For \(x \in(0,1)\), the derivative of \(\sin ^{-1} x\) with respect to \(\cos ^{-1} \sqrt{1-x^2}\) is:

The solution of the differential equation \(2 x \frac{d y}{d x}-y=3\) represents:

Which of the following statement(s) is/are TRUE?
(A) Skew symmetric matrix of even order is always symmetric
(B) Skew symmetric matrix of odd order is non-singular
(C) Skew symmetric matrix of odd order is singular
(D) Skew symmetric matrix is always square matrix
Choose the correct answer from the options given below:

Match List-I with List-II

List-I ( Matrix A )	List-II ( Determinant of adj A )
(A) \(\left[\begin{array}{cc}2 & 1 \\0 & -1\end{array}\right]\)	(I) 6
(B) \(\left[\begin{array}{cc}0 & 1 \\4 & -1\end{array}\right]\)	(II) 5
(C) \(\left[\begin{array}{cc}1 & 2 \\-3 & -1\end{array}\right]\)	(III) \(-4\)
(D) \(\left[\begin{array}{cc}4 & -2 \\3 & 0\end{array}\right]\)	(IV) \(-2\)

Choose the correct answer from the options given below :

The point on the curve \(y=\cos x-1, x \in\left[\frac{\pi}{2}, \frac{3 \pi}{2}\right]\) at which tangent is parallel to the x-axis is:

If \(y=x \sin y\), then \(\frac{d y}{d x}\) is:

If \(A\) and \(B\) are independent events, then which of the following statements are TRUE?
(A) \(P(A \cap B)=P(A) \cdot P(B)\)
(B) \(P(A \cap B)=P(A)-P(B)\)
(C) \(P(A \cup B)=P(A)+P(B)-P(A) \cdot P(B)\)
(D) \(P(A \cap B)=P(A) \cdot P(B \mid A)\)
Choose the correct answer from the options given below :

Who gave the 'chromosomal theory of inheritance'?

Match List-l with List-ll

List-I(Reaction)	List-II(Preparation)
(A) Kolbe's Reaction	(I) Salicylaldehyde
(B) Reimer-Tiemann Reaction	(II) Salicylic acid
(C) Williamson synthesis	(III) Ethyl methyl ether
(D) Cumene Process	(IV) Phenol

Choose the correct answer from the options given below:

Which of the following statements are correct ?
A. The saturation current is constant with collector plate potential for different frequencies of incident radiation.
B. The saturation current is different with collector plate potential for different frequencies of incident radiation.
C. The saturation current is different with collector plate potential for different intensity of incident radiation.
D. The saturation current is constant with collector plate potential for different intensity of incident radiation.
E. Below threshold frequency no photo electrons are emitted.
Choose the correct answer from the options given below :

For the system of equations \(A X=B\), which of the following is correct?

The peak value of current in an ideal inductor of \((2/\pi) \text{ H}\) inductance connected to a 200 V, 50 Hz ac supply will be

The probability of a man hitting a target is \(\frac{1}{2}\).
How many times must he fire so that the probability of hitting the target at least once is more than \(90 \%\) ?