List of top Questions asked in AP ECET BSc Mathematics

The equation of the plane passing through the midpoint of the line joining the points (1,2,3) and (3,4,5) and perpendicular to it is

Consider the planes: $P_{1}: 3x + 15y + 21z = 9$, $P_{2}: x - 3y - z = 5$, $P_{3}: 2x + 10y + 14z = 5$. Which of the following is TRUE?

The direction ratios of the line $x - y + z - 5 = 0 = x - 3y - 6$ are

If the line $\frac{x-2}{3} = \frac{y+1}{2} = \frac{z-1}{-1}$ intersect the curve $xy = c^{2}$ in XY-plane than $c = $

Radius of the circle $x^{2} + y^{2} + z^{2} = 169, x - 2y + 2z = 15$ is}

A non-empty sub-set of real numbers which is bounded below has

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 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}

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

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 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}

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

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

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

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 $b_2 = _$

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}