COMEDK 2024 Morning Shift

The boiling point of a \(4 \%\) aqueous solution of a non-volatile solute \(\mathrm{P}\) is equal to the boiling point of \(\mathrm{X} \%\) solution of another non-volatile solute \(\mathrm{Q}\).
The relation between their Molar masses is $...

\(\mathrm{K}_{\mathrm{H}}\) for \(\mathrm{O}_2\) at \(293 \mathrm{~K}\) is \(34.86 \mathrm{~kbar}\). What should be the partial pressure of \(\mathrm{O}_2\) gas so that it has a solubility of \(0.08 \mathrm{~g} / \mathrm{L}\) in water at $$...

What is the amount of ice that separates out on cooling a solution containing \(60 \mathrm{~g}\) of Ethylene glycol in \(250 \mathrm{~g}\) of water to \(-9.3^{\circ} \mathrm{C}\) ? \(\mathrm{K}_{\mathrm{f}}\) of $$\mathrm{H}_2 \mathrm{O}=1....

Above figure represents Vapour pressure versus Temperature graphs of 2 pure volatile liquids and a solution formed by the 2 liquids.
(i) Which curve represents the solution?
(ii) Which curve represents the liquid with the strongest intermo...

An inorganic salt comprises of atoms of elements \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\). If the oxidation numbers of A, B and \(\mathrm{C}\) are \(+3,+6\) and \(-\)2 respectively, what is the possible formula of the compound?

Choose the group of ions / molecules in which none of the species undergo Disproportionation reaction.

A given mass of a hydrocarbon on complete combustion produced \(176 \mathrm{~g}\) of \(\mathrm{CO}_2\) and \(90 \mathrm{~g}\) of \(\mathrm{H}_2 \mathrm{O}\). What is the Molecular formula of the compound?

The standard enthalpy of formation of \(\mathrm{CH}_4\), the standard enthalpy of sublimation of Carbon and the bond dissociation enthalpy of Hydrogen gas are \(-74.8,+719.6\) and \(436 \mathrm{~kJ} / \mathrm{mol}\) respectively. What is th...

If the enthalpy of formation of a diatomic molecule \(\mathrm{AB}\) is \(-400 \mathrm{~kJ} / \mathrm{mol}\) and the bond dissociation energies of \(\mathrm{A}_2\) and \(\mathrm{B}_2\) and \(\mathrm{AB}\) are in the ratio \(2: 1: 2\), what i...

Given: \(\Delta \mathrm{G}^0{ }_{\mathrm{f}}\) of \(\mathrm{C}_2 \mathrm{H}_2\) is \(2.09 \times 10^5 \mathrm{~J} / \mathrm{mol}\) and \(\Delta \mathrm{G}_{\mathrm{f}}^0\) of \(\mathrm{C}_6 \mathrm{H}_6\) is $$1.24 \times 10^5 \mathrm{~J} /...

\(\text { The point on the curve } x^2=x y \text { which is closest to }(0,5) \text { is }\)

For a given curve \(y=2 x-x^2\), when \(x\) increases at the rate of 3 units/sec, then how does the slope of the curve change?

The most economical proportion of the height of a covered box of fixed volume whose base is a rectangle with one side three times as long as the other, is

If \(f(x)=2 x^3+9 x^2+\lambda x+20\) is a decreasing function of \(x\) in the largest possible interval \((-2,-1)\), then \(\lambda\) is equal to

The side of an equilateral triangle expands at the rate of \(\sqrt{3} \mathrm{~cm} / \mathrm{sec}\). When the side is \(12 \mathrm{~cm}\), the rate of increase of its area is

The coefficient of the third term in the expansion of \(\left(x^2-\frac{1}{4}\right)^n\), when expanded in the descending power of \(x\) is 31, then \(n\) is

The area (in sq units) of the minor segment bounded by the circle \(x^2+y^2=a^2\) and the line \(x=\frac{a}{\sqrt{2}}\) is

The equation of a circle passing through the origin is \(x^2+y^2-6 x+2 y=0\). The equation of one of its diameter is

\(\text { The modulus of the following complex number } \frac{1+i}{1-i}-\frac{1-i}{1+i} \text { is }\)

\(\int_\limits{-1}^1 \frac{d}{d x}\left(\tan ^{-1} \frac{1}{x}\right) d x \text { is }\)

The particular solution of \(\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0\), when \(x=0, y=\frac{1}{2}\) is

The particular solution of the differential equation \(\cos x \frac{d y}{d x}+y=\sin x\) at \(y(0)=1\)

