COMEDK 2023 Morning Shift
Paper was held on Sun, May 28, 2023 4:30 AM
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Chemistry

Which of the following hexoses will form the same osazone when treated with excess phenyl hydrazine?
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Product of the following reaction is
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Acetophenone when reacted with a base, $$\mathrm{C}_2 \mathrm{H}_5 \mathrm{ONa}$$, yields a stable compound which has th
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Gabriel's synthesis is used frequency for the preparation of which of the following?
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The product P in the reaction,
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Pick out the incorrect statement(s) from the following. 1. Glucose exists in two different crystalline forms, $$\alpha$$
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Which of the following is incorrect?
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Rank the following compounds in order of increasing basicity.
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Ammoniacal silver nitrate forms a white precipitate easily with
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Consider the following equilibrium, $$\begin{aligned} & 2 \mathrm{No}(g) \rightleftharpoons \mathrm{N}_2+\mathrm{O}_2 ;
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Which of the following is incorrect regarding Henry's law?
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$$t$$-butyl chloride preferably undergo hydrolysis by
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Which of these represents the correct order of decreasing bond order?
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In a $$0.2 \mathrm{~M}$$ aqueous solution, lactic acid is $$6.9 \%$$ dissociated. The value of dissociation constant is
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Pick up the correct statement.
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Total number of $$\sigma$$ and $$\pi$$ bonds in ethene molecule is
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A buffer solution has equal volumes of $$0.1 \mathrm{~M} \mathrm{~NH}_4 \mathrm{OH}$$ and $$0.01 \mathrm{~M} \mathrm{~NH
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Assuming no change in volume, the time required to obtain solution of $$\mathrm{pH}=4$$ by electrolysis of $$100 \mathrm
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Which of the following compounds would not be expected to decarboxylate when heated?
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Which of these molecules have non-bonding electron pairs on the cental atom? $$\mathrm{I}: \mathrm{SF}_4 : \mathrm{II}:
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For a cell reaction, $$A(s)+B^{2+}(a q) \longrightarrow A^{2+}(a q)+B(s)$$; the standard emf of the cell is $$0.295 \mat
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Which of the following shows negative deviation from Raoult's law?
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$$5 \mathrm{~g}$$ of non-volatile water soluble compound $$X$$ is dissolved in $$100 \mathrm{~g}$$ of water. The elevati
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The correct decreasing order of negative electron gain enthalpy for $$\mathrm{C}, \mathrm{Ca}, \mathrm{Al}, \mathrm{F}$$
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I and II are
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$$\mathrm{Ti}^{2+}$$ is purple while $$\mathrm{Ti}^{4+}$$ is colourless because
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In Friedal-Crafts alkylation reaction of phenol with chloromethane, the product formed will be
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Which among the following is diamagnetic?
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Which one of the following is an important component of chlorophyll?
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A volatile compound is formed by carbon monoxide and
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The complex $$\left[\mathrm{PtCl}_2(\mathrm{en})_2\right]^{2+}$$ ion shows
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$$15 \mathrm{~g}$$ of $$\mathrm{CaCO}_3$$ completely reacts with
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Bohr's radius of 2 nd orbit of $$\mathrm{Be}^{3+}$$ is equal to that of
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How much faster would a reaction proceed at $$25^{\circ} \mathrm{C}$$ than at $$0^{\circ} \mathrm{C}$$ if the activation
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The blue colouration obtained from the Lassaigne's test of nitrogen is due to the formation of
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The ion that is isoelectronic with $$\mathrm{CO}$$ is
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At $$300 \mathrm{~K}$$, the half-life period of a gaseous reaction at an initial pressure of $$40 \mathrm{~kPa}$$ is 350
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If 2 moles of $$\mathrm{C}_6 \mathrm{H}_6(\mathrm{~g})$$ are completely burnt $$4100 \mathrm{~kJ}$$ of heat is liberated
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Abnormal colligative properties are observed only when the dissolved non-volatile solute in a given dilute solution
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Aqueous $$\mathrm{CuSO}_4$$ changes its colour from sky blue to deep blue on addition of $$\mathrm{NH}_3$$ because
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Identify A, B and C.
