List of top Mathematics Questions

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}

Gauss divergence theorem states the relation between

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 $\overline{r} = xi + yj + zk$ 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).

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

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

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

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

Choose the WRONG statement

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}

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 = $

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?

A noncyclic group among the following is

Consider the following statements:
A. Every finite cyclic group of order n is isomorphic to the group $(Z_n, +_n)$.
B. Every infinite cyclic group is isomorphic to the group (Z, +).
Which of the following statement is TRUE?

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

Let H be a subgroup of a group G, where $O(H) = m$ and $O(G) = n$. Then, for any $a \in G$, $O(aH) = $

The permutations $f = \begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 4 & 8 & 2 & 5 & 1 & 3 & 7 & 6 \end{pmatrix}, g = \begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 5 & 1 & 2 & 8 & 7 & 4 & 3 & 6 \end{pmatrix}$ of $S_8$ are respectively}

In the group $(R-\{-1\}, *)$ where $*$ is defined by $a*b = a+b+ab, \forall a,b \in R-\{-1\}$, inverse of the element 2 is}

Solution of $\frac{dx}{yz} = \frac{dy}{zx} = \frac{dz}{xy}$ is}

The highest power of 3 contained in 100! is