Question # 1

If A is a non singular matrix then A^-1= ______

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Z is the set of integers (Z.*) is a group with a * b = a +b +1, a,b ∈ G.then inverse of a is

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-a

a +1

-1-a

None of these

If the st. line 3x + 4y = K touches the circle x²+ y²- 10x = 0 then the value of K is

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-1 or 20

-10 or 40

-2 or 20

2 or 20

The sum of first n even number is

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n2

n(n+1)

n+1

n+2

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

The set of the first elements of the orders pairs forming a relation is called its

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Relation in B

Range

Domain

Relation In 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

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cos 3a =_______;

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3sin a - 4sin3 a

4sin a - 3sin3 a

3cos3 a - 4cos a

4cos3a - 3cos a

(n + 2) (n + 1)n in factorial form is

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The no of term is the expansion of (a+x)n-1 is

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n+1

n-1

n

n-2

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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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The transport of a null matrix is

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Row matrix

Column matrix

Square matrix

Null matrix

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If the 4th term in the expansion of (px + x^-1)^mis 2.5 for all x∈ R, then

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x = 1 is in the solution of the inequality

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x + 1 > 0

x - 2 > 0

3x - 1 < 0

x + 2 < 0

The equation |x + 4| = x has solution

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x = -2

x = 2

x = -4

x = 4

The sum of the focal distance from any point on the ellipse 9x2 +16y2 =144 is

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32

16

18

8

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-2

-1

1

2

sin(180° -θ)=

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cosθ

-cosθ

Tanθ

Sinθ

If A = [a_ij] is (m x n) matrix, then transpose of A is of the order

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m x m

m x n

n x n

n x m

Composition of functions is

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Non-commutative (fg ≠ gf)

non-associative [8(fh) ≠(8f)h]

Commutative (fg = gf)

f of-1≠ 1

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If f(x) = x³- 2x²+ 4x -1 then f(2) is

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7

-16

16

-9

(x-1) is a factor of

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2x³-3x²+9

2x³-5x-8

48x^2-46x-9

x⁹-1

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Ifθ= 60° then

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sinθ= 1/2

tanθ= cot 30°

θ=π/4

secθ= 4

Vector i =

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[1,0]

[0,1,0]

[0,0,1]

None of these

f(x) = ax + b will be a constant function if

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a = 1 , b = 1

a = 1 , b = 0

The distance of the points (3, 4, 5) from y-axis is

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One second is denoted by

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1⁰

1'

1"

1 rad

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The angle of depression of a point A on the ground from the top of the tower is 30𝜊,then the angle of elevation of the top of the tower at the point A is

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60𝜊

40𝜊

41𝜊

30𝜊

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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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)

Point (2,0) lies on trigonometric function f(x)=______;

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sinx

cosx

tanx

secx

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A sequence having no last term is called

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arithmetic sequence

Geometric sequence

Finite sequence

Infinite sequence

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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

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20

10

0

None of these

Tan 180° = ______

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-1

0

1

Undefined

The set {{a,b}} is

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Infinite set

Singleton set

Two points set

None

The distance of the point (2,3) from origin is

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5

2

3

The cube roots of 8 are

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cos2a=______;

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cos2 a-sin2 a

2cos2 a-1

1-2 sin2 a

All of these

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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)

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For graphing a linear inequality, solid line is drawn if the inequality involves the symbols:

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> or <

= or≠

= or >

In R, the additive identity is

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0

1

-1

None

The domain of y =√(x^2-9) is

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R

(0 , +∞)

(-∞ , -3 )∪ (3 , +∞)

(0 ,∞)

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none of these

If ax²+ bx + x = 0 is satisfied by every value of x, then

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b = 0, c = 0

c = 0

b = 0

a = b = c = 0

0 is a symbol of

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singleton set

Empty set

Equivalent set

Infinite set

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Associative law of multiplication

