Tangent and Normal
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Application of Derivatives

85423 Let \(y=e^{x^{2}}\) and \(y=e^{x^{2}}\) sin \(x\) be two given curves. Then, angel between the tangents to the curves at any point of their intersection is

1 0
2 \(\pi\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
Application of Derivatives

85424 The angle of intersection between the curves \(y=\left[|\sin x|+|\cos x|\right.\) and \(\left.x^{2}+y^{2}=10\right]\) where \([x]\) denotes the greatest integer \(\leq x\) is

1 \(\tan ^{-1} 3\)
2 \(\tan ^{-1}(-3)\)
3 \(\tan ^{-1} \sqrt{3}\)
4 \(\tan ^{-1}(1 / \sqrt{3})\)
Application of Derivatives

85425 Suppose that the equation \(f(x)=x^{2}+b x+c=0\) has two distinct real roots \(\alpha\) and \(\beta\). The angle between the tangent to the curve \(y=f(x)\) at the point \(\left(\frac{\alpha+\beta}{2}, f\left(\frac{\alpha+\beta}{2}\right)\right)\) and the positive direction of the \(x\) - axis is

1 \(0^{\circ}\)
2 \(30^{\circ}\)
3 \(60^{\circ}\)
4 \(90^{\circ}\)
Application of Derivatives

85426 If \(y=2 x^{3}-2 x^{2}+3 x-5\), then for \(x=2\) and \(\Delta x=\) 0.1 the value of \(\Delta y\) is

1 2.002
2 1.9
3 0
4 0.9
Application of Derivatives

85423 Let \(y=e^{x^{2}}\) and \(y=e^{x^{2}}\) sin \(x\) be two given curves. Then, angel between the tangents to the curves at any point of their intersection is

1 0
2 \(\pi\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
Application of Derivatives

85424 The angle of intersection between the curves \(y=\left[|\sin x|+|\cos x|\right.\) and \(\left.x^{2}+y^{2}=10\right]\) where \([x]\) denotes the greatest integer \(\leq x\) is

1 \(\tan ^{-1} 3\)
2 \(\tan ^{-1}(-3)\)
3 \(\tan ^{-1} \sqrt{3}\)
4 \(\tan ^{-1}(1 / \sqrt{3})\)
Application of Derivatives

85425 Suppose that the equation \(f(x)=x^{2}+b x+c=0\) has two distinct real roots \(\alpha\) and \(\beta\). The angle between the tangent to the curve \(y=f(x)\) at the point \(\left(\frac{\alpha+\beta}{2}, f\left(\frac{\alpha+\beta}{2}\right)\right)\) and the positive direction of the \(x\) - axis is

1 \(0^{\circ}\)
2 \(30^{\circ}\)
3 \(60^{\circ}\)
4 \(90^{\circ}\)
Application of Derivatives

85426 If \(y=2 x^{3}-2 x^{2}+3 x-5\), then for \(x=2\) and \(\Delta x=\) 0.1 the value of \(\Delta y\) is

1 2.002
2 1.9
3 0
4 0.9
Application of Derivatives

85423 Let \(y=e^{x^{2}}\) and \(y=e^{x^{2}}\) sin \(x\) be two given curves. Then, angel between the tangents to the curves at any point of their intersection is

1 0
2 \(\pi\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
Application of Derivatives

85424 The angle of intersection between the curves \(y=\left[|\sin x|+|\cos x|\right.\) and \(\left.x^{2}+y^{2}=10\right]\) where \([x]\) denotes the greatest integer \(\leq x\) is

1 \(\tan ^{-1} 3\)
2 \(\tan ^{-1}(-3)\)
3 \(\tan ^{-1} \sqrt{3}\)
4 \(\tan ^{-1}(1 / \sqrt{3})\)
Application of Derivatives

85425 Suppose that the equation \(f(x)=x^{2}+b x+c=0\) has two distinct real roots \(\alpha\) and \(\beta\). The angle between the tangent to the curve \(y=f(x)\) at the point \(\left(\frac{\alpha+\beta}{2}, f\left(\frac{\alpha+\beta}{2}\right)\right)\) and the positive direction of the \(x\) - axis is

1 \(0^{\circ}\)
2 \(30^{\circ}\)
3 \(60^{\circ}\)
4 \(90^{\circ}\)
Application of Derivatives

85426 If \(y=2 x^{3}-2 x^{2}+3 x-5\), then for \(x=2\) and \(\Delta x=\) 0.1 the value of \(\Delta y\) is

1 2.002
2 1.9
3 0
4 0.9
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Application of Derivatives

85423 Let \(y=e^{x^{2}}\) and \(y=e^{x^{2}}\) sin \(x\) be two given curves. Then, angel between the tangents to the curves at any point of their intersection is

1 0
2 \(\pi\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
Application of Derivatives

85424 The angle of intersection between the curves \(y=\left[|\sin x|+|\cos x|\right.\) and \(\left.x^{2}+y^{2}=10\right]\) where \([x]\) denotes the greatest integer \(\leq x\) is

1 \(\tan ^{-1} 3\)
2 \(\tan ^{-1}(-3)\)
3 \(\tan ^{-1} \sqrt{3}\)
4 \(\tan ^{-1}(1 / \sqrt{3})\)
Application of Derivatives

85425 Suppose that the equation \(f(x)=x^{2}+b x+c=0\) has two distinct real roots \(\alpha\) and \(\beta\). The angle between the tangent to the curve \(y=f(x)\) at the point \(\left(\frac{\alpha+\beta}{2}, f\left(\frac{\alpha+\beta}{2}\right)\right)\) and the positive direction of the \(x\) - axis is

1 \(0^{\circ}\)
2 \(30^{\circ}\)
3 \(60^{\circ}\)
4 \(90^{\circ}\)
Application of Derivatives

85426 If \(y=2 x^{3}-2 x^{2}+3 x-5\), then for \(x=2\) and \(\Delta x=\) 0.1 the value of \(\Delta y\) is

1 2.002
2 1.9
3 0
4 0.9