COMEDK 2024 Afternoon Shift

In the following question a statement of Assertion (A) followed by a statement of Reason (R) is given. Choose the correct option out of the choices given below.
Assertion (A): van't Hoff factor for a solution of benzoic acid in benzene is l...

The system that forms minimum boiling azeotrope is :

Among the following, which is not according to the property indicated against it?

When \(3.92 \mathrm{~g}\) of Mohr salt is dissolved in \(100 \mathrm{~mL}\) of water, and titrated against \(\mathrm{KMnO}_4\) solution, \(20 \mathrm{~mL}\) of this solution required \(18 \mathrm{~mL}\) of \(\mathrm{KMnO}_4\) for complete o...

Identify the oxidation reaction in which acidified \(\mathrm{KMnO}_4\) is required

In the reaction,

\(2 \mathrm{~S}_2 \mathrm{O}_3^{2-}+\mathrm{I}_2 \rightarrow \mathrm{S}_4 \mathrm{O}_6^{2-}+2 \mathrm{I}^{-}\)

When 1 mole of \(\mathrm{O}_2\) and 1 mole of ammonia are made to react in the reaction,
\(4 \mathrm{NH}_3(\mathrm{~g})+5 \mathrm{O}_2(\mathrm{~g}) \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_2 \mathrm{O}(\mathrm{g})\)

The correct option for free expansion of an ideal gas under adiabatic condition is:

At Constant volume, the heat required to raise the temperature of \(4.48 \mathrm{~L}\) of an ideal gas at STP by \(15^{\circ} \mathrm{C}\) is 12.0 calories.
The \(\mathrm{C_p}\) of the gas is _____________
$$(\mathrm{R}=2 \mathrm{~Cal} \ma...

The \(\Delta \mathrm{H}_{(\mathrm{f})}^{\mathrm{o}}\) of \(\mathrm{NO}_2(\mathrm{~g})\) and \(\mathrm{N}_2 \mathrm{O}_4(\mathrm{~g})\) are 16.0 and \(4.0 \mathrm{k} \mathrm{cal} \mathrm{mol}^{-1}\) respectively. The heat of dimerisation of ...

\(\text { If } f(x)=\frac{a \sin x+b \cos x}{c \sin x+d \cos x} \text { is decreasing for all } x \text {, then }\)

If \((x-a)^2+(y-b)^2=c^2\), where \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are some constants, \(c>0\) then \(\frac{\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{2}}}{\frac{d^2 y}{d x^2}}\) is independent of

\(\text { The function } y=\tan x-x \text { is }\)

If \(f(x)=\log x+b x^2+a x, x \neq 0\) has extreme values (or turning points) at \(x=-1\) and \(x=2\) then the values of \(\mathrm{a}\) and \(\mathrm{b}\) are

The dimensions of the largest rectangle of side \(x\) and \(y\) that can be inscribed in the right angled triangle of sides \(\mathrm{a}\) and \(\mathrm{b}\) is

The area of the region (in sq units) bounded by the curve \(y=\sqrt{16-x^2} \text { and } x \text {-axis is }\)

\(\text { The area of the region (in square units) bounded by the line } y+3=x ; x=1 \text { and } x=5 \text { is }\)

If the sum of the coefficients of the first three terms in the expansion of \(\left(x-\frac{a}{x^2}\right)^{12}, x \neq 0\) is 559. Find the value of '\(a\)' if '\(a\)' belongs to positive integers

\(\text { The value of } \frac{i^{1004}+i^{1006}+i^{1008}+i^{1010}+i^{1012}}{i^{510}+i^{508}+i^{506}+i^{504}+i^{502}} \text { is }\)

\(\int_\limits{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sqrt{\cos x-\cos ^3 x} d x \text { is equal to }\)

\(\int_\limits0^{\frac{\pi}{2}} \frac{\cos x}{1+\cos x+\sin x} d x=\)

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

\(\text { The general solution of } \frac{d y}{d x}=\sin ^{-1} x \text { is }\)

\(\text { The general solution of the differential equation } \frac{d y}{d x}=\frac{x y}{x^2+y^2} \text { is }\)

Degree of the differential equation \(\log \left(\frac{d y}{d x}\right)^{\frac{1}{2}}=5 x+4 y\) is

