Which of the following functions are increasing on \(x \in\left(0, \frac{\pi}{2}\right)\) ?
(A) \(f(x)=\sin x\)
(B) \(f(x)=\cos x\)
(C) \(f(x)=\tan x\)
(D) \(f(x)=\cos 3 x\)
Choose the correct answer from the options given below :

Match List - I with List - II.

LIST - I	LIST - II
(A) \(x^x\) has a stationary point at \(x\) equal to	(I) \(e\)
(B) For \(x>0\), minimum value of \(x^x\)	(II) \(1 / e\)
(C) The greatest value of \(\left(\frac{1}{x}\right)^x\)	(III) \(e^{1 / e}\)
(D) The stationary point of \(\frac{\log x}{x}\) for \(x\), where \(x>0\), is	(IV) \(e^{-1 / e}\)

Choose the correct answer from the otions given below:

The interval in which \(f(x)=2 x^3-9 x^2+12 x+1\) is decreasing is:

The minimum value of \(\left|\begin{array}{ccc}2 & 2 & 2 \\ 2 & 2+x & 2 \\ 2 & 2 & 2+x\end{array}\right|, x \in R\) is

If \(x=a \cos \alpha+b \sin \alpha\) and \(y=a \sin \alpha-b \cos \alpha\), then \(\left(x \frac{d y}{d x}-y^2 \frac{d^2 y}{d x^2}\right)\) is equal to :

\(\text{If} A \text{ and } B \text{ are independent events with }P(A)=0.8 \text{ and } P(B)=0.4,\text{ then the value of } P(A\cup B) \text{ is: \)

During lockdown, Amit was suffering from heart problem. After proper check-up it was deducted that he has \(45\%\) chance of having heart attack, but yoga and meditation assumed to reduce the chance of heart attack by \(25\%\) and \(20\%\) respectively. He has option to choose any of the two options with equal probabilities. If Amit choose yoga to reduce the chance of heart attack, then the chance of heart attack is:During lockdown, Amit was suffering from heart problem. After proper check-up it was deducted that he has \(45\%\) chance of having heart attack, but yoga and meditation assumed to reduce the chance of heart attack by \(25\%\) and \(20 \%\) respectively. He has option to choose any of the two options with equal probabilities.
If Amit choose yoga to reduce the chance of heart attack, then the chance of heart attack is:

The equation of plane which cuts equal intercepts of unit length on the coordinate axes is:

Arrange the various ovarian events occurring during a menstrual cycle in sequence :
(A) Maturation of follicle
(B) Development of primary follicle
(C) Ovulation
(D) Transformation of graafian follicle into corpus luteum
Choose the correct answer from the options given below:

A cell of constant emf is first connected to a resistance \( R_1 \) and then connected to a resistance \( R_2 \). If power delivered in both cases is same, then the internal resistance of the cell is

The gene controlling the ABO blood groups in humans is :

Conditions for obtaining a interference pattern of light are
(A) Two waves should be coherent
(B) The distance of the screen from the slits should be small
(C) The separation between slits should be small
(D) Two coherent waves should have nearly the same amplitude
Choose the correct answer from the options given below:

Which refining method is represented by the following equations ?
\(Zr+2I_2 \rightarrow ZrI_4\)
\(ZrI_4 \rightarrow Zr+ 2I_2\)