List of top Physics Questions on Motion in a straight line asked in WBJEE

Consider the function \(y=f(x)\) defined implicitly by the equation \[ y^{3}-3y+x=0 \] on the interval \((-\infty,-2)\cup(2,\infty)\). The area of the region bounded by the curve \(y=f(x)\), the x-axis and the lines \(x=a,x=b\), where \(-\infty<a<b<-2\) is:

The equation \[ |x+1|^{\log_{x+1}(3+2x-x^{2})}=(x-3)|x| \] has:

The least positive value of \(a\) for which the equation \[ \int_{0}^{x}(t^{2}-8t+13)dt=x\sin\frac{a}{x} \] has a solution is:

If \[ \int_{0}^{1}\left(\sum_{r=1}^{2013}\frac{x}{x^{2}+r^{2}}\right)\left(\prod_{r=1}^{2013}(x^{2}+r^{2})\right)dx =\frac{1}{2}\left[\left(\prod_{r=1}^{2013}(1+r^{2})\right)-K\right], \] then \(K\) is:

For a real number \(y\), consider \([y]\) denotes the greatest integer less than or equal to \(y\). If \[ f(x)=\frac{\tan(\pi[x-\pi])}{1+[x]^{2}}, \] then:

The term independent of \(x\) in the expansion of \[ \left(\frac{x+1}{x^{\frac{2}{3}}-x^{\frac{1}{3}}+1}-\frac{x-1}{x-x^{\frac{1}{2}}}\right)^{15} \] is equal to:

The total number of polynomials of the form \[ x^{3}+ax^{2}+bx+c \] which are divisible by \(x^{2}+1\), where \(a,b,c\in\{1,2,3,\dots,10\}\) is:

The value of the integral \[ \int\frac{\left(\sqrt[3]{x+\sqrt{2-x^{2}}}\right)\left(\sqrt[6]{1-x\sqrt{2-x^{2}}}\right)}{\sqrt[3]{1-x^{2}}}\,dx \] for \(x\in(0,1)\) is:

The solution of the differential equation \[ 2x^{2}y\frac{dy}{dx}=\tan(x^{2}y^{2})-2xy^{2}, \] given \(y(1)=\sqrt{\frac{\pi}{2}}\) is: