If A= [ c -1 2 3 ], B= [ lll 3 & 1 & -2 ], find B^ A^

If A is a square matrix such that $A^2 = A$, then write the value of $7A − (I + A)^3,$ where I is the identity matrix.

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Evaluate the following:

$\int \frac{\log (\log x)}{x} d x$

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Let $C$ denote the set of all complex numbers. A function $f: C \rightarrow C$ is defined by $f(x)=x^3$. Write $f^{-1}(1)$.

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Find the principal solutions of the following equations :

$\cot \theta=\sqrt{3}$

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Evaluate the following integrals:
$\int\frac{\log\text{x}}{\text{x}}\text{dx}$

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Evaluate the following:
$\sin^{-1}\Big(\sin\frac{7\pi}{6}\Big)$

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In $\triangle ABC$, if $A =60^{\circ}, b =3$ and $c =8$ then find $a$. Also find the circumradius of the triangle.

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Find the values of x for which the following functions are strictly increasing:

$f(x)=x^3-6 x^2-36 x+7$

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A random variable X has the following probability distribution:

Values of X:	-2	-1	0	1	2	3
P(X)	0.1	k	0.2	2k	0.3	k

Find the value of k.

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$\int \frac{\sin (x-a)}{\cos (x+ b )} d x$

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Answer