A particle moves in a straight line so that its displacement \(x\) at any time \(t\) is given by \(x^2=1+t^2\). Its acceleration at any time \(\mathrm{t}\) is \(\mathrm{x}^{-\mathrm{n}}\) where \(\mathrm{n}=\) _______.

A Carnot engine absorbs \(1000\,J\) of heat energy from a reservoir at \(127\,^oC\) and rejects \(600\,J\) of heat energy during each cycle. The efficiency of engine and temperature of sink will be

Given below are two statements : Statement-I: When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be \(0^{\circ}\). Statement-II: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well : In the light of above statement, choose the correct answer from the options given below.

Two hypothetical planets of masses \(m_1\) and \(m_2\) are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres . What is their speed when their separation is \('d'\) ? (Speed of \(m_1\) is \(v_1\) and that of \(m_2\) is \(v_2\) )

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have _________.

A sample of gas expands from \(V_1\) to \(V _2\). In which of the following, the work done will be greatest ?

An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at \(x =+2\,m\), its velocity is \(-4 \hat{ j }\, m / s\). The object's velocity \((v)\) and acceleration \((a)\) at \(x =-2\,m\) will be

Different combination of \(3\) resistors of equal resistance \(R\) are shown in the figures.
The increasing order for power dissipation is:

Match List I with List \(II\) Choose the correct answer from the options given below:

The vehicles carrying inflammable fluids usually have _______ metallic chains touching the ground.