Show that the system of equations is inconsistent. 2x + 5y= 7, 6x + 15y = 13.

If (cosθ + i sinθ)² = x + iy, then show that x²+y² =1

Find the modules of (1+ 3i)³

Find x If \(x=\sqrt { 2+\sqrt { 2+\sqrt { 2+....+upto\infty } } } \)

Find the principal value of \({ cos }^{ -1 }\left( \frac { -1 }{ 2 } \right) \)

Prove that \(2{ tan }^{ -1 }\left( \frac { 2 }{ 3 } \right) ={ tan }^{ -1 }\left( \frac { 12 }{ 5 } \right) \)

Find the equation of the parabola with vertex at the origin, passing through (2, -3) and symmetric about x-axis

Find the eccentricity of the hyperbola with foci on the x-axis if the length of its conjugate axis is \({ \left( \frac { 3 }{ 4 } \right) }^{ th }\) of the length of its tranverse axis.

A force of magnitude 6 units acting parallel to \(\overset { \wedge }{ 2i } -\overset { \wedge }{ 2j } +\overset { \wedge }{ k } \) displaces the point of application from (1, 2, 3) to (5, 3, 7). Find the work done.

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Find the equation of the plane containing the line of intersection of the planes x + y + Z - 6 = 0 and 2x + 3y + 4z + 5 = 0 and passing through the point (1, 1, 1)

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x = -1 is one root

A man 2 m high walks at a uniform speed of 5 km/ hr away from a lamp post 6 m high. Find the rate at which the length of his shadow increases?

Verify Lagrange’s Mean Value theorem for \(f(x)=\sqrt { x-2 } \) in the interva [2,6]

Prove that the function f(x)=2x²+3x is strictly increasing on \(\left[ -\frac { 1 }{ 2 } ,\frac { 1 }{ 2 } \right] \)

Use differentials to find \(\sqrt{25.2}\)

If w=xye^xy find \(\frac { { \partial }^{ 2 }u }{ \partial x\partial y } \)

Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ log(tanx)dx } =0\)

Find the area enclosed between the parabola y2=4ax and the line x=a,x=9a.

Solve: x \(\frac{dy}{dx}=x+y\)

Form the D.E of family of parabolas having vertex at the origin and axis along positive y-axis.

In the set of integers under the operation * defined by a * b = a + b - 1. Find the identity element.