List of top Mathematics Questions asked in AP ECET BSc Mathematics

The radius of the sphere whose centre is \((4,4,-2)\) and which passes through origin is

If a plane passes through a fixed point \((a,b,c)\) and cuts the axes in \(A,B,C\), then the locus of the centre of the sphere \(OABC\) is

The equation of the sphere passing through \((1,0,0),(0,1,0),(0,0,1)\) and has its centre on the plane \(x+y+z=6\) is

The angle of intersection of the two spheres \(x^2+y^2+z^2+6y+2z+8=0\) and \(x^2+y^2+z^2+6x+8y+4z+20=0\) is

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