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ab - ba

a(bc) = (ab) c

a(b + c) = ab +ac

(a +b)c = ac + bc

The set {1, -1, i, -i}

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Form a group w.r.t addition

Form a group w.r.t multiplication

Does not form a group w.r.t multiplication

Not closed under multiplication

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cos 2x + c

- cos 2x + c

tan 2x + c

cot 2x + c

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12

6

8

none of these

cos 2α=

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1 - 2 sin²α

sin ²α+ cos²β

sin²α- cos²β

None of these

Range of cotθis

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(+∞to -∞)

(-1 to +1)

(-5 to +5)

Set of even numbers only

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The equation of the circle wit (-1, 1) and radius 2 is

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Range if y = cos x is

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-1≤ y≤ 1

-1 < y < 1

-∞ < x < +∞

None of these

If k2x2 +2hxy- 4y2 =0 represents two perpendicular lines then

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k = 2

k = ±2

k = -2

k ≠0

If uv= Projuv then

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Uandvare parallel

vis a unit vector

Uis a unit vector

Both b and c

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tan 3x + c

cot 3x + c

- cot 3x + c

If f(x) = -x²then f(-2) is

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-2

2

-4

4

The corner point of the boundary lines, x-2y

2x + y = 2 is:

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(2,6)

(6,2)

(-2,2)

(2,-2)

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Which is a proper rational fraction

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2π+θwill have terminal side in Quad

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I

II

III

IV

The sum of first 60 natural numbers is

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1830

3660

1640

1770

The vertex of the standard position angles lies on

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(0,0)

(0,1)

(1,0)

(1,1)

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1

-1

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A statement which is either true or false is called

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Induction

Deduction

Propositicon

Logic

Multiplicative inverse of "1" is

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+- 1

0

1

None of these

The product of the four fourth roots of unity is

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0

1

-1

None of these

How many 3 digit numbers can be formed by using each one of the digit 2, 3, 5, 7, 9 only once?

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15

24

60

120

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3/4

r

v

None of these

The number of arbitrary constants in the general solution of a differential equation is equal to the different equation

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Order

Degree

Variables

All are correct

If f (x) = 2x+1 then fof (x) = _______;

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4x+3

2x +3

4x +1

None of these

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R/[0,4]

R/(0,4)

(0,4)

[0,4]

In natural logarithm the base is

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1

0

10

e

Identity w.r.t intersection in a power set of any set is

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∅

Set itself

Singleton set

{0}

1 degree = _______

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0.00175 rad

0.175 rad

0.0175 rad

1.75 rad

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Two real roots

Two positive roots

Two negative roots

One positive and one negative root

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0

1

2

4

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images

pre-images

constants

none of these

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

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-5

5

0

1

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Identify Error

I fear that they would have more trouble in reaching there than us. No error

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A

B

C

D

E

To deprive a thing of its holy characters

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Desecrate

Blasphemy

Consecrate

Sacrilege

Choose Relative Pair Of Word

ARGUMENT : DEBATE

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Violence : Peace

Fight : Constest

Challenge : Opponent

Doe : Stag

PARK : RECREATION

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Kitchen : Cooking

Fence : Sitting

Tree : Climbing

Yard : Playing

One who does not care for literature or art

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Philistine

Primitive

Barbarian

Illiterate

A high concentration of red blood cells increases its viscosity from

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3 - 5 times that of mercury

5 - 8 times that of mercury

3 - 5 times that of water

5 - 8 times that of water

The stopping voltage for a certain metal is 100 volts, then the work function for the cathode plate is

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100 J

1.6 x 10^-17J

100 eV

1.6 x 10^-17eV

Triple point of water is

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273.16°F

372.16K

273.16°F

273.16

The pattern of NaCl particles have a shape which is :

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Cubic

Body centred cubic

Simple cubic

face centred

Both (A) and (C)

