COMEDK 2026 Afternoon Shift

A $5 \%$ solution (by mass) of cane sugar in water has a freezing point of 271 K . The freezing point of a $5 \%$ solution (by mass) of glucose in water is: [freezing point of pure water: 273.15 K ]

Identify the law which is stated as "For any solutions, the partial vapour pressure of each volatile component in the solution is directly proportional to its mole fraction".

Which of the following is an INCORRECT match?

$x$ moles of $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ oxidises 1 mole of ferrous oxalate, in acidic medium. Hence ' $x$ ' is:

In the redox reaction, taking place in acidic medium: $\mathrm{X} \mathrm{MnO}_4^{-}(\mathrm{aq})+\mathrm{YSO}_2(\mathrm{~g}) \rightarrow \mathrm{Mn}^{+2}(\mathrm{aq})+\mathrm{HSO}_4^{-}(\mathrm{aq})$, the ratio of $X: Y$ in a stoichiometri...

How many molecules of $\mathrm{CO}_2(\mathrm{~g})$ are obtained on reaction of 24 grams of methane with 4 moles of oxygen?

500 mL of an aqueous solution of glucose $\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6$ (Molar mass $180 \mathrm{gmol}^{-1}$ ) contains $6.02 \times 10^{22}$ molecules.
The concentration of the solution will be:

Identify the INCORRECT statement

For an ideal gas undergoing an isothermal change, there is $\_\_\_\_$

The standard enthalpies of formation of $\mathrm{CH}_4(\mathrm{~g}), \mathrm{CO}_2(\mathrm{~g})$ and $\mathrm{H}_2 \mathrm{O}(\mathrm{l})$ are $-74.8 \mathrm{~kJ} \mathrm{~mol}^{-1},-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $-285.8 \mathr...

The function $f(x)=e^{a x}+e^{-a x}, x \in \mathbb{R}$ and $a<0$, is strictly decreasing for all values of ' $x$ ', where

The absolute maximum and minimum values of the function $f(x)=\sin x+\sqrt{3} \cos x$ in $[0, \pi]$ are

An open hemispherical storage tank has radius 13 m . Oil flows into the tank such that the depth ' $\boldsymbol{h}$ ' of oil in the tank changes at the rate of $3 \mathrm{~m} / \mathrm{hr}$. When the depth $\boldsymbol{h}=1 \mathrm{~m}$, th...

A movie screen on a wall is $\mathbf{2 0}$ feet high and $\mathbf{1 0}$ feet above the floor. What is the maximum viewing angle $\boldsymbol{\theta}$ (in radians) that can be achieved by positioning yourself at the optimal distance from the...

If $f(x)=x^3+\frac{3}{2} x^2+3 x+3$, then $f(x)$ is

Find the area bounded by the curve $y=|2-x|$, the $x$-axis, and the lines $x=0$ and $x=5$

The area enclosed by the curve $y=-x^2$ and the line $x+y+2=0$ is

If the coefficients of $x^2$ and $x^3$ in the expansion of $(3+k x)^9$ are equal, then the value of ' $\boldsymbol{k}$ ' is

The conjugate of the multiplicative inverse of the complex number $\boldsymbol{z}=\frac{\mathbf{1}+\mathbf{7} \boldsymbol{i}}{\mathbf{3}+\boldsymbol{i}}$ is:

\(\int_0^{\frac{\pi}{2}} \frac{3 \sin x+4 \cos x}{\sin x+\cos x} d x=\)

\(\text { The particular solution of the differential equation }(x-y)(d x+d y)=(d x-d y) \text { when } y=-1 \text { and } x=0 \text { is }\)

The function $\boldsymbol{x}+\boldsymbol{y}=\boldsymbol{\operatorname { t a n }}^{-\mathbf{1}} \boldsymbol{y}$ is the solution of which of the following differential equations?

\(\text { The degree of the differential equation } \sqrt{1+\left(\frac{d y}{d x}\right)^{1 / 3}}=\frac{d^2 y}{d x^2} \text { is: }\)

Let the population of a species of birds surviving at a time ' $\boldsymbol{t}$ ' be governed by the differential equation $\frac{d p}{d t}-p=-100$. If $p(0)=50$, then $p\left(-\log _e 2\right)$ is equal to

\(\text { The second derivative of } \sin 3 \boldsymbol{x} \boldsymbol{\operatorname { c o s }} \mathbf{5 x} \text { is: }\)

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

If $\log y=\log (\sin x)-x^2$, then $\frac{d^2 y}{d x^2}+\mathbf{4} x \frac{d y}{d x}+\mathbf{4} x^2 y=$

