COMEDK 2023 Evening Shift

Para and ortho hydrogen differ in:

The group number of the element in the periodic table with the electronic configuration \((\mathrm{n}-1) \mathrm{d}^2 \mathrm{~ns}^2\).
For \(n=4\) is:

In neutral medium \(\mathrm{KMnO}_4\) oxidises \(\mathrm{MnSO}_4\) to _________

In the given Redox equation, identify the stoichiometric coefficients \(\mathrm{w}, \mathrm{x}, \mathrm{y}\) and \(\mathrm{z}\).
$$\mathrm{ClO}_3^{-1}+\mathrm{w} \mathrm{Cl}^{-1}+\mathrm{xH}^{+} \rightarrow \mathrm{y} \mathrm{H}_2 \mathrm{O...

Identify the catalyst used in the reaction between Iodide and persulphate ions.
\(2 \mathrm{I}^{-}+\mathrm{S}_2 \mathrm{O}_8{ }^{2-} \rightarrow \mathrm{I}_2+2 \mathrm{SO}_4{ }^{2-}\)

Choose the incorrect statement.

\(\mathrm{Mg}(\mathrm{OH})_2\) is used as an antacid. If a person, suffering from acidity, produces \(2.5 \mathrm{~L}\) of Gastric juice in a day, approximately how many antacid tablets, each containing \(600 \mathrm{~mg}\) of $$\mathrm{Mg}...

\(5.8 \mathrm{~g}\) of a gas maintained at \(95^{\circ} \mathrm{C}\) occupies the same volume as \(0.368 \mathrm{~g}\) of hydrogen gas maintained at a temperature of \(17^{\circ} \mathrm{C}\) and pressure being the same atmospheric pressure...

Gaseous Nitrous oxide decomposes at \(298 \mathrm{~K}\) to form Nitrogen gas and Oxygen gas. The \(\Delta \mathbf{H}\) for the reaction at \(1.0 \mathrm{~atm}\) pressure and \(298 \mathrm{~K}\) is \(\mathbf{- 1 6 3 . 1 5} \mathbf{~ k J}\). ...

A Gas taken in a closed vessel is heated from \(54^{\circ} \mathrm{C}\) to \(1254^{\circ} \mathrm{C}\). The pressure of the gas becomes ___________ times its original pressure \(\mathrm{P_1}\)

\(f(x)=2 x-\tan ^{-1} x-\log (x+\sqrt{x^2+1}) \text { is monotonically increasing, when }\)

If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is

The altitude of a cone is \(20 \mathrm{~cm}\) and its semi vertical angle is \(30^{\circ}\). If the semi vertical angle is increasing at the rate of \(2^0\) per second, then the radius of the base is increasing at the rate of

The function \(f(x)=\frac{x}{2}+\frac{2}{x}\) has a local minimum at

The area bounded by the curve \(y^2=4 a^2(x-1)\) and the lines \(x=1, y=4 a\) is

The area of the upper half of the circle whose equation is \((x-1)^2+y^2=1\) is given by

The centre of the circle passing through \((0,0)\) and \((1,0)\) and touching the circle \(x^2+y^2=9\) is

If the conjugate of \((x+i y)(1-2 i)\) be \(1+i\), then

\(\int_0^2\left|x^2+2 x-3\right| d x \text { is equal to }\)

The sum of the degree and order of the following differential equation \(\left[1-\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{2}}=k x \frac{d^2 y}{d x^2}\)

The general solution of the differential equation \(\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y\)

The solution of the differential equation \(\frac{d y}{d x}+y \cos x=\frac{1}{2} \sin 2 x\)

The particular solution of \(e^{\frac{d y}{d x}}=2 x+1\) given that \(y=1\) when \(x=0\) is

\(\text { If } f(x)=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^x}\right) \text { then } f^{\prime}(0) \text { is equal to }\)

If \(f(x)=\frac{(x+1)^7 \sqrt{1+x^2}}{\left(x^2-x+1\right)^6}\) then the value of \(f^{\prime}(0)\) is equal to

If the length of the major axis of an ellipse is 3 times the length of the minor axis, then its eccentricity is

The range of \(x\) which satisfy the inequation : \(-5 \leq \frac{2-3 x}{4} \leq 9\) is

The distance between the foci of a hyperbola is 16 and its eccentricity is \(\sqrt{2}\). Then its equation is

\(\int x^x(1+\log x) d x\) is equal to

\(\int e^x\left(1+\tan x+\tan ^2 x\right) d x \text { is equal to }\)

\(\int \sqrt{\operatorname{cosec} x-1} d x=\)

\(\int \frac{\cos 4 x+1}{\cot x-\tan x} d x=\)

\(\text { The value of } \sin ^{-1}\left[\cos \left(39 \frac{\pi}{5}\right)\right] \text { is }\)

\(\text { Let } f(x)=\cos ^{-1}(3 x-1) \text {, then domain of } f(x) \text { is equal to }\)

$$
\text { The function defined by } f(x)=\left\{\begin{array}{cc}
\frac{\sin x}{x}+\cos x & x>0 \\
-5 k & x=0 \\
\frac{4(1-\sqrt{1-x})}{x} & x<0
\end{array} \quad \text { is continous at } x=0, \quad \text { then } k\right. \text { equals ...

\(\lim _\limits{x \rightarrow 0} \frac{a^x-b^x}{x} \text { is equal to }\)

The minimum value of \(Z=3 x+5 y\), given subject to the constraints \(x+y \geq 2, x+3 y \geq 3, x, y \geq 0\) is

If $$2 A+3 B=\left[\begin{array}{ccc}2 & -1 & 4 \\ 3 & 2 & 5\end{array}\right]$$ and $$A+2 B=\left[\begin{array}{lll}5 & 0 & 3 \\ 1 & 6 & 2\end{array}\right]$$ then \(B=\)

$$
\text { If } A=\left(\begin{array}{ll}
1 & 2 \\
0 & 1
\end{array}\right) \quad P=\left(\begin{array}{cc}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta
\end{array}\right) \quad Q=P^T A P, \quad \text { then } P Q^{2014} P^T \tex...

\(A\) and \(B\) are invertible matrices of the same order such that \(\left|(A B)^{-1}\right|=8\) if \(|A|=2\) then \(|B|\) is

Solution of \(x-y+z=4 ; x-2 y+2 z=9\) and \(2 x+y+3 z=1\) is

If $$\left[\begin{array}{ccc}2+x & 3 & 4 \\ 1 & -1 & 2 \\ x & 1 & -5\end{array}\right]$$ is a singular matrix, then \(x\) is

How many factors of \(2^5 \times 3^6 \times 5^2\) are perfect squares?

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. The number of ways in which he can choo...

In a 12 storey house, 10 people enter a lift cabin. It is known that they will leave the lift in pre-decided groups of 2, 3 & 5 people at different storeys. The number of ways they can do so if the lift does not stop up to the second storey...

Bag A contains 3 white and 2 red balls. Bag B contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from bag A and put into bag B. However if tail appears then 2 balls are drawn at random from bag...

\(\text { If } P(B)=\frac{3}{5} \quad P(A / B)=\frac{1}{2} \text { and } P(A \cup B)=\frac{4}{5} \text { then } P(A \cup B)^{\prime}+P\left(A^{\prime} \cup B\right)=\)

The probability distribution of a discrete random variable X is given as

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overfl...

A die is thrown twice and the sum of numbers appearing is observed to be 8 . What is the conditional probability that the number 5 has appeared atleast once?

18 Points are indicated on the perimeter of a triangle \(\mathrm{ABC}\) as shown below. If three points are chosen then probability that it will from a triangle is