Using mathematical induction, the value of $1^{3}+2^{3}+ ....n^{3}$ is :
1). $\frac{n^{2}(n^{2}+1)}{4}$
2). $\frac{n(n+1)(2n+1)}{6}$
3). $\frac{n^{2}(n+1)^{2}}{4}$
4). $\frac{n(n+2)}{4}$
If set A has m elements and set B has n elements, then the possible number of distinct functions from A to B is:
1). $n^{m}$
2). mn
3). $2^{mn}$
4). $m^{n}$
The greatest common divisor of three integers 105, 140 and 350 is:
1). 5
2). 70
3). 15
4). 35
If a, b and c are any three complex numbers such that $a^{2}+b^{2}+c^{2}=0$ and $\begin{bmatrix}b^{2}+c^{2} & ab & ca \\ab & c^{2}+a^{2} & bc \\ca & bc & a^{2}+b^{2} \end{bmatrix}=k(abc)^{2}$,
then the value of k is :
1). 4
2). -2
3). 3
4). 1
The solution of the differential equation $2ysinx(\frac{dy}{dx})=sin2x-y^{2}cosx$ with $y(\frac{\pi}{2})=1$ is :
1). $y^{2}=sinx$
2). $x^{2}=siny$
3). $y=sin^{2}x$
4). $y^{2}=1+cosx$