If the two ends of the major axis of an ellipse are $(5,0)$ and $(-5,0)$ and one focus lies on the line $3 x-5 y-9=0$, then its equation is

The function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x)=\frac{x}{x^2+1} \quad \forall x \in \mathbb{R}$ is

The foci of a hyperbola are the same as those of the ellipse with equation $9 x^2+16 y^2=144$.
If the length of the transverse axis of this hyperbola is $2 \cos \alpha$, then its equation is:

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

\(\int \tan ^{-1}\left(\sqrt{\frac{1-\sin x}{1+\sin x}}\right) d x=\)

\(\int\left(\sin ^6 x+\cos ^6 x+3 \sin ^2 x \cos ^2 x\right) d x=\)

\(\int \frac{\log x}{(1+x)^2} d x\)

\(\text { The domain of the function } f(x)=\sin ^{-1}(\sqrt{x-1})\)

If $X=\tan ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right]+\cos ^{-1}\left[\cos \left(\frac{7 \pi}{6}\right)\right]$ and $Y=\sin ^{-1}\left[\sin \left(\frac{11 \pi}{6}\right)\right]+\tan ^{-1}\left[\tan \left(\frac{4 \pi}{3}\...

\(\mathop {\lim }\limits_{x \to {\pi \over 2}}\left(\frac{1-\sin x}{\cos x}\right) \text { is equal to }\)

If $\mathop {\lim }\limits_{x \to 0}\left(\frac{p \sin 2 x+1-\cos 2 x}{x+\tan x}\right)=1$ then the value of ' $p$ ' is

The function $\boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}|+|\boldsymbol{x}-\mathbf{1}|$ is:

The feasible region represented by the constraints:
$$ \begin{aligned} & x+2 y \leq 120 \\ & x+y \geq 60 \\ & x-2 y \geq 0 \\ & x \geq 0 \text { and } y \geq 0 \end{aligned} $$

Matrix $A=\left[\begin{array}{ccc}1 & 1 & 2 \\ 1 & -2 & 2 \\ 1 & 0 & -1\end{array}\right]$,
Given $\boldsymbol{M}_{\mathbf{2 2}}$ and $\boldsymbol{A}_{\mathbf{3 2}}$ are the minor and cofactor of the adjoint matrix of $\boldsymbol{A}$ respe...

If the matrix $M=\left[\begin{array}{ccc}x+5 & a & -4 \\ -2 & 0 & b \\ c & 6 & y+1\end{array}\right]$ is a skew symmetric matrix, the value of the expression $\boldsymbol{a} \boldsymbol{b}+\boldsymbol{c}^{\mathbf{2}}-\boldsymbol{x} \boldsym...

Let A be a square matrix of order $3 \times 3$. If $|A|=-4$, then the value of $\left|\frac{A^{-1}}{-2}\right|$ is:

Let $A=\left[a_{i j}\right]$ be a square matrix of order $3 \times 3$, where the elements are defined as $a_{i j}=\left\{\begin{array}{ll}i-2 j & \text { if } i=j \\ 0 & \text { if } i> j \\ 1 & \text { if } i < j\end{array} \quad\right.$ t...

Given $A=\left[\begin{array}{lll}x & 1 & -2\end{array}\right]$ and $B=\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ If $\boldsymbol{A} \boldsymbol{B} \boldsymbol{A}^{\boldsymbol{t}}=[-\mathbf{2 0}]$ then the...

A coach needs to select a $\mathbf{4}$-player starting lineup from a pool of $\mathbf{1 0}$ players:

5 guards
3 forwards
2 centres

Find the number of different selections if the 4-player starting lineup must include:

At least 1 guard
At ...

\(\text { If }{ }^{\mathrm{n}} C_{13},{ }^{\mathrm{n}} C_{14} \text { and }{ }^{\mathrm{n}} C_{15} \text { are in arithmetic progression, then the positive integer value of ' } \mathbf{n} \text { ' can be }\)

A company is migrating its database, and two software engineers, Ishaan and Kavya, take turns running a data-sync script that has a constant success rate of $\frac{3}{8}$ per attempt.
If Ishaan initiates the first attempt and they persist u...

Vishnu has two jars of marbles, Jar A and Jar B.

Jar A contains 3 yellow marbles and 2 green marbles.
Jar B contains 4 yellow marbles and 3 green marbles.

Vishnu flips a fair coin.

If it lands heads, he picks two marbles at random withou...

If $P(A \cup B)=0.85, P(B)=0.50$ and $P(A \cap B)=0.30$. Then $P\left(A \cap B^{\prime}\right)=$