List of top Questions asked in AP ECET BSc Mathematics

The distance between the planes \(2x+y+2z=8\) and \(4x+2y+4z+5=0\) is

The equation of the plane which is parallel to \(x+3y+5z+1=0\) and \(5\) units from the origin is

A plane which bisects the angle between the two given planes \(x+2y+2z-2=0\) and \(2x-y+2z-4=0\), passes through the point

The radical plane of the spheres \(x^2+y^2+z^2+4x-2y+2z+6=0\) and \(x^2+y^2+z^2+2x-4y-2z+6=0\) is

The equation of a plane containing the line of intersection of the planes \(2x-y-4=0\) and \(y+2z-4=0\), and passing through the point \((1,1,0)\), is

If \(f(2)=2\hat i-\hat j+2\hat k\) and \(f(3)=4\hat i-2\hat j+3\hat k\), then the value of \(\int_2^3\left(f\cdot\dfrac{df}{dt}\right)dt\) is

The value of \(\iint_S (x^2+2y^2+3z^2)\,ds\) over the sphere \(x^2+y^2+z^2=9\) is

The value of the triple integral \(\displaystyle \int_0^1\int_0^y\int_0^x (9+2z)\,dz\,dy\,dx\) is

If \(\vec r\) is the position vector of any point on a closed surface \(S\) that encloses the volume \(V\), then \(\iint_S \vec r\cdot d\vec s\) is equal to

Stokes theorem connects

For a vector field \(\vec F\), the divergence theorem states that

If \(\vec V_1\) and \(\vec V_2\) are the vectors joining the fixed points \((x_1,y_1,z_1)\) and \((x_2,y_2,z_2)\) respectively to a variable point \((x,y,z)\), then \(\operatorname{curl}(\vec V_1\times \vec V_2)=\)

Which of the following holds for any non-zero vector \(\vec a\)?

The value of the line integral of \(\vec{F}=yz\hat{i}\) in the counter clockwise direction, along the circle \(x^2+y^2=1\) at \(z=1\) is

If \(\vec F=3xy\hat i-y^2\hat j\), then the value of \(\int_C \vec F\cdot d\vec r\), where \(C\) is the curve \(y=2x^2\) in the \(xy\)-plane from \((0,0)\) to \((1,2)\), is

If \(S\) is any closed surface enclosing a volume \(V\) and \(\vec F=x\hat i+2y\hat j+3z\hat k\), then \(\iint_S \vec F\cdot \hat n\,ds=\)

The angle in degrees between two vectors \(\vec a=\dfrac{\sqrt3}{2}\hat i+\dfrac{1}{2}\hat j\) and \(\vec b=-\dfrac{\sqrt3}{2}\hat i+\dfrac{1}{2}\hat j\) is

The maximum value of the directional derivative of \(f=2x^2+3y^2+z^2\) at \((2,1,3)\) in the direction of \(\hat i+2\hat j-2\hat k\) is

If \(f(x,y,z)=x^2y+y^2z+z^2x\), then the value of \(\nabla\cdot(\nabla\times\nabla f)+\nabla\cdot(\nabla f)\) at \((1,1,1)\) is

If \(\vec V=(x+3y)\hat i+(y-2x)\hat j+(x+az)\hat k\) is a solenoidal, then \(a=\)

Let \(T(x,y,z)=xy^2+2z-x^2z^2\) be the temperature at the point \((x,y,z)\). The unit vector in the direction in which the temperature decreases most rapidly at \((1,0,-1)\) is

Which of the following is NOT TRUE?

If \(\vec F(t)\) has constant direction, then

If \(\vec r=x\hat i+y\hat j+z\hat k\) and \(r=|\vec r|\), then the value of \(\operatorname{div}\left(\dfrac{\vec r}{r^3}\right)\) is

Let \(G\) be a finite group. Then \(G\) is necessarily a cyclic group if the order of \(G\) is