A card is picked up at random from 52 playing cards. Given that the picked card is a queen, then the probability of this card to be a card of spade is:

The programming problem
Max Z = 2x + 3y subject to the conditions \(0 \leq x \leq 3,0 \leq y \leq 4\) is:

\(\int \frac{e^{7 \log _e x}-e^{6 \log _e x}}{e^{4 \log _e x}-e^{3 \log _e x}} d x\) is equal to:
(Here, c is an arbitrary constant)

If the system of equation
\(x-y+z=4\)
\(x-2 y-2 z=9\)
\(2 x+y+\lambda z=1\)
has a unique solution, then

The corner points of the bounded feasible region determined by the system of linear inequalities are \((0,0),(2,4),(0,5)\) and \((4,0)\). If the maximum value of \(Z=a x+b y\), where \(a, b>0\) occurs at both \((2,4)\) and \((4,0)\), then

The correct arrangement of electromagnetic spectrum in decreasing order of wavelength is :

Which of the following is a correct statement?

If \(|\vec{a}|=3\) and \(|\vec{b}|=4\), then a value of \(\lambda\) for which \(\vec{a}+\lambda \vec{b}\) and \(\vec{a}-\lambda \vec{b}\) are perpendicular is :

Answer the question on basis of passage given below:
Organic compounds containing carbon -oxygen double bonds ( \(C = O\) ) are called carbonyl compounds. These are highly polar molecules. Hence, their boiling points are higher than hydrocarbons and ethers. Aldehydes can be prepared from dehydrogenation or oxidation of alcohols and by reduction of acylhalides. Ketones are prepared by oxidation of secondary alcohols or by hydration of alkynes etc.
Aldehydes and ketones undergo nucleophilic addition reaction with the number of nucleophiles such as HCN, NaHSO3 ammonia derivatives. Carboxylic acids are prepared by the oxidation of primary alcohols, aldehydes and alkenes, by hydrolysis of nitriles. Carboxylic acids are more acidic than alcohols and phenols.

Let \(A\) be a matrix such that \(A=\left[\begin{array}{cc}1 & 2 \\ -2 & 3\end{array}\right]\) Then which of the following are TRUE?
(A) \(A\) is a non-singular matrix
(B) \(A^T=A\)
(C) \(A\) is not an invertible matrix
(D) \(A\) is not a skew-symmetric matrix
Choose the correct answer from the options given below :

A solution of \(\text{AgSO}_4\) is electrolysed for 30 minutes with a current of 5 amperes. What is the mass of silver deposited? (Given At. Mass of Ag = 108 g/mol)

Three identical polaroid sheets \(P_1, P_2, P_3\) are oriented so that pass axis of \(P_2\) and \(P_3\) are inclined to \(P_1\) at 60° and 90° respectively. A monochromatic source of intensity \(I_0\) is used to pass through \(P_1, P_2, P_3\). Intensities after passing through \(P_1, P_2, P_3\) will be respectively :
(A) \(I_0, \frac{I_0}{2}, \frac{I_0}{8}\)
(B) \(\frac{I_0}{2}, \frac{I_0}{8}, \frac{I_0}{32}\)
(C) \(\frac{I_0}{2}, \frac{I_0}{8}, \frac{3 I_0}{32}\)
(D) \(I_0, \frac{I_0}{2}\), zero
Choose the correct answer from the options given below :

The critical angle for light ray going from medium-1 to medium-2 is \(i_c\). What will be the speed of light in medium-2, if its value in medium-1 is \(u\) ?