A line through the points \(A(3,4,1)\) and \(B(5,1,6)\) is drawn.
The coordinates of the points where the line through the points \(A \backslash \& B\) crosses the \(X Y\) plane is:

If the matrix \(\left[\begin{array}{ccc}-1 & x-y & 4 \\ 2 & 0 & 5 \\ x+y & z & 6\end{array}\right]\) is symmetric, then \(x+3 y+2 z\) is equal to

For \(x>e\),\(\int \frac{d x}{x-\sqrt{x}}\) is equal to

Match List-I with List-II

List-I	List-II
(A) The minimum value of \(f(x)=(2 x-1)^2+3\)	(I) 4
(B) The maximum value of \(f(x)=-|x+1|+4\)	(II) 10
(C) The minimum value of \(f(x)=\sin (2 x)+6\)	(III) 3
(D) The maximum value of \(f(x)=-(x-1)^2+10\)	(IV) 5

Choose the correct answer from the options given below:

Let \(f: R \rightarrow R\) be defined as \(f(x)=100 x+1\) where \(R\) is a set of real numbers, then

A problem in Mathematics is given to two students \(X\) and \(Y\) whose chances of solving it are \(\frac{1}{3}\) and \(\frac{1}{4}\) respectively. The probability that only \(X\) solves the problem, is:

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

The desirable properties of core of a transformer are

Which one of the followings cells are attacked by HIV?

If \(A=\left[\begin{array}{ccc}a & 4 & -5 \\ d & b & -6 \\ 5 & e & c\end{array}\right]\) is a skew symmetric matrix, then value of \(a+b+c+d+e\) is equal to

Arrange the following alkyl halides in increasing order of boiling points
(A) 1-Iodobutane
(B) 1-Bromobutane
(C) 1-Chlorobutane
(D) Butane
Choose the correct answer from the options given below:

Read the passage carefully and answer the Questions
Molar conductivity \(\left( \Lambda _m\right)\) of a solution at a given concentration (c) is the conductance of volume, V of solution, containing one mole of electrolyte kept between the two electrodes with area of cross-section A and at a distance of unit length. It increases with the decrease in concentration and when the concentration approaches zero, the molar conductivity is called limiting molar conductivity \(\Lambda_m^0\). For a strong electrolyte, \(\left( \Lambda _m\right)\) increases linearly with dilution and is given by \(\Lambda_m=\Lambda_m^0-A c^{1 / 2}\).The value of the constant A for a given solvent depends on the type of electrolyte along with temperature. According to Kohlrausch law, the value of \(\Lambda_m^0\) for an electrolyte is \(\Lambda_m^0=\nu_{+} \lambda_{+}^0+\nu_{-} \lambda_{-}^0\), where \(\nu_{+}\)and \(\nu_{-}\) where v₊ and v_- are the number of cations and anions, respectively, per molecule of the electrolyte and \(\lambda_{+}^0\) and \(\lambda_{-}^0\) are limiting molar conductivities of cation and anion, respectively. Kohlrausch law
finds many applications, like determining the solubility of a sparingly soluble salt, determining the degree of dissociation \(\left(\Lambda_m / \Lambda_m^0\right)\), and the dissociation constant of a weak electrolyte.
Which one of the following has a different value of constant A in water?

The electric field of a plane electromagnetic wave in a medium is given by
\( E = 100 \sin(300z - 6 \times 10^{10}t) \text{ V/m} \).
The velocity of the electromagnetic wave in this medium will be: