MCQ
$\int_0^{\pi / 8} \tan ^2(2 x) d x$ is equal to
- ✓$\frac{4-\pi}{8}$
- B$\frac{4+\pi}{8}$
- C$\frac{4-\pi}{4}$
- D$\frac{4-\pi}{2}$
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$a x+2 y=\lambda$
$3 x-2 y=\mu$Which of the following statement($s$) is(are) correct?
($A$) If $a=-3$, then the system has infinitely many solutions for all values of $\lambda$ and $\mu$
($B$) If $a \neq-3$, then the system has a unique solution for all values of $\lambda$ and $\mu$
($C$) If $\lambda+\mu=0$, then the system has infinitely many solutions for $a=-3$
($D$) If $\lambda+\mu \neq 0$, then the system has no solution for $a=-3$
where $[x]$ denotes the greatest integer less than or equal to $x$. Let $f \circ:(-1,1) \rightarrow R$ be the composite function defined by $(f \circ g)(x)=f(g(x))$. Suppose $c$ is the number of points in the interval $(-1,1)$ at which $f \circ g$ is NOT continuous, and suppose $d$ is the number of points in the interval $(-1,1)$ at which $f \circ g$ is $NOT$ differentiable. Then the value of $c+d$ is. . . . .