\(\text { If } y=\log _e\left(\frac{x^2}{e^2}\right) \text {, then } \frac{d^2 y}{d x^2} \text { is equal to }\)

\(\text { If } y=\tan ^{-1}\left(\frac{3-2 x}{1+6 x}\right) \text { then } \frac{d y}{d x} \text { is }\)

If \(f(x)=f^{\prime}(x)\) and \(f(1)=2\), then \(f(3)\) is

\(\text { If } \sin y=x(\cos (a+y)) \text {, then find } \frac{d y}{d x} \text { when } x=0\)

The equation of an ellipse, whose focus is \((1,0)\), directrix is \(x=4\) and whose eccentricity is a root of the quadratic equation \(2 x^2-3 x+1=0\), is

Let \(f: R \rightarrow R\) be a function defined by \(f=\frac{e^{|x|}-e^{-x}}{e^x+e^{-x}}\) then

Which of the following is not a homogenous function of \(x\) and \(y\)

\(\text { The value of } \int \frac{1}{x+\sqrt{x-1}} d x \text { is }\)

If \(\int \frac{1}{\sqrt{\sin ^3 x \cos x}} d x=\frac{k}{\sqrt{\tan x}}+c\) then the value of \(k\) is

\(\int \sqrt{x^2-4 x+2} d x=\)

\(\int \frac{x}{x^4-16} d x=\)

Evaluate : \(\cos ^{-1}\left[\cos \left(-680^{\circ}\right)\right]+\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]-\cos ^{-1}\left(\sin 270^{\circ}\right)\)

\(\text { The value of } \sin ^{-1}\left[\cot \left(\frac{1}{2} \tan ^{-1} \frac{1}{\sqrt{3}}+\cos ^{-1} \frac{\sqrt{12}}{4}+\sin ^{-1} \frac{1}{\sqrt{2}}\right)\right]\) is

\(\lim _\limits{x \rightarrow 0} \frac{\sqrt{a+x}-\sqrt{a}}{x \sqrt{a(a+x)}}\) equals to

$$ \text { If } f(x)=\left\{\begin{array}{cc} \frac{1-\sin x}{(\pi-2 x)^2} & , \quad \text { if } x \neq \frac{\pi}{2} \\ \lambda, & \text { if } x=\frac{\pi}{2} \end{array}\right. $$
Then \(f(x)\) will be continues function at $$x=\frac{\p...

\(\lim _\limits{x \rightarrow 0}\left(\frac{\sin a x}{\sin b x}\right)^k \text { equals }\)

The minimum value of \(Z=150 x+200 y\) for the given constraints
$$\begin{aligned} & 3 x+5 y \geq 30 \\ & x+y \geq 8 ; x \geq 0, y \geq 0 \text { is } \end{aligned}$$

$$ \text { If } x, y, z \text { are non zero real numbers, then inverse of matrix } A=\left[\begin{array}{lll} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{array}\right] \text { is } $$

$$ \text { If the matrix } A=\left(\begin{array}{cc} 1 & -1 \\ -1 & 1 \end{array}\right) \text { then } A^{n+1}= $$

If $$A=\left[\begin{array}{ccc}-1 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right]$$ then the inverse of \((A I)^t\) (where \(\mathrm{I}\) is an identity matrix) is

If $$ \left[\begin{array}{lll} 1 & x & 1 \end{array}\right]\left[\begin{array}{ccc} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{array}\right]\left[\begin{array}{l} 1 \\ 2 \\ x \end{array}\right]=[0] $$ then x is equal to

$$ \text { If } P=\left[\begin{array}{lll} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{array}\right] \text { is the adjoint of a } 3 \times 3 \text { matrix } A \text { and }|A|=4 \text { then } \alpha \text { is equal to } $$

\(\text { The area (in sq units) enclosed by the parabola } y^2=8 x \text {, its latus-rectum and the } x \text {-axis is }\)

If \(\left[{ }^{n+1} C_{r+1}\right]:\left[{ }^n C_r\right]:\left[{ }^{n-1} C_{r-1}\right]=11: 6: 3\) then \(n r=\)

In how many ways can the word "CHRISTMAS" be arranged so that the letters '\(\mathrm{C}\)' and '\(\mathrm{M}\)' are never adjacent?

If the events A and B are mutually exclusive events such that \(P(A)=\frac{1}{3}(3 x+1)\) and \(P(B)=\frac{1}{4}(1-x)\) then the possible values of $x$ lies in the interval

A random variable X with probability distribution is given below

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An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white it is not replaced into the urn. Otherwise it is replaced along with another ball of the same colour. The process is repeated. The probability that the thi...