Which of the given values of \(x\) and \(y\) make the following pair of matrices equal?
\(\left[\begin{array}{cc}2 x-1 & 4 \\ y-1 & 3+2 x\end{array}\right]\) and \(\left[\begin{array}{cc}0 & y-2 \\ 5 & 4\end{array}\right]\)

A measure of an average yearly growth of an investment over a certain time period when returns are reinvested is

The differentiation of \(\frac{x^3}{1-x^3}\) w.r.t. \(x^3\) is:

If the matrix \(A=\left[\begin{array}{cc}2-x & 3 \\ 2 & 1-x\end{array}\right]\) is singular, then value(s) of \(x\) are :

If \(x \sqrt{1+y}+y \sqrt{1+x}=0\), where \(|x|<1,|y|<1\) and \(x \neq y\), then

The interval in which the function \(f(x)=2 x^3+3 x^2-12 x+1\) is strictly increasing, is

A matrix which is symmetric as well as skew symmetric is:

A resistor develops 800 J of thermal energy in 20 s on applying a potential difference of 20 V. Its resistance is

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.
Which one of the followings cannot cause cancer:

In the depression of freezing point experiment, it is found that :
(A) The vapour pressure of the solution is less than that of the pure solvent.
(B) The vapour pressure of solution is more than that of the pure solvent.
(C) Only the solute molecules solidify at the freezing point.
(D) Only the solvent molecules solidify at the freezing point.
Choose the correct answer from the options given below :

Which of the following will not give iodoform reaction?

A plane electromagnetic wave of frequency 50 MHz travels in free space in the X- direction. At a particular point in space and time, the magnetic field is 0.003 G in the Z-direction. The magnitude and direction of the electric field is

Match List-l with List-ll
Let \(A\) be any invertible square matrix. Then

List-l	List-ll
(A) \(A-A^T\)	(I) \(|A| A^{-1}\)
(B) \(A A^T\)	(II) Skew-symmetric
(C) \(\operatorname{det}\left(A^{-1}\right)\)	(III) Symmetric
(D) \(\operatorname{adj} A\)	(IV) \([\operatorname{det}(A)]^{-1}\)

Choose the correct answer from the options given below :