\(\text { If } x^2+y^2=t+\frac{1}{t} \text { and } x^4+y^4=t^2+\frac{1}{t^2} \text { then } \frac{d y}{d x}=\)

The points on the ellipse \(16 x^2+9 y^2=400\) at which the ordinate decreases at the same rate at which the abscissa increases are

If an ellipse has an equation in the standard form and it passes through the points \(\left(\frac{5}{2}, \frac{\sqrt{6}}{4}\right)\) and \(\left(-2, \frac{\sqrt{15}}{5}\right)\) then the length of its latus rectum is

\(\text { Which of the following function is injective? }\)

If the distance between the foci and the distance between the two directrixes are in the ratio \(3: 2\) for a hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), then a : b is

\(\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x \text { is equal to }\)

\(\int \frac{f^{\prime}(x)}{f(x) \log (f(x))} d x \text { is equal to }\)

\(\int \log x(\log x+2) d x \text { equals to }\)

\(\text { If } \alpha=\tan ^{-1}\left(\tan \frac{5 \pi}{4}\right) \text { and } \beta=\tan ^{-1}\left(-\tan \frac{2 \pi}{3}\right) \text { then }\)

Evaluate :

\(\operatorname{cosec}^{-1}\left(-\frac{2 \sqrt{3}}{3}\right)+\tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right)+\sec ^{-1} 2+\cos ^{-1}\left(-\frac{1}{2}\right)-\sin ^{-1}\left(\frac{\sqrt{2}}{2}\right)\)

\(\text { If } y=\sin ^{-1}(\sqrt{\sin x}) \text {, then } \frac{d y}{d x} \text { equals }\)

\(\lim _\limits{x \rightarrow 0} \frac{a^x-b^x}{c^x-d^x}=\)

\(\text { The value of } \lim _\limits{x \rightarrow 0} \frac{\sin (a+x)-\sin (a-x)}{x} \text { is }\)

\(\text { The number of points of discontinuity of the rational function } f(x)=\frac{x^2-3 x+2}{4 x-x^3}\)

\(\text { The maximum value of } Z=3 x+4 y \text { for the given constraints } x+2 y \leq 76,2 x+y \leq 104, x \geq 0, y \geq 0 \text { is }\)

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

If $$A=\left[\begin{array}{lll}5 & 0 & 4 \\ 2 & 3 & 2 \\ 1 & 2 & 1\end{array}\right] \quad B^{-1}=\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{array}\right]$$ then \((A B)^{-1}\) is equal to

$$ \left|\begin{array}{ccc} \cos (\alpha+\beta) & -\sin (\alpha+\beta) & \cos 2 \beta \\ \sin \alpha & \cos \alpha & \sin \beta \\ -\cos \alpha & \sin \alpha & \cos \beta \end{array}\right| $$ is independent of

\(\text { If A }(\operatorname{adj} A)=5 I \text {, where I is the identity matrix of order } 3 \text {, then }|\operatorname{adj} A|=\)

\(\text { A square matrix } P \text { satisfies } P^2=I-P \text { where } I \text { is identity matrix. If } P^n=5 I-8 P \text {, then } n \text { is equal to }\)

The number of four digit numbers strictly greater than 4321 formed using the digits \(0,1,2,3,4,5\) with repetition of digit is

A student has 3 library cards and 8 books of his interest in the library. Out of these 8 books he does not want to borrow Chemistry part 2 unless he can borrow Chemistry part 1 also. In how many ways can he choose the three books to be borr...

There are some baskets. The chances of picking a loaded basket and choosing a red coloured one is 0.2 . For every 100 tries to pick one basket, 60 times a basket is either loaded or red in colour. What is the probability of choosing an empt...

A and B are two independent events. The probability of their simultaneous occurrence is \(\frac{1}{8}\) and the probability that neither of them occurs is \(\frac{3}{8}\). Then their individual probabilities are

P and Q are considering to apply for a job. The probability that P applies for the job is \(\frac{1}{4}\). The probability that \(\mathrm{P}\) applies for the job given that \(\mathrm{Q}\) applies for the job is \(\frac{1}{2}\), and the pro...