COMEDK 2025 Morning Shift

Choose the correct statement.

A non-volatile solute A weighing 60 g when dissolved in 212 g of the solvent Xylene reduces its vapour pressure to $60 \%$. What is the Molar mass of A in $\mathrm{g} / \mathrm{mol}$ ? [MM of xylene $=106 \mathrm{~g} / \mathrm{mol}$ ]

Choose the pair of elements $[(\mathrm{A})$ to $(\mathrm{F})]$ which:
(i) belong to the Chalcogen family
(ii) form monovalent oxides which give alkalies in aqueous solution
(iii) form stable monovalent anions
(A) $1 s^2 2 s^2 2 p^6 3 s^2 3 ...

The concentration and percentage purity of Oxalic acid can be determined by titration with $\mathrm{KMnO}_4$ in presence of dil. $\mathrm{H}_2 \mathrm{SO}_4$. Instead of dil. $\mathrm{H}_2 \mathrm{SO}_4$, dil HCl cannot be used because

Choose the correct statement.

Which one of the following options represents the decreasing order of oxidation number of the central atom in:
\(\mathrm{Cr}_2 \mathrm{O}_7^{2-}, \mathrm{Cr} \mathrm{O}_2^{-}, \mathrm{MnO}_4^{-}, \mathrm{BrO}_3^{-}\)

If X is a haloalkane with a single Chlorine atom per molecule and the percentage of Cl is 55 , what would be the number of Cl atoms present in 0.1 g of the haloalkane?
Atomic mass of $\mathrm{Cl}=35.5 \mathrm{~g} / \mathrm{mol}$

For a reaction $\mathrm{X}_2(\mathrm{l})+\mathrm{Y}_2(\mathrm{~g}) \leftrightharpoons 2 \mathrm{XY}(\mathrm{g})$, the $\Delta \mathrm{H}^0$ and $\Delta \mathrm{S}^0$ are $+29.3 \mathrm{~kJ} / \mathrm{mol}$ and $104.1 \mathrm{~J} \mathrm{~K}...

0.4 g of Propane burns completely at 300 K in a bomb calorimeter. The temperature of the calorimeter and surrounding water rises by $0.4^0 \mathrm{C}$. If the heat capacity of the calorimeter and contents is $24 \mathrm{~kJ} \mathrm{~K}^{-1...

Given that the standard enthalpy of combustion of $\mathrm{C}_{(\mathrm{S})}$ and $\mathrm{CS}_2(\mathrm{l})$ are -393.3 and $-1108.76 \mathrm{~kJ} / \mathrm{mol}$ respectively and the standard enthalpy of formation of $\mathrm{CS}_2$ is $1...

The curve $a x^3+b x^2+c x+d$ has a point of minima at $x=1$, then

A solid S is made from a cylinder surmounted by a hemisphere on top with both its circular faces sharing a common centre. The radius of cylinder and radius of hemisphere are $x \mathrm{~cm}$. The height of the cylinder is $(20-4 x) \mathrm{...

A spherical snowball is melting such that its volume is decreasing at the rate of $1 \mathrm{~cm}^3 / \mathrm{min}$. The rate at which the diameter is decreasing when the diameter is 10 cm is

The least value of ' $a$ ' such that the function $x^2+a x+1$ is increasing on $[1,2]$ is

Oil from a conical funnel is dripping at the rate of $5 \mathrm{~cm}^3 / \mathrm{s}$. If the radius and height of the funnel are 10 cm and 20 cm respectively, then the rate at which the oil level drops when it is 5 cm from the top is

The area bounded by the parabola $y^2=36 x$ and its latus rectum is

Area of the region bounded by the curve $y=\sin \left(\frac{x}{2}\right)$ between $-4 \pi$ and 0 is

If the third and fourth terms in the expansion $\left(2 x+\frac{1}{8}\right)^{10}$ are equal, then the value of $x$ is __________

Equation of a circle whose area is 154 sq units and having $2 x-3 y+12=0$ and $x+4 y-5=0$ as diameters is

