List of top Questions asked in AP ECET BSc Mathematics- 2026

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}