MCQ
$\int_{}^{} {{{\sin }^2}x\cos x\;dx} $ is equal to
- A$\frac{{{{\cos }^2}x}}{2} + c$
- B$\frac{{{{\sin }^2}x}}{3} + c$
- ✓$\frac{{{{\sin }^3}x}}{3} + c$
- D$ - \frac{{{{\cos }^2}x}}{2} + c$
Put $\sin x = t \Rightarrow \cos x\,dx = dt$
$\therefore \,\,\,I = \int_{}^{} {{t^2}dt} = \frac{{{t^3}}}{3} + c = \frac{{{{\sin }^3}x}}{3} + c$.
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$1.$ The number of matrices in $\Omega$ is
$(A)$ $12$ $(B)$ $6$ $(C)$ $9$ $(D)$ $3$
$2.$ The number of matrices $A$ in $\Omega$ for which the system of linear equations
$A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has a unique solution, is
$(A)$ less than $4$
$(B)$ at least $4$ but less than $7$
$(C)$ at least $7$ but less than $10$
$(D)$ at least $10$
$3.$ The number of matrices $A$ in $\Omega$ for which the system of linear equations
$A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ is inconsistent, is
$(A)$ $0$ $(B)$ more than $2$ $(C)$ $2$ $(D)$ $1$