Angle Between the Curve
Application of Derivatives

85791 If \(\theta\) is an angle between the curves \(x^{2}+4 y=0\) and \(x y=2\), then \(\tan \theta=\)

1 -1
2 \(\frac{1}{3}\)
3 \(\frac{1}{2}\)
4 3
Application of Derivatives

85792 The angle between the curves \(y^{2}=8(x+4)\) and \(y^{2}=\mathbf{2 4}(4-x)\) is

1 \(\tan ^{-1}\left(\frac{1}{6}\right)\)
2 \(\tan ^{-1}(3)\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
Application of Derivatives

85793 A ladder \(5 \mathrm{~m}\) long is leaning against a wall. If the top of the ladder slides downwards at a rate of \(10 \mathrm{~cm} . \mathrm{sec}^{-1}\), then the rate at which the angle between the floor and the ladder decreases, when the lower end of ladder is \(2 \mathrm{~m}\) from the wall, is radian. sec

1 \(\frac{1}{10}\)
2 \(\frac{1}{20}\)
3 20
4 10
Application of Derivatives

85794 The angle between the curves \(\mathrm{y}^{2}=4 \mathrm{ax}\) and ay \(=\)

1 \(\tan ^{-1} \frac{3}{4}\)
2 \(\tan ^{-1} \frac{3}{5}\)
3 \(\tan ^{-1} \frac{4}{3}\)
4 \(\tan ^{-1} \frac{5}{3}\)
Application of Derivatives

85795 If the angle between the curves \(y^{2}=4 x\) and \(y=\) \(\mathrm{e}^{-\mathrm{x} / 2}\) is \(\theta\), then \(\operatorname{cosec}^{2}(\theta / 2)=\)

1 2
2 3
3 \(\sqrt{3}\)
4 \(\sqrt{2}\)
Application of Derivatives

85791 If \(\theta\) is an angle between the curves \(x^{2}+4 y=0\) and \(x y=2\), then \(\tan \theta=\)

1 -1
2 \(\frac{1}{3}\)
3 \(\frac{1}{2}\)
4 3
Application of Derivatives

85792 The angle between the curves \(y^{2}=8(x+4)\) and \(y^{2}=\mathbf{2 4}(4-x)\) is

1 \(\tan ^{-1}\left(\frac{1}{6}\right)\)
2 \(\tan ^{-1}(3)\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
Application of Derivatives

85793 A ladder \(5 \mathrm{~m}\) long is leaning against a wall. If the top of the ladder slides downwards at a rate of \(10 \mathrm{~cm} . \mathrm{sec}^{-1}\), then the rate at which the angle between the floor and the ladder decreases, when the lower end of ladder is \(2 \mathrm{~m}\) from the wall, is radian. sec

1 \(\frac{1}{10}\)
2 \(\frac{1}{20}\)
3 20
4 10
Application of Derivatives

85794 The angle between the curves \(\mathrm{y}^{2}=4 \mathrm{ax}\) and ay \(=\)

1 \(\tan ^{-1} \frac{3}{4}\)
2 \(\tan ^{-1} \frac{3}{5}\)
3 \(\tan ^{-1} \frac{4}{3}\)
4 \(\tan ^{-1} \frac{5}{3}\)
Application of Derivatives

85795 If the angle between the curves \(y^{2}=4 x\) and \(y=\) \(\mathrm{e}^{-\mathrm{x} / 2}\) is \(\theta\), then \(\operatorname{cosec}^{2}(\theta / 2)=\)

1 2
2 3
3 \(\sqrt{3}\)
4 \(\sqrt{2}\)
Application of Derivatives

85791 If \(\theta\) is an angle between the curves \(x^{2}+4 y=0\) and \(x y=2\), then \(\tan \theta=\)

1 -1
2 \(\frac{1}{3}\)
3 \(\frac{1}{2}\)
4 3
Application of Derivatives

85792 The angle between the curves \(y^{2}=8(x+4)\) and \(y^{2}=\mathbf{2 4}(4-x)\) is

1 \(\tan ^{-1}\left(\frac{1}{6}\right)\)
2 \(\tan ^{-1}(3)\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
Application of Derivatives

85793 A ladder \(5 \mathrm{~m}\) long is leaning against a wall. If the top of the ladder slides downwards at a rate of \(10 \mathrm{~cm} . \mathrm{sec}^{-1}\), then the rate at which the angle between the floor and the ladder decreases, when the lower end of ladder is \(2 \mathrm{~m}\) from the wall, is radian. sec

