COMEDK 2025 Evening Shift

An aqueous solution of an electrolyte $\mathrm{A}_3 \mathrm{~B}$ is prepared by dissolving 0.5625 g in 750 ml of water and is found to be $80 \%$ ionised. If $\mathrm{K}_{\mathrm{b}}$ for water is $0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol...

At 300 K the vapour pressure of an ideal solution containing 1.0 mole each of volatile liquids X and Y is 1000 mm . Keeping the temperature constant, when 2.0 moles of liquid X is added to the solution, its vapour pressure increases by 200 ...

The first electron gain enthalpy of oxygen is $-141 \mathrm{~kJ} \mathrm{~mol}^{-1}$, its second electron gain enthalpy is :

The oxidation number of potassium in $\mathrm{K}_2 \mathrm{O}, \mathrm{K}_2 \mathrm{O}_2$ and $\mathrm{KO}_2$ respectively are:

Identify the correct coefficients (a), (b), (c) and (d) in the following equations
i) $\quad \mathrm{xMnO}_4^{--}+$(a) $\mathrm{SO}_3{ }^{2-}+$ (b) $\mathrm{H}^{+} \cdots \longrightarrow \mathrm{xMn}^{2+}+$ (a) $\mathrm{SO}_4{ }^{2-}+$ (c) ...

An example of disproportionation reaction is :

The mole fraction of an unknown solute in 1560 g of Benzene is 0.5 . What is the molality of the solution? (M. M of Benzene:78 amu)

The enthalpies of combustion of $\mathrm{H}_2, \mathrm{C}$ (graphite) and $\mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})$ are $-286.0,-394.0$ and $-1560.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at $25^{\circ} \mathrm{C}$ and 1 atm pressure. The enthalpy...

In the decomposition of limestone to lime, the values of $\Delta H^o$ and $\Delta S^o$ are $+179.1 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $160.2 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$. Calculate the temperature above which conversio...

Two moles of an ideal gas at 1 bar pressure and 298 K is expanded into vacuum to double the volume. The work done is :

If the function $f(x)=\mu \sin x+\frac{1}{3} \sin 3 x$ has its derivative equal to zero at $x=\frac{\pi}{3}$, then the value of ' $\mu$ ' is

A man is moving away from a tower 41.6 m high at a rate of $2 \mathrm{~m} / \mathrm{s}$. If the eyelevel of the man is 1.6 m above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a di...

If a quadratic function in $x$ has the value 19 when $x=1$ and has a maximum value 20 when $x=2$, then the function is

If the length of the diagonal of a square is increasing at the rate of $0.1 \mathrm{~cm} / \mathrm{sec}$.

What is the rate of increase of its area when the side is $\frac{15}{\sqrt{2}} \mathrm{~cm}$ ?

Let $f(x)=x \sqrt{4 a x-x^2}, a>0$ then $f^{\prime}(x)$ at $x=2 a$ is :

The function $y=\frac{\log x}{x^3}$ is strictly increasing function for

If the area under the curve $y=\sqrt{a^2-x^2}$ included between the lines $x=0$ and $x=a$ is 4 sq units. Then the value of ' $a$ ' is

Area of the region bounded by the curve $y=\cos x$ between $x=-\frac{\pi}{2}$ and $x=\pi$ is ------------------

Given that $z$ is a real number and $z=\frac{\lambda+4 i}{1+\lambda i}$ where $\lambda \in R$, then the possible value of $\lambda$ is :

If $z=\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^5+\left(\frac{\sqrt{3}}{2}-\frac{i}{2}\right)^5$, then

$\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{1}{1+\sqrt{\tan x}} d x=$

$\int_0^1 x(1-x)^{99} d x=$

$\int\limits_{-2}^2 \frac{|x-3|}{x-3} d x=$

Find the function ' $f$ ' which satisfies the equation $\frac{d f}{d x}=2 f$, given that $f(0)=e^3$

The number of solutions of $\frac{d y}{d x}=\frac{y+1}{x-1}$, when $y(1)=2$ is :

The solution of the differential equation: $x \cos y d y=\left(x e^x \log x+e^x\right) d x$ is