The absolute temperature for an ideal gas is

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directly proportional to the rotational K.E of gas molecules

directly proportional to the vibrational K.E of gas molecules

directly proportional to the average translational K.E.of gas molecules

directly proportional to the P.E. of gas molecules

The quantity having dimension of ML²T⁰²will earth is:

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80 sec

500 sec

1.802 X 10⁴sec

Aerophysics

if the field is directed along the normal to the area, then flux is:

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Maximum

Equal to zero

Equal to BA

Minimum

Both (A) and (C)

The amplifier which us used to perform mathematical operations electronically is known as

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calculator

OP-AMP

computer

any one of them

The tidal energy is produced due to rotation of Earth relative to:

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Moon

Sun

Oceans

Water

The coefficient of linear expansion of iron is 0.000011 per°K. An iron rod is 10 metre long at 27°C. The length of the rod will be decreased by 1.1 mm when the temperature of the rod changes to

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0°C

10°C

17°C

20°C

When the pn-junction is connected reversed biased, its resistance is of the order of

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few ohms

few kilo-ohms

few mega-ohms

few mili-ohms

When a bicycle is in motion, the frictional forces exerted by the ground are

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In the forward direction on both the wheels

In the backward direction on both the wheels

In the forward direction on the front wheel and the backward direction on the rear wheel

In the backward direction on the front wheel and the forward direction on the rear wheel

Neutrons are

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positive charge

negatively charged

massless

neutral

At what temperature the adiabatic change is equivalent to the isothermal change?

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Zero degree Celsius

Zero Kelvin

Critical temperature

Above critical temperature

The value of resistivity is the least for:

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Copper

Aluminimum

Silver

Tungsten

Iron

There is no way to detect:

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Absolute uniform motion

Accelerated motion

State rest

State of motion

None of these

A mass spectrograph sort out

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molecules

atoms

elements

isotopes

The total charge of any nucleus is given as

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Ze²

Z²e

Z/e

Ze

Examples of moderators used in a fission reactor is/are:

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Water

Heavy water

Carbon

Hydrocarbon

All of these

Blood is an

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Compressible fluid

incompressible fluid

hard

none of them

A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three seconds. The body has fallen for a time of

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3 s

5 s

7 s

9 s

In case of destructive interference of two waves, the amplitude of the resultant wave will be ____ either of the waves:

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Greater than

Smaller than

Equal to

None of these

The resistance offered by a fluid to a solid moving inside it is called:

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Drag force

Surface force

Viscosity

None of these

The direction of vector in space is specified by:

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One angle

Two angles

Three angles

None of these

If the acceleration of a body is negative, then slope of the velocity-time graph will be:

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Zero

Positive

Negative

Infinity

Unit of viscosity is:

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Kg m^-1sec^-1

N s m^-2

J s m^-3

All of these

During the positive half-cycle in the half-wave rectification,the diode

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does not conduct

conducts

either of these

neither of these

The distance covered by the wave during one period is called its:

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Wave number

Frequency

Wavelength

Time period

A rheostat can e used:

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As variable resistor

As potential divider

For varying the current

All of these

None of these

A body of weight 1 N has a kinetic energy of 1 joule when its speed is:

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1.46 m sec^-1

2.44 m sec^-1

3.42 m sec^-1

4.43 m sec^-1

The expression F x t is called impulse if the time 't' is

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zero

very large

very small

infinite

Due to relative motion of observer and the frame of reference of events, time always:

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Dilates itself

Contracts itself

Stretches itself

Both (A) and (C)

None of these

In the doping process, the ratio of the doping atoms to the semi conductor atom is

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1 to 10

1 to 10³

1 to 10⁶

1 to 10⁹

Albert Einstein got the Nobel prize in physics for his explanation of photoelectric effect in

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1916

1919

1921

1923

The electric field, magnetic field and the direction of their propagation are mutually

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perpendicular

parallel

none of these

In deriving the Bernoulli's equation, we assume that the fluid is

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incompressible

no viscous

flows in a steady manner

all of them

Two conductors having the same type of charges are connected by a conducting wire. There would not be any amount of charges on them if

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They have the same potential

They have the same amount of charge

They have the same capacity

They have the same shape

Work done is maximum when angle between force and displacement is

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0°

90°

180°

None of these

A lift is descending at a constant speed V. A passenger in the lift drops a coin. The acceleration of the coin towards the floor will be

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Zero

g

-g

V + g

Alternating current can induce voltage because it has a

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High peak value

Varying magnetic field

Stronger field than direct curren

Constant magnetic field

If we connected the ordinary DC ammeter to measure alternating current, it would measure its:

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Instantaneous value

RMS value

Value averaged over a cycle

Either (B) or (C)

Either (A) or (C)

When two protons are brought closer potential energy of both of them:

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Increases

Decreases

Remains same

None of these

The current sensitivity of the galvanometer is

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C/BAN

BAN/C

CAN/B

CBN/A

A grating with high resolving power can distinguish _______ difference in wavelengths :

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Smaller

Larger

Zero

None of these

A particle executes SHM with frequency. The frequency with which its K.E oscillates is

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f/2

2f

f

4f

Absolute temperature can be calculated by

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Means squares velocity

Motion of the molecule

Both A and B

None of these

The waves which propagate out in space due to oscillation of electric and magnetic fields are known as

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e.m. waves

mechanical waves

sound waves

water waves

The Einstein's changes in length, mass and time are not observed in common life because

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We dont observer then seriously

The masses are too large

Their speed is too small than the speed of right

All of the above

The SI unit of magnetic flux is.

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weber

Nm^-1A^-1

tesla

gauss

A carnot cycle consists of

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One step

two step

three steps

four steps

The photon of radio-waves has energy of about

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1 Me V

1 Ke v

10^-10e v

10¹⁰e v

The unit of viscosity is SI system is:

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Kg^-1m sec^-1

Kgm^-1 sec^-1

Kg^-1m^-1 sec

None of these

If 42 J heat is transferred to the system and the work done by the system is 32 J then what will be the change in internal energy

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0 J

2 J

5 J

10 J

If a ball comes back to its starting point after bouncing off the wall several times, then its

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total displacement is zero

average velocity is zero

none of them

both of them

Amplitude in SHM is equivalent to ______ in circular motion

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Diameter

Radius

Circumference

None of these

Blood has a density

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Equal to water

Greater then water

Lesser then water

None of these

The total reactance of a series RLC circuit at resonance is

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zero

Equal to the resistance

Infinity

Capacitive

Such an inductor coil which does not consume energy and is often employed for controlling a.c. without consumption of energy is called

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Choke

impedance

Semi-conductor

None

The solids which has structure in-between order and disorder are called

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amorphous solids

polymeric solids

crystalline solids

all of them

A medium of dielectric constant 'K' is introduced between the plates of parallel plate condenser. As a result its capcitance

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Increase k time

Decreases k times

Decreases 1/K times

Remains unchanged

The waves produced in a microwave oven have frequency

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2450 Hz

2450 K Hz

2450 M Hz

2450 G Hz

In an elevator moving vertically up with an acceleration 'g' the force exerted on the floor by a passenger of mass M is

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Mg

1/2 Mg

Zero

2 Mg

The density of water is 10³kg/m³. The water pressure on a submarine is 2.0 x 10⁷N/m². The depth of the submarine below the surface of the water, in maters, is approximately

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200 m

11000 m

2000 m

8000 m

When there is no relative motion between the magnet and coil, the galvanometer indicates:

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No current in circuit

An increasing current

A decreasing current

Either B or C

The velocity given to a body to go out of the influence of earth's gravity is known as:

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Terminal velocity

Orbital velocity

Escape velocity

None of these

A rotating body tends to be slower, when its angular acceleration is:

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Positive

Negative

Zero

Infinity

The least distance of distinct vision is:

