COMEDK 2024 Evening Shift

Given that the freezing point of benzene is \(5.48^{\circ} \mathrm{C}\) and its \(\mathrm{K}_{\mathrm{f}}\) value is \(5.12{ }^{\circ} \mathrm{C} / \mathrm{m}\). What would be the freezing point of a solution of \(20 \mathrm{~g}\) of propan...

Study the graph between partial pressure and mole fraction of some gases and arrange the gases P, Q, R and S dissolved in H\(_2\)O, in the decreasing order of their KH values.

With reference to Pauling's Electronegativity scale, which one of the following options shows the correct order of electronegativity values of elements?

In the estimation of element \(\mathrm{X}\) in an organic compound, \(0.8 \mathrm{~g}\) of the compound containing \(\mathrm{X}\) was heated with fuming \(\mathrm{HNO}_3\) and the cooled product was treated with barium chloride. The mass of...

In the redox reaction between \(\mathrm{Cr}_2 \mathrm{O}_7^{2-} / \mathrm{H}^{+}\) and sulphite ion, what is the number of moles of electrons involved in producing 3.0 moles of the oxidised product?

Sulphuric acid used in Lead Storage battery has a concentration of \(4.5 \mathrm{~M}\) and a density of \(1.28 \mathrm{~g} / \mathrm{~ml}\). The molality of the acid is __________.

What mass of Silver chloride, in grams, gets precipitated when \(150 \mathrm{~ml}\) of \(32 \%\) solution of Silver nitrate is reacted with \(150 \mathrm{ml}\) of \(11 \%\) Sodium chloride solution? Atomic mass in $$\mathrm{g} / \mathrm{mol...

Given :
$$
\begin{gathered}
\Delta \mathrm{H}^0 \mathrm{f}_{\text {of }} \mathrm{CO}_2(\mathrm{~g})=-393.5 \mathrm{~kJ} / \mathrm{mol} \\
\Delta \mathrm{H}^0{ }_{\mathrm{f}} \text { of } \mathrm{H}_2 \mathrm{O}(\mathrm{l})=-286 \mathrm{~kJ}...

The Enthalpy of combustion of \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{COOH}(\mathrm{s})\) at \(25^{\circ} \mathrm{c}\) and 1.0 atm pressure is \(-2546 \mathrm{~kJ} / \mathrm{mol}\). What is the Internal energy change for this reaction?

5.0 moles of an Ideal gas at 3.0 atm pressure and \(27^{\circ} \mathrm{C}\) is compressed isothermally to half its volume by application of an external pressure of \(3.5 \mathrm{~atm}\). What is the amount of work done (in joules) on the ga...

\(\text { The rate of change of the volume of a sphere with respect to its surface area } \mathrm{S} \text { is }\)

The turning point of the function \(y=\frac{a x-b}{(x-1)(x-4)}\) at the point \(P(2,-1)\) is

The side of a cube is equal to the diameter of a sphere. If the side and radius increase at the same rate then the ratio of the increase of their surface area is

What is the nature of the function \(f(x)=x^3-3 x^2+4 x\) on real numbers?

The area bounded by the curve \(y=\cos x, x=0\) and \(x=\pi\) is

In the expansion \(\left(\frac{1}{x}+x \sin x\right)^{10}, \quad\) the co - efficient of \(6^{\text {th }}\) term is equal to \(7 \frac{7}{8}\), then the principal value of \(x\) is

The equation of the circle which touches the \(x\)-axis, passes through the point \((1,1)\) and whose centre lies on the line \(x+y=3\) in the first quadrant is

\(\text { If }(1-4 i)^3=a+i b \text { then the value of } \mathrm{a} \text { and } \mathrm{b} \text { is }\)

If \(a\) is a real number such that \(\int_\limits0^a x d x \leq a+4\) then

\(\text { If } I_n=\int_\limits0^{\frac{\pi}{4}} \tan ^n x d x \text {, for } n \geq 2 \text {, then } I_n+I_{n-2}=\)

\(\text { The value of the integral } \int_\limits{\frac{1}{3}}^1 \frac{\left(x-x^3\right)^{\frac{1}{3}}}{x^4} d x \text { is }\)

\(\text { If } \frac{d y}{d x}=y+3>0 \text { and } y(0)=2 \text { then } y(\log 2) \text { is equal to }\)

The general solution of the differential equation \(x \frac{d y}{d x}=y+x \tan \left(\frac{y}{x}\right)\) is

\(\text { The general solution of the differential equation }(1+\tan y)(d x-d y)+2 x d y=0 \text { is }\)

