KCET 2023

A body is moving along a straight line with initial velocity \(v_0\). Its acceleration \(a\) is constant. After \(t\) seconds, its velocity becomes \(v\). The average velocity of the body over the given time interval is

The degree of the differential equation \(1+\left(\frac{d y}{d x}\right)^2+\left(\frac{d^2 y}{d x^2}\right)^2=\sqrt[3]{\frac{d^2 y}{d x^2}+1}\) is

The number of protons, neutrons and electrons in the ion \({ }_{16}^{32} \mathrm{~S}^{2-}\) respectively are

The true length of a wire is \(3.678 \mathrm{~cm}\). When the length of this wire is measured using instrument \(A\), the length of the wire is \(3.5 \mathrm{~cm}\). When the length of the wire is measured using instrument \(B\), it is found to have length \(3.38 \mathrm{~cm}\). Then, the

If a curve passes through the point \((1,1)\) and at any point \((x, y)\) on the curve, the product of the slope of its tangent and \(x\) coordinate of the point is equal to the \(y\) coordinate of the point, then the curve also passes through the point

A gas at a pressure of \(2 \mathrm{~atm}\) is heated from \(25^{\circ} \mathrm{C}\) to \(323^{\circ} \mathrm{C}\) and simultaneously compressed of \(\frac{2}{3}\)rd of its original value. Then the final pressure is