List of top Mathematics Questions asked in AP ECET BSc Mathematics

The radius of the sphere $x^{2} + y^{2} + z^{2} + 2x - 4y + 6z + 1 = 0$ is}

If the plane $lx + my + nz = p$ touches the sphere $x^{2} + y^{2} + z^{2} = a^{2}$ then}

The angle between the tangent plane to the sphere $x^{2} + y^{2} + z^{2} = 9$ at the point (2,1,2) and the XY - plane is}

The distance between the point (1,2,3) and the sphere $x^{2} + y^{2} + z^{2} = 9$ is}

The plane XOZ divides the line joining of (1,-1,5) and (2,3,4) in the ratio $\lambda : 1$ then the value of $\lambda = $

If $r$ is the position vector of any point on a closed surface S that encloses the volume V then $\iint_{S}(\overline{r} \cdot ds)$ is equal to}

If $\overline{r}(t) = ti - t^{2}j + (t - 1)k$ and $\overline{s}(t) = 2t^{2}i + 6tk$ then the value of $\int_{0}^{2}\overline{r} \cdot \overline{s} dt$ is}

Gauss divergence theorem states the relation between

If the surface $mx^{2} - 2nyz = (m + 4)x$ is orthogonal to the surface $4x^{2}y + z^{3} = 4$ at the point (1, -1, 2), then the values m and n will be}

Let $u = x + y + z, v = x^{2} + y^{2} + z^{2}, w = yz + zx + xy$. Then the vectors $\nabla u, \nabla v, \nabla w$ are}

Let $F = (3xy)i + (2y^{2})j$. The value of the line integral $\int_{C}F \cdot dr = _. $ where C is the arc of the parabola $y = 2x^{2}$ from (0,0) to (1,2).

Let $F = (2xy + z^{3})i + x^{2}j + 3xz^{2}k$. The work done in moving a particle in this field from (1, -2, 1) to (3, 1, 4) is}

If $\overline{r} = xi + yj + zk$ and $r = |\overline{r}| \neq 0$ then div. ($r^{n}\overline{r}$) =}

If C is the rectangle bounded by the lines $x = 0, x = a, y = 0, y = b$, then the value of $\int_{C}(x^{2} + y^{2})dx - 2xy dy$ is}

The vector field $\vec{V} = e^{x}\sin y~i + e^{x}\cos y~j$ is}

If $\overline{a}$ is constant vector then $\nabla \times (\overline{a} \times \overline{r}) = _?$

The velocity field on an incompressible flow is given by $\overline{v} = (a_1x + a_2y + a_3z)i + (b_1x + b_2y + b_3z)j + (c_1x + c_2y + c_3z)k$ where $a_1 = 2, c_3 = -4$ then the value of $b_2 = _$

Find the directional derivative of $f = xyz$ at the point $(1,-1,-2)$ in the direction of the vector $2i-2j+k$ is

If $f$ and $F$ are scalar and vector functions respectively, then which of the following is Not Correct?

For a vector $\overline{A}$, which of the following statement is NOT TRUE?

The velocity vector is given as $\overline{V} = 5xyi + 2y^{2}j + 3yz^{2}k$. The divergence of this vector at (1,1,1) is}

If $\phi = 2x^{3}y^{2}z^{4}$ then $\nabla^{2}\phi = $

Consider the group homomorphism $f: (Z, +) \to (G = \{i^n : n \in Z\}, \cdot)$ defined by $f(n) = i^n, \forall n \in Z$. Then, $Ker f = $

Choose the WRONG statement

The intersection of the subgroups 2Z, 3Z and 5Z, i.e., $2Z \cap 3Z \cap 5Z$ of (Z, +) is