If \(A\) and \(B\) are two invertible matrices, then which of the following statements are correct?
(A) \(\left|A^{-1}\right|=|A|^{-1}\)
(B) \(\operatorname{adj} A=|A| A^{-1}\)
(C) \((A B)^{-1}=A^{-1} B^{-1}\)
(D) \((A+B)^{-1}=A^{-1}+B^{-1}\)
Choose the correct answer from the options given below:

The area (in sq. units) of the region bounded by the curve \(y=\cos x\) between \(x=-\frac{\pi}{2}, x=\frac{\pi}{2}\) and the \(x\)-axis is

The value of \(\lambda\), so that the vector \(\vec{a}=2 \hat{i}+\lambda \hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}-2 \hat{j}+3 \hat{k}\) are perpendicular to each other, is :

All positive integral powers of a symmetric matrix are:

The probability distribution of a discrete random variable x is given below:

\(x\)	\(2\)	\(3\)	\(4\)	\(5\)
\(p(x)\)	\(\frac{5}{k}\)	\(\frac{7}{k}\)	\(\frac{9}{k}\)	\(\frac{10}{k}\)

The value of \(k\) is

The solution of the differential equation \(\left(x^2+x y\right) d y=\left(x^2+y^2\right) d x\) is

The unit digit of \(12^{12}\) is :

The area of the region bounded by \(x=y^2\) and the line \(x=4\) in square units is :

The increasing order of stability is :
(A) \(\left[ Cu \left( NH _3\right)_4\right]^{2+}\)
(B) \(\left[ Cu \left( CN _4\right]^{2-}\right.\)
(C) \(\left[ Cu (e n)_2\right]^{2+}\)
(D) \(\left[ Cu \left( H _2 O \right)_4\right]^{2+}\)
Choose the correct answer from the options given below :

The particular solution of the differential equation \(x\left(1+y^2\right) d x-y\left(1+x^2\right) d y=0\), given that \(y(0)=1\) is :

'r' in exponential growth equation implies:

Read the following passage carefully and answer the given questions.
Cancerous cells just continue to divide giving rise to masses of cells called tumors. Benign tumors normally remain confined to their original location and do not spread to other parts of the body and cause little damage. The malignant tumors, on the other hand are a mass of proliferating cells called neoplastic or tumor cells. Transformation of normal cells into cancerous neoplastic cells may be induced by physical, chemical or biological agents. Ionising radiations like X-rays and gamma rays and non-ionizing radiations like UV cause cancer. Cancer-causing viruses are called oncogenic viruses which have viral oncogenes. The substances to which an immune response is produced are called allergens. The antibodies produced to these are of IgE type. Common examples of allergens are mites in dust, pollens, animal dander, etc. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs provide the sites for interaction of lymphocytes with the antigen, which then proliferate to become effector cells.
The tumors that remain confined to their original location and do not spread to other parts of the body are:

Consider the line \(\vec{r}=-2 \hat{i}+3 \hat{j}+\hat{k}+\lambda(5 \hat{i}-3 \hat{j}-\hat{k})\). Match List-I with List-II

List-I	List-II
(A) A point on the given line	(I) \(\left(\frac{5}{\sqrt{35}}, \frac{-3}{\sqrt{35}}, \frac{-1}{\sqrt{35}}\right)\)
(B) Direction ratios of the given line	(II) (2, 3, 1)
(C) Direction cosines of the given line	(III) (5, -3, -1)
(D) Direction ratios of a line perpendicular to given line	(IV) (-2, 3, 1)

Choose the correct answer from the options given below: