If \(A\) is a non-zero square matrix of order \(n\) with \(\operatorname{det}(I+A) \neq 0\) and \(A^3=O\), where \(I, O\) are unit and null matrices of order \(n \times n\) respectively, then \((I+A)^{-1}\) is equal to

\(\int_{-\pi / 4}^{\pi / 3}\left|\tan \left(x-\frac{\pi}{6}\right)\right| d x=\)

Let ' \(\mathrm{O}\) ' be the origin, \(\mathrm{A}\) and \(\mathrm{B}\) be two points with position vectors \(-3 \hat{i}-3 \hat{j}+4 \hat{k}\) and \(4 \hat{i}-4 \hat{j}-3 \hat{k}\) respectively. Let \(P\) be a point such that the line drawn through \(P\) parallel to \(\overrightarrow{\mathrm{OB}}\) meets \(\mathrm{OA}\) in \(\mathrm{L}\) and another line through \(\mathrm{P}\) parallel to \(\overrightarrow{\mathrm{OA}}\) meets \(\mathrm{OB}\) in \(\mathrm{M}\). If \(\mathrm{L}\) divides \(\mathrm{OA}\) in the ratio \(2: 3\) and \(\mathrm{M}\) divides \(\mathrm{OB}\) in the ratio \(3: 2\), then the distance from 0 to \(\mathrm{P}\) is

If \(y=a \sin x+(5+2 x) \cos x\), then \(y^{\prime \prime}+y=\)

Let \(A\) and \(B\) be two events with \(P(A)=\frac{1}{7}\), \(P\left(\frac{A}{B}\right)=\frac{2}{3}\) and \(P(B)=\frac{2}{7}\). Then, the value \(P\left(\frac{B}{A}\right)\) is

The equation of a circle with centre \((5,4)\) and touch the \(Y\)-axis is

The number of positive divisors of 1080 is

If \(\frac{3 x}{(x-a)(x-b)}=\frac{2}{x-a}+\frac{1}{x-b}\), then \(a: b\) is equal to

If \(a, b, c\) and \(d \in R\) such that \(a^2+b^2=4\) and \(c^2+d^2=2\) and if \((a+i b)^2=(c+i d)^2(x+i y)\), then \(x^2+y^2\) is equal to

The cartesian form of the polar equation \(\theta=\tan ^{-1} 2\) is

If the sum of any two roots of the equation $x^3+p{x}^2+qx+r=0$ is zero, then

Maximum number of electrons possible with spin quantum number \(+\frac{1}{2}\) with principal quantum number \(\mathrm{n}=4\) in an atom is

Zinc oxide (white) is heated to high temperature for some time. Observe the following statement regarding above process
I. Zinc oxide colour changes to pale yellow
II. The type of defect formed is 'metal deficiency'
III. Some \(\mathrm{Zn}^{2+}\) and \(e^{-}\)are present in interstitial places
The correct statements are