If \(2 x^2-5 x y+2 y^2=0\) represents two sides of a triangle whose centroid is \((1,1)\), then the equation of the third side is

The substitution \(\frac{d y}{d x}=z\), reduces the differential equation \(\frac{d^2 y}{d x^2}-\frac{d y}{d x}=0\) to a differential equation whose solution is \(\mathrm{z}=\)

The distance between two parallel planes \(a x+b y+c z+d_1=0\), \(a x+b y+c z+d_2=0\) is given by \(\frac{\left|d_1-d_2\right|}{\sqrt{a^2+b^2+c^2}}\).
If the plane \(2 x-y+2 z+3=0\) has the distances \(\frac{1}{3}\) and \(\frac{2}{3}\) units from the planes \(4 x-2 y+4 z+\lambda=0\) and \(2 x-y+2 z\) \(+\mu=0\) respectively, then the maximum value of \(\lambda+\mu\) is

If \(A(3,4,5), B(4,6,3), C(-1,2,4)\) and \(D(1,0,5)\) are such that the angle between the lines \(D C\) and \(A B\) is \(\theta\), then \(\cos \theta\) is equal to

A point \(C\) with position vector \(\frac{3 \bar{a}+4 \bar{b}-5 \bar{c}}{3}\) (where \(\bar{a}, \bar{b}\) and \(\bar{c}\) are non coplanar vectors) divides the line joining \(A\) and \(B\) in the ratio \(2: 1\). If the position vector of \(A\) is \(\bar{a}-2 \bar{b}+3 \bar{c}\), then the position vector of \(B\) is

If the roots of the equation \(3 x^2+4 k x+3=0\) are non-real, then \(\mathrm{k}\) lies in the interval

One card is drawn at random from a well shuffled pack of 52 cards. The probability that the card drawn is a face card (Jack, Queen and King only) is

Which halogen can be oxidised by concentrated nitric acid?

Consider the following reaction
\(A \longrightarrow\) Products
This reaction is completed in \(100 \mathrm{~min}\). The rate constant of this reaction at \(t_1=10\) \(\mathrm{min}\), is \(10^{-2} \mathrm{~min}^{-1}\). What is the rate constant \(\left(\right.\) in \(\min ^{-1}\) ) at \(t_2=20 \mathrm{~min} ?\)

Observe the following statements :
a. The thermal stability of hydrides of group 16 elements follow the order :
\(\mathrm{H}_2 \mathrm{O}>\mathrm{H}_2 \mathrm{~S}>\mathrm{H}_2 \mathrm{Se}>\mathrm{H}_2 \mathrm{Te}\)
b. Acidic nature of hydrides of group 16 elements follow the order :
\(\mathrm{H}_2 \mathrm{O}>\mathrm{H}_2 \mathrm{~S}>\mathrm{H}_2 \mathrm{Se}>\mathrm{H}_2 \mathrm{Te}\)
c. The reducing nature of \(\mathrm{H}_2 \mathrm{~S}, \mathrm{H}_2 \mathrm{Se}\) and \(\mathrm{H}_2\) Te follow the order :
\(\mathrm{H}_2 \mathrm{~S} < \mathrm{H}_2 \mathrm{Se} < \mathrm{H}_2 \mathrm{Te}\)
The correct statement are:

The pressure and density of a given mass of a diatomic gas \(\left(\gamma=\frac{7}{5}\right)\) change adiabatically from \((P, d)\) to \(\left(P^{\prime}, d^{\prime}\right)\). If \(\frac{d^{\prime}}{d}=32\), then \(\frac{P^{\prime}}{P}\) is ( \(\gamma=\) ratio of specific heats \()\)

Assertion (A) Finely divided charcoal can act as an adsorbent.
Reason (R) Finely divided material has small surface area.