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10 cm

25 cm

50 cm

100 cm

Particles have the mass smallest of following is

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Electron

Proton

Neutron

Quark

The total number of lines of magnetic induction pasing through a surface perpendicular to the magnetic field is called

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magnetic flux

magnetic flux density

magnetic induction

magnetic field intensity

The restoring force always directed towards the

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extreme position

mean position

both of them

none of them

The magnetic field in the middle of a solenoid due to current is

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weak

strong and uniform

none-uniform

zero

The distance from eye to near point is taken as:

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10 cm

15 cm

20 cm

25 cm

The SI unit of strain is

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N

Dynes

Pascal

Dimensionless

When two protons are brought are brought closer potential energy of both of them:

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Increases

Decreases

Remains same

None of these

If a molecule with momentum mv strikes a wall and rebound then the change in momentum will be:

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-2 mv

Zero

2 mv

mv

Semi-conductor elements have atoms with

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2 valence electrons

3 valence electrons

4 valence electrons

5 valence electrons

The combined effect of resistance and reactance in a.c. circuit is called

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conductance

resistance

impedance

choke

According to the de-Brogile relation, an object of large mass and ordinary speed has

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very small wavelength

very large wavelength

very small frequency

all of these

The year when A.H. compton was awarded Nobel Prize is:

Choose an answer

1923

1927

1931

1935

None of these

The number of vibration in two seconds can be expressed as

______ of frequency of vibration is f:

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f

2 f

3 f

1/2 f

The electric intensity outside the two oppositely charged parallel metal plates is

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Maximum

Minimum

Zero

Infinite

A labourer carrying a distance a load on his head moves from rest on a horizontal road to another point where he comes to rest. He has done:`

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Minimum work

Maximum work

Zero work

Negative work

A body of mass 5 kg is acted upon by a total change n momentum will be:

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10 NS

100 NS

140 NS

200 NS

The volume of universal gas constant R is:

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8.314 J/K mole K

8314 J/K mole K

8.314 J/mole K

None of these

The projectile motion is composed of

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horizontal motion only

vertical motion only

horizontal and vertical motion

none of them

When a high energy photon interact with a metal, which of the following effect is most likely to be taken place

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pair production

photoelectric effect

Compton effect

None of these

In the formula for finding the speed of waves in the spring, unit of m in SIn units is:

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kg

kg-meter

kg/meter

Meter/kg

One coulomb per second is equal to

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One volt

One ampere

One hom

One henry

Acceleration of a body is negative if the velocity of the body is

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constant

increasing

decreasing

none of them

The charge carries in the electrolyte are:

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Positive ions

Negative ions

Either (A) or (B)

Both (A) and (B)

Neither (A) nor (B)

The lasing or active medium in He-Ne laser discharge tube is:

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Nitrogen

Helium

Hydrogen

Neon

None of these

The concept of entropy was introduced into the study of thermodynamics in

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1856

1865

1656

1685

The bridge circuit of full wave rectification uses

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one diode

two diode

three diode

four diode

When a nucleus emits an alpha particles, its charge number decreases by

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3

2

6

5

The vibratory or oscillatory motion of a body is

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translatory motion

back and forth motion about its mean position

free all motion

circular motion

A relationship between Gauses of magnetic induction and Tesla(T) is given by

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G 10^-3T

G = 10^-2T

G = 10^-4T

G = 10^-1T

If we increase the length of a simple pendulum four times, its time period will become

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2 times

3 times

4 times

6 times

The focal length of convex lens having magnifying power of 5.55 is:

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5.5 cm

5 cm

4.5 cm

6 cm

A magnifier gives an image which is:

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Virtual, inverted

Real, erect

Virtual, erect

Real, inverted

The velocity of a projectile is maximum

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at the point of projection

just before striking the ground

at none of them

at both of them

It is possible to recognize a person by hearing his voice even if he is hidden behind a solid wall. This is due to the fact that his voice

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Has a definite pitch

Has a definite quality

Has a definite capacity

Can penetrate the wall