If $\frac{x-1}{3+i}+\frac{y-1}{3-i}=i$ then $(y, x)=$

$\int_0^\pi \frac{e^{\cos x}}{e^{\cos x}+e^{-\cos x}} d x$ is equal to

The solution of the differential equation $\frac{d y}{d x}+y \log y \cot x=0$ is

The solution of $(x+\log y) d y+y d x=0$ when $y(0)=1$ is

The order of the differential equation $\frac{d}{d x}\left[\left(\frac{d y}{d x}\right)^3\right]=0$ is

The general solution of the differential equation $(x-y) d y=(x+y) d x$ is

If $y=\sqrt{\frac{x}{a}}+\sqrt{\frac{a}{x}}, \quad$ then $2 x y \frac{d y}{d x}$ is equal to

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

If $f(x)=\left(\frac{3+x}{1+x}\right)^{2+3 x}$, then $f^{\prime}(0)=$

If the distance between the foci is equal to the length of the latus rectum, then the eccentricity of the ellipse is

$\int \frac{1}{\sqrt{9+8 x-x^2}} d x=\varphi(x)+c$ then $\varphi(x)=$

$\int \tan ^2\left(5-\frac{x}{2}\right) d x=$

$\int \frac{d x}{(x+2)\left(x^2+1\right)}=p \log |x+2|+q \log \left|x^2+1\right|+r \tan ^{-1} x+c$ then $p+q+r=$

$\int \log x^2 d x=$

The range of $x$ for which the equation $\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)=2 \tan ^{-1} x$ holds true

$-\frac{2 \pi}{5}$ is the principal value of

Find the value of $\lim\limits_{h \rightarrow 0} \frac{(a+h)^2 \sin (a+h)-a^2 \sin a}{h}$

The value of $\lim _\limits{x \rightarrow 0} \frac{(1-x)^n-1}{x}=$

If $f(x)=\left\{\begin{array}{ll}\frac{1-x^m}{1-x} & \text { if } x \neq 1 \\ 2 m-1 & \text { if } x=1\end{array}\right.$ and the function is discontinuous at $x=1$, then

For a given Linear Programming problem, the objective function is
\(z=3 x+2 y\)
Subject to constraints are
$$\begin{aligned} & 4 x+3 y \leq 60 \\ & x \geq 3 \\ & y \leq 2 x \\ & y \geq 0 \end{aligned}$$
P is one of the corner points of the ...

If $A(t)=\left[\begin{array}{cc}\cos t & \sin t \\ -\sin t & \cos t\end{array}\right]$ then the product of $A(t)$ and $A(-t)$ is

If $A=\left[\begin{array}{cc}1 & -2 \\ 4 & 5\end{array}\right] ; f(t)=t^2-3 t+7$ then $f(A)+\left[\begin{array}{cc}3 & 6 \\ -12 & -9\end{array}\right]=$

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

For two matrices $A$ and $B$, given that $A^{-1}=\frac{1}{8} B$ then inverse of $(8 A)$ is

The sum of three numbers is 6 .
Twice the third number, when added to the first number gives 7 ,
On adding the sum of the second and third numbers to thrice the first number, we get 12 .
The above situation can be represented in matrix form...

Let $M$ be the set of all $2 \times 2$ matrices with entries from the set R of real numbers. Then the function $f: M \rightarrow R$ defined by $f(A)=|A|$ for every $A \in M$ is

A shopkeeper sells three varieties of fruit juice. He has a large number of bottles of same size of each variety. The number of different ways of displaying all the three varieties on the shelf with 5 places in a row and each display must h...

Codes used for vehicle identification consists of two distinct English alphabets followed by two distinct digits from 1 to 9 . How many of them end with an even number.

Let $A$ and $B$ be two events such that one of the two events must occur. Given that the chance of occurrence of $A$ is $\frac{2}{3}$ the chance of occurrence of $B$, then odds in favour of $B$ is

In an entrance test, there are multiple choice questions. There are four possible answers to each question of which only one is correct. The probability that a student knows the answer to a question is $90 \%$. If he gets the correct answer...

A person writes four letters and address four envelopes. If the letters are placed in the envelopes at random, then the probability that not all letters are placed in the right envelope is