The sum of the order and degree of the differential equation \(\left(\frac{d^2 y}{d x^2}\right)^5+\frac{4\left(\frac{d^2 y}{d x^2}\right)^3}{\left(\frac{d^3 y}{d x^3}\right)}+\frac{d^3 y}{d x^3}=x^2-1\) is

\(\text { If } y=\sin ^{-1}\left(\frac{5 x+12 \sqrt{1-x^2}}{13}\right) \text { then } \frac{d y}{d x} \text { equals }\)

\(\text { If } y=f(x), \quad p=\frac{d y}{d x} ; q=\frac{d^2 y}{d x^2} \text { then } \frac{d^2 x}{d y^2} \text { is equal to }\)

\(\text { If } y=\sqrt{\sin x+y} \text { then find } \frac{d y}{d x} \text { at } x=0, \quad y=1\)

\(\text { The area of the region enclosed by the curve }\left\{(x, y): 4 x^2+25 y^2=100\right\} \text { is }\)

The domain of the function \(y=\frac{1}{\log _{10}(3-x)}+\sqrt{x+7}\) is

\(\int e^x\left[\frac{x^2+1}{(x+1)^2}\right] d x \quad \text { is equal to }\)

\(\text { The value of } \int \frac{d x}{\sqrt{2 x-x^2}} \text { is }\)

\(\text { Evaluate: } \cot ^{-1}\left(-\frac{3}{\sqrt{3}}\right)-\sec ^{-1}\left(-\frac{2}{\sqrt{2}}\right)-\operatorname{cosec}^{-1}(-1)-\tan ^{-1}(1)\)

\(\text { Evaluate: } \cos ^{-1}\left(\cos \frac{35 \pi}{18}\right)-\sin ^{-1}\left(\sin \frac{35 \pi}{18}\right)\)

\(\text { The function } f(x)=\tan ^{-1}(\sin x+\cos x) \text { is an increasing function in }\)

Let \(\alpha\) and \(\beta\) be the distinct roots of \(a x^2+b x+c=0\), then \(\lim _\limits{x \rightarrow \alpha} \frac{1-\cos \left(a x^2+b x+c\right)}{(x-\alpha)^2}\) is equal to

\(\text { The value of } \lim _\limits{x \rightarrow 1} \frac{x^{15}-1}{x^{10}-1}=\)

$$ \text { If } f(x)=\left\{\begin{array}{cc} x & , \quad 0 \leq x \leq 1 \\ 2 x-1 & , \quad x>1 \end{array}\right. \text { then } $$

The maximum value of \(P=500 x+400 y\) for the given constraints \(x+y \leq 200, \quad x \geq 20, \quad y \geq 4 x, \quad y \geq 0\) is

$$ \text { If } 3 A+4 B^t=\left(\begin{array}{ccc} 7 & -10 & 17 \\ 0 & 6 & 31 \end{array}\right) \text { and } 2 B-3 A^t=\left(\begin{array}{cc} -1 & 18 \\ 4 & -6 \\ -5 & -7 \end{array}\right) \text { then }(5 B)^t= $$

$$ \text { If } A=\left[\begin{array}{cc} 5 a & -b \\ 3 & 2 \end{array}\right] \text { and } A \operatorname{adj} A=A A^t \text {, then } 5 a+b \text { is equal to } $$

If $$A=\left[\begin{array}{ccc}0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x\end{array}\right]$$ is a singular matrix then \(x\) is equal to

If the matrix $A$ is such that $$A\left(\begin{array}{cc}-1 & 2 \\ 3 & 1\end{array}\right)=\left(\begin{array}{cc}-4 & 1 \\ 7 & 7\end{array}\right)$$ then \(A\) is equal to

In the parabola \(y^2=4 a x\) the length of the latus rectum is 6 units and there is a chord passing through its vertex and the negative end of the latus rectum. Then the equation of the chord is

For an examination a candidate has to select 7 questions from three different groups \(\mathrm{A}, \mathrm{B}\) and C. The three groups contain 4, 5 and 6 questions respectively. In how many different ways can a candidate make his selection...

The letters of the word "COCHIN" are permuted and all the permutations are arranged in alphabetical order as in an English dictionary. The number of words that appear before the word "COCHIN" is

Let \(\mathrm{A}\) and \({B}\) be two events such that \(P(A / B)=\frac{1}{2}\) and \(P(B / A)=\frac{1}{3}\) and \(P(A \cap B)=\frac{1}{6}\) then, which one of the following is not true?

Suppose we have three cards identical in form except that both sides of the first card are coloured red, both sides of the second are coloured black, and one side of the third card is coloured red and the other side is coloured black.
The t...

While shuffling a pack of cards, 3 cards were accidently dropped, then find the probability that the missing cards belong to different suits?

What is the probability of a randomly chosen 2 digit number being divisible by 3 ?