term of a G.P. is positive and also every term is the sum of two preceding terms. Then the common ratio of the G.P. is

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3/2 is

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An irrational number

Whole number

A positive integer

A rational number

The sum of all odd numbers between 100 and 200 is

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6200

7500

6500

3750

If T = {2,4,6,8,10,12}, then

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T = (First six natural numbers)

T = (First six odd numbers)

T = (First six real numbers)

T = ( First six even numbers)

For trival solution |A| is

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A

|A| is non zero

A = 0

None of these

√-1 b=

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b

2

2b

None of these

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sin h x

cos h x

sec h x

cosec h x

99th term of the series 2 + 7 + 14 + 23 + 34 + ..... is

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9998

9999

10000

None of these

6! = ______

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360

720

6.5.4

None of these

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Closure law of addition

Associative law of addition

Commutative law of multiplication

Associative law of multiplication

The square roots of negative numbers is called

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Real no

Complex no

Positive no

Negative no

Given two independent event A and B such that P(A) = 0.30 and P(B) = 0.60. Probability of getting neither A nor B is

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0.28

0.13

0.12

0.42

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The seventh term of an A.P whose first term is P and common difference is q. is

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P-6q

P+6q

P-4q

P-nq

If one end of the diameter of the circle 2x²+ 2y²-8x - 4y = 2 = 0 is (2 ,3), the other end is:

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(2,1)

(-2,1)

(2,-1)

(1,-1)

G = {e, a, b, c} is an Abelian group with e as identity element. The order of the other elements are

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2, 2, 2

3, 3, 3

2, 2, 4

2, 3, 4

The minimum value of the quadratic function f(x) = 5 x 2-11,is

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7

-7

6

-11

Domain of sec x is ______

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In the interval 0≤ x ≤ π, the sine is

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Not a function

Not defined

Infinity

Not one-to-one function

When we expand (a + 2b)⁵then

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a⁵+ 10a⁴b + 40a³b²+ 80a²b³+ 80ab⁴+ 32b⁵

a⁵+ a⁴b + a³b²+ a²b³+ ab⁴+ b⁵

5a⁵+ 4a⁴b + 3a³b²+ 2a²b³+ 1 ab⁴+ b⁵

None

Co-ordinate of a point on the parabola y² = 8x whose focal distance is 4 are:

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(2 , 4)

(-2 ,-4)

(-2, 4)

(2,-4)

x = -1 is in the solution of the inequality

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x + 5 < 0

2x + 3 < 0

x > 0

2x + 3 > 0

If all members of a sequence are real numbers then it is called a

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Series

Function

Real sequence

Range

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xa^x-1

a^x

x in a

a^xIn a

Root of the equation 3^x-1+ 3^1-x= is

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2

1

0

-1

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0

undefined

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Principle of equality of Fractions

Rule for product of fraction

Golden rule of fraction

Rule of quotient of Fraction

Group of none-singular matrices under multiplication is

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None-Abelian group

Semi group

Abelian group

None of these

The equation of the circle with centre origin and radius r is

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x²+ y²= 1

x²+ y²= r²

x²+ y²= 0

x²- y²= r²

If y is an image of x under the function f, then we write

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y = f(x)

x = f(y)

y = x

none of these

an - an-1 will be common difference in an A.P if

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n = 1∀n∈ N

n>1∧n∈N

n∈Z

None of the above

The physical quantity which possesses both magnitude and direction is called a

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scalar

vector

constant

none of these

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