If the length and time period of an oscillating pendulum have errors of 1% and 3% respectively then the error in measurement of acceleration due to gravity is

(a)

4%

(b)

5%

(c)

6%

(d)

7%

The density of a material in CGS system of units is 4 g cm^-3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, then the value of density of material will be

(a)

0.04

(b)

0.4

(c)

40

(d)

400

The law of electricity and magnetism is used to ____________

(a)

Wireless communication

(b)

Nuclear reactor

(c)

Steam engine

(d)

Aeroplane

The fraction of \(1\over 273.16\) temperature of the triple point of water represents __________.

(a)

celsius

(b)

fahrenheit

(c)

centigrade

(d)

kelvin

Which of the following is the most accurate?

(a)

200.0 m

(b)

20\(\times\)10¹m

(c)

2\(\times\)10² m

(d)

data is inadequate

If C is the capacitance and V is the potential, the dimensional formula for CV² is _______________.

(a)

ML²T^-2

(b)

ML^-1T^-2

(c)

ML^-2T^-3

(d)

ML²T^-1

The ratio of one nanometer to one micron is__________________

(a)

10^-3

(b)

10³

(c)

10^-9

(d)

10^-6

The displacement of particle is given by X = a_o + \(\frac{a_1t}{2}-\frac{2_2t^2}{3}\) What is its acceleration?

(a)

\(\frac{2a_2}{3}\)

(b)

\(-\frac{2a_2}{3}\)

(c)

a₂

(d)

zero

A passenger in the moving train throws a coin. If the coin falls in front of him, train must be moving with ________________.

(a)

uniform speed

(b)

acceleration

(c)

deceleration

(d)

uniform velocity

The vectors \(\vec A\) and \(\vec B\) to be mutually orthogonal when _________.

(a)

\(\vec A+\vec B=0\)

(b)

\(\vec A-\vec B=0\)

(c)

\(\vec A.\vec B=0\)

(d)

\(\vec A\times \vec B=0\)

A car starting from rest, accelerates at a constant rate x from sometimes after which it decelerates at a constant rate y to come to rest. If the total time elapsed is t, the maximum velocity attained by the car is given by ______________.

(a)

\(\frac{xy}{x+y}t\)

(b)

\(\frac{xy}{x-y}t\)

(c)

\(\frac{x^2y^2}{x^2+y^2}t\)

(d)

\(\frac{x^2y^2}{x^2-y^2}t\)

The second derivative of position vector with respect to time is _____________.

(a)

velocity

(b)

acceleration

(c)

force

(d)

displacement

For free falling body, its initial velocity is _____________.

(a)

0

(b)

1

(c)

\(\infty\)

(d)

none

In oblique projection horizontal range of the projectile is _______________. 

(a)

\(\frac{u^2\sin^2\theta}{2g}\)

(b)

\(\frac{2u\sin\theta}{g}\)

(c)

\(\frac{u^2\sin2\theta}{g}\)

(d)

\(\frac{u^2}{g}\)

In non-uniform circular motion, the resultant acceleration makes an angle with the radius vector is ___________.

(a)

\(\tan^{-1}(\frac{ra_t}{V^2})\)

(b)

\(\tan_{-1}(\frac{a_t}{(\frac{r}{v^2})})\)

(c)

\(\tan^{-1}(\frac{rv^2}{at})\)

(d)

\(\tan^{-1}(\frac{r+at^2}{v^2})\)

Which of the following graph represents the equation y = kx²?

(a)

(b)

(c)

(d)

\(X\propto \frac { 1 }{ Y } \) (or) XY = constant is represented by ___________.

(a)

(b)

(c)

(d)

Two blocks A & B of masses 2m & m are connected by a massless and inextensible strong. The magnitudes of acceleration of A & B immediately after the string is cut are ____________.

(a)

\(\frac { g }{ 2 } \),g

(b)

g,g

(c)

g,\(\frac { g }{ 2 } \)

(d)

\(\frac { g }{ 2 } \),\(\frac { g }{ 2 } \)

If the potential energy of the particle is \(\alpha -\frac { \beta }{ 2 } { x }^{ 2 }\), then force experienced by the particle is

(a)

F = \(\frac { \beta }{ 2 } { x }^{ 2 }\)

(b)

F = βx

(c)

F = -βx

(d)

F = -\(\frac { \beta }{ 2 } { x }^{ 2 }\)

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

(a)

a line perpendicular to the plane of rotation

(b)

the line making an angle of 45^o to the plane of rotation

(c)

the radius

(d)

tangent to the path

In the following, what are the quantities which that are conserved?

(a)

Linear momentum of planet

(b)

Angular momentum of planet

(c)

Total energy of planet

(d)

Potential energy of a planet

With an increase in temperature, the viscosity of liquid and gas, respectively will

(a)

increase and increase

(b)

increase and decrease

(c)

decrease and increase

(d)

decrease and decrease

A hot cup of coffee is kept on the table. After some time it attains a thermal equilibrium with the surroundings. By considering the air molecules in the room as a thermodynamic system, which of the following is true

(a)

ΔU > 0, Q = 0

(b)

ΔU > 0, W < 0

(c)

ΔU > 0, Q > 0

(d)

ΔU = 0, Q > 0

Two identically sized rooms A and B are connected by an open door. If the room A is air conditioned such that its temperature is 4°C lesser than room B, which room has more air in it?

(a)

Room A

(b)

Room B

(c)

Both room has same air

(d)

Cannot be determined

A simple pendulum has a time period T₁. When its point of suspension is moved vertically upwards according as y = k t², where y is vertical distance covered and k = 1 ms⁻², its time period becomes T₂. Then, \(\frac { { T }_{ 1 }^{ 2 } }{ { T }_{ 2 }^{ 2 } } \) is (g = 10 m s⁻²).

(a)

\(\frac{5}{6}\)

(b)

\(\frac{11}{10}\)

(c)

\(\frac{6}{5}\)

(d)

\(\frac{5}{4}\)