COMEDK 2025 Afternoon Shift

Lead storage battery contains $4.25 \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4$ which has a density of $1.24 \mathrm{~g} / \mathrm{ml}$. Calculate the molality of aqueous solution of $\mathrm{H}_2 \mathrm{SO}_4$.

When $0.4 \mathrm{~g} \mathrm{CH}_3 \mathrm{COOH}$ is added to 40 g of Benzene to form a solution, the freezing point is depressed by $0.45^{\circ} \mathrm{C}$. If Acetic acid undergoes dimerisation in Benzene ( $\mathrm{K}_{\mathrm{f}}=5.1...

A dilute solution of $\mathrm{K}_2 \mathrm{HgI}_4$ reagent is $95 \%$ ionised. What would be the approximate value of its van't Hoff factor?

An aqueous solution which contains $42 \%$ by weight $(\mathrm{w} / \mathrm{W})$ of a volatile liquid "A" of molar mass of $140 \mathrm{~g} / \mathrm{mol}$, has a vapour pressure of 2141.4 mm of Hg at $37^{\circ} \mathrm{C}$. What is the va...

The first ionisation enthalpy of Al in $\mathrm{kJ} \mathrm{mol}^{-1}$ is:
[Given the first ionisation enthalpy of $\mathrm{Na}, \mathrm{Mg}$ and Si in $\mathrm{kJ} \mathrm{mol}^{-1}$ are 497,738 and 787 respectively]

The best method for the separation of $o$-nitrophenol and $p$-nitrophenol from their mixture is :

Given below are 2 statements: one Assertion and the other Reason. Which one of the following options is correct?
Assertion : Sulphur dioxide and Hydrogen peroxide can act as both oxidising and reducing agents but Nitric acid can act as only...

For the reaction $\mathrm{A}_2+\mathrm{B}_2 \cdots \cdots>2 \mathrm{AB}, \Delta \mathrm{H}_{\mathrm{f}}=-400 \mathrm{~kJ} / \mathrm{mol}$. The bond dissociation enthalpies of $\mathrm{A}_2$, $\mathrm{B}_2$ and AB are in the ratio $1: 0.75: ...

The Enthalpy of combustion of 1.0 mole of a reactive metal X at $27^{\circ} \mathrm{C}$ and 1.0 bar pressure to form a solid oxide ( XO ) is $-601.83 \mathrm{~kJ} / \mathrm{mol}$. The Internal energy change for this reaction is ___________ ...

For a hypothetical chemical reaction $\mathrm{A}_2+3 \mathrm{~B}_2+$ Heat $\cdots\rightarrow 2 \mathrm{AB}_3$, which one of the following combinations of state variables would support the spontaneity of the reaction at a particular temperat...

Let $A$ and $G$ denote the arithmetic mean and geometric mean of positive real numbers $5^x$ and $5^{1-x}$. Then the minimum value of the expression $5^x+5^{1-x}$ where $x \in R$ is

The curve $4 y=3 x^4-2 x^2$ attains ----------- at the points $x=-\frac{1}{\sqrt{3}}$ and $x=\frac{1}{\sqrt{3}}$

In the interval $(0,1)$ the function $f(x)=x^2-x+1$ is

$x=a(\theta+\sin \theta)$ and $y=a(1-\cos \theta)$ represents the equation of a curve. If $\theta$ changes at a constant rate $k$ then the rate of change of the slope of the tangent to the curve at $\theta=\frac{\pi}{3}$ is

The least area of a circle circumscribing any right-angle triangle of area $\frac{9}{\pi}$ sq units is

Quadrilateral PQRS is inscribed inside a rectangle of dimensions $10 \mathrm{~cm} \times 8 \mathrm{~cm}$. The value of ' $x$ ', if the area of the quadrilateral is minimum is

The area of the region enclosed by the lines $2 x+y=10, y=1, y=5$ and the $y$-axis is

Evaluate the value of $(1.02)^8$ using binomial theorem up to two decimal places.

