MCQ
The solution of the differential equation ${\cos ^2}x\frac{{{d^2}y}}{{d{x^2}}} = 1$ is
- A$y = \log \cos x + cx$
- B$y = \log \sec x + {c_1}x + {c_2}$
- C$y = \log \sec x - {c_1}x + {c_2}$
- ✓Both $(b)$ and $(c)$
On integrating, we get $\frac{{dy}}{{dx}} = \tan x \pm {c_1}$
Again integrating, we get $y = \log \sec x \pm {c_1}x \pm {c_2}$.
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$x-2 y=1, x-y+k z=-2, k y+4 z=6, k \in R$
consider the following statements :
$(A)$ The system has unique solution if $k \neq 2$, $k \neq-2$
$(B)$ The system has unique solution if $k =-2$.
$(C)$ The system has unique solution if $k =2$.
$(D)$ The system has no-solution if $k =2$.
$(E)$ The system has infinite number of solutions if $k \neq-2$
Which of the following statements are correct?
$\int\limits_{ - \,1}^x {\,\left( {8{t^2} + \frac{{28}}{3}t + 4} \right)\,dt} $ $=$ $\frac{{\left( {{\textstyle{3 \over 2}}} \right)x + 1}}{{{{\log }_{(x + 1)}}\sqrt {x + 1} }}$ , is