1 \(\frac{1}{10}\)
2 \(\frac{1}{20}\)
3 20
4 10
Application of Derivatives

85794 The angle between the curves \(\mathrm{y}^{2}=4 \mathrm{ax}\) and ay \(=\)

1 \(\tan ^{-1} \frac{3}{4}\)
2 \(\tan ^{-1} \frac{3}{5}\)
3 \(\tan ^{-1} \frac{4}{3}\)
4 \(\tan ^{-1} \frac{5}{3}\)
Application of Derivatives

85795 If the angle between the curves \(y^{2}=4 x\) and \(y=\) \(\mathrm{e}^{-\mathrm{x} / 2}\) is \(\theta\), then \(\operatorname{cosec}^{2}(\theta / 2)=\)

1 2
2 3
3 \(\sqrt{3}\)
4 \(\sqrt{2}\)
Application of Derivatives

85791 If \(\theta\) is an angle between the curves \(x^{2}+4 y=0\) and \(x y=2\), then \(\tan \theta=\)

1 -1
2 \(\frac{1}{3}\)
3 \(\frac{1}{2}\)
4 3
Application of Derivatives

85792 The angle between the curves \(y^{2}=8(x+4)\) and \(y^{2}=\mathbf{2 4}(4-x)\) is

1 \(\tan ^{-1}\left(\frac{1}{6}\right)\)
2 \(\tan ^{-1}(3)\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
Application of Derivatives

85793 A ladder \(5 \mathrm{~m}\) long is leaning against a wall. If the top of the ladder slides downwards at a rate of \(10 \mathrm{~cm} . \mathrm{sec}^{-1}\), then the rate at which the angle between the floor and the ladder decreases, when the lower end of ladder is \(2 \mathrm{~m}\) from the wall, is radian. sec

1 \(\frac{1}{10}\)
2 \(\frac{1}{20}\)
3 20
4 10
Application of Derivatives

85794 The angle between the curves \(\mathrm{y}^{2}=4 \mathrm{ax}\) and ay \(=\)

1 \(\tan ^{-1} \frac{3}{4}\)
2 \(\tan ^{-1} \frac{3}{5}\)
3 \(\tan ^{-1} \frac{4}{3}\)
4 \(\tan ^{-1} \frac{5}{3}\)
Application of Derivatives

85795 If the angle between the curves \(y^{2}=4 x\) and \(y=\) \(\mathrm{e}^{-\mathrm{x} / 2}\) is \(\theta\), then \(\operatorname{cosec}^{2}(\theta / 2)=\)

1 2
2 3
3 \(\sqrt{3}\)
4 \(\sqrt{2}\)
Application of Derivatives

85791 If \(\theta\) is an angle between the curves \(x^{2}+4 y=0\) and \(x y=2\), then \(\tan \theta=\)

1 -1
2 \(\frac{1}{3}\)
3 \(\frac{1}{2}\)
4 3
Application of Derivatives

85792 The angle between the curves \(y^{2}=8(x+4)\) and \(y^{2}=\mathbf{2 4}(4-x)\) is

1 \(\tan ^{-1}\left(\frac{1}{6}\right)\)
2 \(\tan ^{-1}(3)\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
Application of Derivatives

85793 A ladder \(5 \mathrm{~m}\) long is leaning against a wall. If the top of the ladder slides downwards at a rate of \(10 \mathrm{~cm} . \mathrm{sec}^{-1}\), then the rate at which the angle between the floor and the ladder decreases, when the lower end of ladder is \(2 \mathrm{~m}\) from the wall, is radian. sec

1 \(\frac{1}{10}\)
2 \(\frac{1}{20}\)
3 20
4 10
Application of Derivatives

85794 The angle between the curves \(\mathrm{y}^{2}=4 \mathrm{ax}\) and ay \(=\)

1 \(\tan ^{-1} \frac{3}{4}\)
2 \(\tan ^{-1} \frac{3}{5}\)
3 \(\tan ^{-1} \frac{4}{3}\)
4 \(\tan ^{-1} \frac{5}{3}\)
Application of Derivatives

85795 If the angle between the curves \(y^{2}=4 x\) and \(y=\) \(\mathrm{e}^{-\mathrm{x} / 2}\) is \(\theta\), then \(\operatorname{cosec}^{2}(\theta / 2)=\)

1 2
2 3
3 \(\sqrt{3}\)
4 \(\sqrt{2}\)