The complex number $\frac{1+7 i}{(2-i)^2}$ lies in

$\int\limits_0^{\frac{\pi}{2}} \log \left(\frac{5+4 \sin x}{5+4 \cos x}\right) d x=$

Solution of the differential equation $y \frac{d y}{d x}+x=0$ represents a family of

The degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{4}}=\left(\frac{d^2 y}{d x^2}\right)^{\frac{1}{3}}$

Integrating factor of the differential equation $\frac{d y}{d x}+y=\frac{x^3+y}{x}$ is

Which of the following transformations reduce the differential equation $\frac{d z}{d x}+\frac{z}{x} \log z=\frac{z}{x^2}(\log z)^2$ into the form $\frac{d u}{d x}+P(x) u=Q(x)$

If $ 2 y=\left[\cot ^{-1}\left(\frac{\sqrt{3} \cos x+\sin x}{\cos x-\sqrt{3} \sin x}\right)\right]^2 \forall x \in\left(0, \frac{\pi}{2}\right)$ then $\frac{d y}{d x}$ is equal to :

If $y=\left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2$,
then $\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}=$

Differentiate $\log _a x$ with respect to $a^x$

The radius of the circle passes through the foci of a conic $\frac{x^2}{16}+\frac{y^2}{9}=1$ and has its centre at $(0,3)$, then the diameter of the circle is ---

The area of the region bounded by the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is

If a function $f:[2, \infty) \rightarrow R$ defined by $f(x)=x^2-4 x+5$, then the range of $f$ is

The length of the latus rectum of a conic $49 y^2-16 x^2=784$ is

$\int \frac{d x}{x \sqrt{4 x^2-9}}=$

$\int \frac{x}{(x-1)(x-2)^2} d x=a \log \left|\frac{x-1}{x-2}\right|+\frac{b}{(x-2)}+c$ then

$\int \frac{\sin x+\cos x}{\sqrt{1+2 \sin x \cos x}} d x=\varphi(x)+C$ Then $\varphi(x)=$

$\int \frac{e^{\tan ^{-1} x}}{\left(1+x^2\right)}\left(1+x+x^2\right) d x=$

Domain of the function $f(x)=\sqrt{\sin ^{-1}(2 x)+\frac{\pi}{6}}$ for real valued of $x$ is

The value of $\tan ^{-1}\left(\tan \frac{7 \pi}{6}\right)$ is

$\lim _\limits{\theta \rightarrow \frac{\pi}{2}} \frac{1-\sin \theta}{\left(\frac{\pi}{2}-\theta\right) \cos \theta}$ is equal to :

$\lim _\limits{x \rightarrow 1} \frac{(\sqrt{x}-1)(2 x-3)}{2 x^2+x-3}$ is

The function $f(x)=\left\{\begin{array}{l}\frac{|x|}{x}, \text { if } x \neq 0 \\ 0, \text { if } x=0\end{array}\right.$ is discontinuous at

The corner points of the feasible region determined by the system of linear constraints are $(0,3),(1,1)$ and $(3,0)$, If objective function is $Z=p x+q y, p, q>0$ then the condition on $p$ and $q$ so that the minimum of $Z$ occurs at $(3,0...

If $A=\frac{1}{\pi}\left[\begin{array}{cc}\sin ^{-1} \frac{1}{2} & \tan ^{-1} \frac{x}{\pi} \\ \sin ^{-1} \frac{x}{\pi} & \cot ^{-1} \sqrt{3}\end{array}\right] \quad B=\frac{1}{\pi}\left[\begin{array}{cc}-\cos ^{-1} \frac{1}{2} & \tan ^{-1}...

If $A(\operatorname{adj} A)=\left[\begin{array}{lll}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{array}\right]$, then the value of $|A|+|\operatorname{adj} A|$ is equal to :

The cofactor of the element $a_{21}$ in the expansion of $\Delta=\left|\begin{array}{ccc}1 & 4 & 4 \\ -3 & 5 & 9 \\ 2 & 1 & 2\end{array}\right|$ is

The cost of 4 kg onion, 3 kg wheat and 2 kg rice is ₹ 500 .
The cost of 1 kg onion, 2 kg wheat and 3 kg rice is ₹ 300 .
The cost of 6 kg onion, 2 kg wheat and 3 kg rice is ₹ 575 .
The above situation can be represented in matrix form as $\m...

If $A=\left[\begin{array}{ccc}0 & -1 & 2 \\ 1 & 0 & 3 \\ -2 & -3 & 0\end{array}\right]$, then $A+2 A^T=$

If ${ }^{n+2} C_8:{ }^{n-2} P_4=57: 16$, then ' $n$ ' is

On each working day of a school there are six periods. The number of ways in which five subjects are arranged if each subject is allotted at least one period and no period remains vacant is

If for two events $A$ and $B, P(A-B)=\frac{1}{5}$ and $P(A)=\frac{3}{5}$ then $P(B / A)=$

In a kabaddi league, two matches are being played between Jaipur and Delhi. It is assumed that the outcomes of the two games are independent. The probability of Jaipur winning, drawing and losing the game against Delhi are $\frac{1}{2}, \fr...