Solve the following differential equation $\cos ^2 x \frac{d y}{d x}+y=\tan x$, given that $y(0)=1$. Hence find $y\left(\frac{\pi}{4}\right)$

If $y=x+e^x$ then $\frac{d^2 x}{d y^2}=$

If $x=a\left[\left\{\cos t+\frac{1}{2} \log \left(\tan ^2 \frac{t}{2}\right)\right\}\right]$ and $y=a \sin t$ then $\frac{d y}{d x}=$

A function $f$ from the set of natural numbers to integers defined by
$$f(n)=\left\{\begin{array}{l}
\frac{n-1}{2}, \quad \text { when } n \text { is odd } \\
-\frac{n}{2}, \quad \text { when } n \text { is even }
\end{array} \quad\right. \...

If the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ and the foci of the hyperbola $\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}$ coincide, then the value of $b^2$ is

\(\int \frac{\sin 2 x}{(1+\sin x)(2+\sin x)} d x=a \log |1+\sin x|-b \log |2+\sin x|+c\)
then the value of $a$ and $b$ is ----------------

$\int\left(e^{x \log _e 6}\right) e^x d x=\phi(x)+c$ then $\phi(x)=$

The value of $\tan \left\{\cos ^{-1}\left(\frac{\sqrt{2}}{2}\right)-\frac{\pi}{2}\right\}$ is

$\sin ^{-1}(x-1)+\cos ^{-1}(x-3)+\tan ^{-1}\left(\frac{x}{2-x^2}\right)=\cos ^{-1} k+\pi$, then the value of ' $k$ ' is

The relationship between a and b for the continuous function
$f(x)=\left\{\begin{array}{ll}a x+1, & \text { if } x \leq 3 \\ b x+3, & \text { if } x>3\end{array}\right.$ at $x=3$ is

Evaluate: $\lim _\limits{x \rightarrow 0} \frac{\sqrt[3]{1+x}-\sqrt[3]{1-x}}{x}$

If $\lim\limits_{x \rightarrow 1} \frac{x^4-1}{x-1}=\lim\limits_{x \rightarrow k} \frac{x^3-k^3}{x^2-k^2}$, then the value of K is :

Given $Z=80 x+120 y$, subject to constraints are $x+3 y \leq 30 ; 3 x+4 y \leq 60 ; x \geq 0 ; y \geq 0$.
P is one of the corner points of the feasible region for the given Linear Programming Problem.
Then the coordinate of $P$ is

The solution for the following system of inequalities $3 x-7<5+x$ and $11-5 x \leq 1$ on a real number line is

If $A=\left[\begin{array}{ccc}4 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3\end{array}\right]$ then $A^{-1}$ exists if :

Value of the determinant of a matrix $A$ of order $3 \times 3$ is 7 . Then the value of the determinant formed by the cofactors of matrix A is

If $X=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ and $Y=\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]$ and $B=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$ then $B...

If $A=\left[\begin{array}{ll}a & b \\ b & a\end{array}\right]$ and $(A I)^2=\left[\begin{array}{ll}\alpha & \beta \\ \beta & \alpha\end{array}\right]$ where I is the identity matrix then

Kiran purchased 3 pencils, 2 notebooks and one pen for ₹41.
From the same shop Manasa purchased 2 pencils, one notebook and 2 pens for ₹ 29 , while Shreya purchased 3 pencils, 2 notebooks and 2 pens for ₹ 44.
The above situation can be repr...

The area of a triangle formed by the lines joining the vertex of the parabola $x^2=\lambda y$ to the ends of its latus rectum is 18 sq units then the value of $\lambda$ is

How many natural numbers are there between 100 and 1000 such that at least one of their digits is $6 ?$

The number of words that can be formed with the letters of the word 'DEFINITE' if two vowels are together and the other two are also together but separated from the first two is

Two numbers are selected at random from integers 1 to 9 .
If their sum is even, what is the probability that both the numbers are odd?

If A and B are two events such that $P(\bar{A})=0.3, P(B)=0.4, P(A \cap \bar{B})=0.5$, then find the value of $P(B / A \cup \bar{B})$