80211 If \(y=\left(1+x^{1 / 4}\right)\left(1+x^{1 / 2}\right)\left(1-x^{1 / 4}\right)\), then \(d y / d x\) equals-

80212 If \(f(t)=\frac{1-t}{1+t}\), then \(f^{\prime}(1 / t)\) is equal to

80213 Let \(f(x+y)=f(x) . f(y)\) for all \(x, y\) where \(f(0) \neq 0\). If \(f(5)=2\) and \(f^{\prime}(0)=3\), then \(f^{\prime}(5)\) is equal to-

80214 Let \(f(x)=\left(x^{5}-1\right)\left(x^{3}+1\right)\), \(g(x)=\left(x^{2}-1\right)\left(x^{2}-x+1\right)\) and let \(h(x)\) be such that \(f(x)=g(x) h(x)\). Then \(\lim _{x \rightarrow 1} h(x)\) is

80215 The number of points, where the function \(f: R\) \(\rightarrow R, f(x)=|x-1| \cos |x-2| \sin |x-1|+(x-3)\)
\(\left|x^{2}-5 x+4\right|\), is NOT differentiable, is :

80211 If \(y=\left(1+x^{1 / 4}\right)\left(1+x^{1 / 2}\right)\left(1-x^{1 / 4}\right)\), then \(d y / d x\) equals-

80212 If \(f(t)=\frac{1-t}{1+t}\), then \(f^{\prime}(1 / t)\) is equal to

80213 Let \(f(x+y)=f(x) . f(y)\) for all \(x, y\) where \(f(0) \neq 0\). If \(f(5)=2\) and \(f^{\prime}(0)=3\), then \(f^{\prime}(5)\) is equal to-

80214 Let \(f(x)=\left(x^{5}-1\right)\left(x^{3}+1\right)\), \(g(x)=\left(x^{2}-1\right)\left(x^{2}-x+1\right)\) and let \(h(x)\) be such that \(f(x)=g(x) h(x)\). Then \(\lim _{x \rightarrow 1} h(x)\) is

80215 The number of points, where the function \(f: R\) \(\rightarrow R, f(x)=|x-1| \cos |x-2| \sin |x-1|+(x-3)\)
\(\left|x^{2}-5 x+4\right|\), is NOT differentiable, is :

80211 If \(y=\left(1+x^{1 / 4}\right)\left(1+x^{1 / 2}\right)\left(1-x^{1 / 4}\right)\), then \(d y / d x\) equals-

80212 If \(f(t)=\frac{1-t}{1+t}\), then \(f^{\prime}(1 / t)\) is equal to

80213 Let \(f(x+y)=f(x) . f(y)\) for all \(x, y\) where \(f(0) \neq 0\). If \(f(5)=2\) and \(f^{\prime}(0)=3\), then \(f^{\prime}(5)\) is equal to-

80214 Let \(f(x)=\left(x^{5}-1\right)\left(x^{3}+1\right)\), \(g(x)=\left(x^{2}-1\right)\left(x^{2}-x+1\right)\) and let \(h(x)\) be such that \(f(x)=g(x) h(x)\). Then \(\lim _{x \rightarrow 1} h(x)\) is

80215 The number of points, where the function \(f: R\) \(\rightarrow R, f(x)=|x-1| \cos |x-2| \sin |x-1|+(x-3)\)
\(\left|x^{2}-5 x+4\right|\), is NOT differentiable, is :

80211 If \(y=\left(1+x^{1 / 4}\right)\left(1+x^{1 / 2}\right)\left(1-x^{1 / 4}\right)\), then \(d y / d x\) equals-

80212 If \(f(t)=\frac{1-t}{1+t}\), then \(f^{\prime}(1 / t)\) is equal to

80213 Let \(f(x+y)=f(x) . f(y)\) for all \(x, y\) where \(f(0) \neq 0\). If \(f(5)=2\) and \(f^{\prime}(0)=3\), then \(f^{\prime}(5)\) is equal to-

80214 Let \(f(x)=\left(x^{5}-1\right)\left(x^{3}+1\right)\), \(g(x)=\left(x^{2}-1\right)\left(x^{2}-x+1\right)\) and let \(h(x)\) be such that \(f(x)=g(x) h(x)\). Then \(\lim _{x \rightarrow 1} h(x)\) is

80215 The number of points, where the function \(f: R\) \(\rightarrow R, f(x)=|x-1| \cos |x-2| \sin |x-1|+(x-3)\)
\(\left|x^{2}-5 x+4\right|\), is NOT differentiable, is :

80211 If \(y=\left(1+x^{1 / 4}\right)\left(1+x^{1 / 2}\right)\left(1-x^{1 / 4}\right)\), then \(d y / d x\) equals-

80212 If \(f(t)=\frac{1-t}{1+t}\), then \(f^{\prime}(1 / t)\) is equal to

80213 Let \(f(x+y)=f(x) . f(y)\) for all \(x, y\) where \(f(0) \neq 0\). If \(f(5)=2\) and \(f^{\prime}(0)=3\), then \(f^{\prime}(5)\) is equal to-

80214 Let \(f(x)=\left(x^{5}-1\right)\left(x^{3}+1\right)\), \(g(x)=\left(x^{2}-1\right)\left(x^{2}-x+1\right)\) and let \(h(x)\) be such that \(f(x)=g(x) h(x)\). Then \(\lim _{x \rightarrow 1} h(x)\) is

80215 The number of points, where the function \(f: R\) \(\rightarrow R, f(x)=|x-1| \cos |x-2| \sin |x-1|+(x-3)\)
\(\left|x^{2}-5 x+4\right|\), is NOT differentiable, is :