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For a reaction, $$2 A+B \longrightarrow$$ products, If concentration of $$B$$ is kept constant and concentration of $$A$
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For an adiabatic change in a system, the condition which is applicable is
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In dilute alkaline solution $$\mathrm{MnO}_4^{-}$$ changes to
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Which of the following complex show optical isomerism? (i) $$c i s-\left[\mathrm{COCl}(\mathrm{en})_2\left(\mathrm{NH}_3
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Mohr's salt has the formula
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Mathematics

The value of $$a^{\log _b c}-c^{\log _b a}$$, where $$a, b, c>0$$ but $$a, b, c \neq 1$$, is
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The slope of the tangent to the curve, $$y=x^2-x y$$ at $$\left(1, \frac{1}{2}\right)$$ is
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The value of $$\lim _\limits{x \rightarrow 0} \frac{e^{a x}-e^{b x}}{2 x}$$ is equal to
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The points of intersection of circles $$(x+1)^2+y^2=4$$ and $$(x-1)^2+y^2=9$$ are $$(a, \pm b)$$, then $$(a, b)$$ equals
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The approximate value of $$f(5.001)$$, where $$f(x)=x^3-7 x^2+10$$
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The circle $$x^2+y^2+3 x-y+2=0$$ cuts an intercept on $$X$$-axis of length
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Let $$f(x)=a+(x-4)^{\frac{4}{9}}$$, then minima of $$f(x)$$ is
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If $$f(x) = \left\{ {\matrix{ {2\sin x} & ; & { - \pi \le x \le {{ - \pi } \over 2}} \cr {a\sin x + b} & ; & {
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The value of $$\lim _\limits{x \rightarrow \infty}\left(\frac{x^2-2 x+1}{x^2-4 x+2}\right)^{2 x}$$ is
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$$S \equiv x^2+y^2-2 x-4 y-4=0$$ and $$S^{\prime} \equiv x^2+y^2-4 x-2 y-16=0$$ are two circles the point $$(-2,-1)$$ li
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A number $$\mathrm{n}$$ is chosen at random from $$s=\{1,2,3, \ldots, 50\}$$. Let $$\mathrm{A}=\{n \in s: n$$ is a squar
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The feasible region for the inequations $$x+2 y \geq 4,2 x+y \leq 6, x, y \geq 0$$ is
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The maximum value of $$Z=10 x+16 y$$, subject to constraints $$x \geq 0, y \geq 0, x+y \leq 12,2 x+y \leq 20$$ is
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If $$A=\left[\begin{array}{ll}2 & 2 \\ 3 & 4\end{array}\right]$$, then $$A^{-1}$$ equals to
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If $$A$$ is a matrix of order $$4 \operatorname{such}$$ that $$A(\operatorname{adj} A)=10 \mathrm{~I}$$, then $$|\operat
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If $$A=\left[\begin{array}{cc}k+1 & 2 \\ 4 & k-1\end{array}\right]$$ is a singular matrix, then possible values of $$\ma
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The angle between the vectors $$\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ and $$\mathbf{b}=\ha
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If the vectors $$\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} ; \mathbf{b}=\hat{\mathbf{i}}+2 \ha
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The maximum value of $$Z=12 x+13 y$$, subject to constraints $$x \geq 0, y \geq 0, x+y \leq 5$$ and $$3 x+y \leq 9$$ is
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$$\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}$$ and $$
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The place $$x-2 y+z=0$$ is parallel to the line
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$$\int \frac{x d x}{2(1+x)^{3 / 2}}$$ is equal to
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$$\int \frac{4^x}{\sqrt{1-16^x}} d x$$ is equal to
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$$\int\limits_{-\pi / 2}^{\pi / 2} \sin ^2 x d x$$ is equal to
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The lines $$\frac{x-1}{2}=\frac{y-4}{4}=\frac{z-2}{3}$$ and $$\frac{1-x}{1}=\frac{y-2}{5}=\frac{3-z}{a}$$ are perpendicu
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If two lines $$L_1: \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$$ and $$L_2: \frac{x-3}{1}=\frac{y-k}{2}=z$$ intersect at
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A five-digits number is formed by using the digits $$1,2,3,4,5$$ with no repetition. The probability that the numbers 1
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If a number $n$ is chosen at random from the set $$\{11,12,13, \ldots \ldots, 30\}$$. Then, the probability that $$n$$ i
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Three vertices are chosen randomly from the nine vertices of a regular 9-sided polygon. The probability that they form t
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If $$A, B$$ and $$C$$ are mutually exclusive and exhaustive events of a random experiment such that $$P(B)=\frac{3}{2} P
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Using mathematical induction, the numbers $$a_n \delta$$ are defined by $$a_0=1, a_{n+1}=3 n^2+n+a_n, (n \geq 0)$$. Then
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If $$49^n+16^n+k$$ is divisible by 64 for $$n \in N$$, then the least negative integral value of $$k$$ is
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$$2^{3 n}-7 n-1 \text { is divisible by }$$
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The sum of $$n$$ terms of the series, $$\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+\ldots$$ is
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The value of $$\frac{1}{2 !}+\frac{2}{3 !}+\ldots+\frac{99}{100 !}$$ is equal to
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If the sum of 12th and 22nd terms of an AP is 100, then the sum of the first 33 terms of an $$\mathrm{AP}$$ is
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The differential equation of all non-vertical lines in a plane is
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The general solution of $$\left(\frac{d y}{d x}\right)^2=1-x^2-y^2+x^2 y^2$$ is
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The solution of the differential equation $$\left(\frac{d y}{d x}\right) \tan y=\sin (x+y)+\sin (x-y)$$ is
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$$\text { Find }{ }^n C_{21} \text {, if }{ }^n C_{10}={ }^n C_{12}$$
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In a trial, the probability of success is twice the probability of failure. In six trials, the probability of at most tw
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If $$\cos A=m \cos B$$ and $$\cot \left(\frac{A+B}{2}\right)=\lambda \tan \left(\frac{B-A}{2}\right)$$, then $$\lambda$$
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The expression $$\frac{2 \tan A}{1-\cot A}+\frac{2 \cot A}{1-\tan A}$$ can be written as
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The general solution of $$2 \cos 4 x+\sin ^2 2 x=0$$ is
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If $$2 f\left(x^2\right)+3 f\left(\frac{1}{x^2}\right)=x^2-1, \forall x \in R-\{0\}$$, then $$f\left(x^8\right)$$ is equ
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If $$A=\{a, b, c\}, B=\{b, c, d\}$$ and $$C=\{a, d, c\}$$ then $$(A-B) \times(B \cap C)$$ is equal to
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If $$n(A)=p$$ and $$n(B)=q$$, then the numbers of relations from the set $$A$$ to the set $$B$$ is
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If $$z=\sqrt{3}+i$$, then the argument of $$z^2 e^{z-i}$$ is equal to
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If $$i=\sqrt{-1}$$ and $$n$$ is a positive integer, then $$i^n+i^{n+1}+i^{n+2}+i^{n+3}$$ is equal to
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If $$\left(\frac{3}{2}+i \frac{\sqrt{3}}{2}\right)^{50}=3^{25}(x+i y)$$, where $$x$$ and $$y$$ are real, then the ordere
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There are 10 points in a plane out of which 4 points are collinear. How many straight lines can be drawn by joining any
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The total number of numbers greater than 1000 but less than 4000 that can be formed using 0, 2, 3, 4 (using repetition a
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A polygon of n sides has 105 diagonals, then n is equal to
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Let the equation of pair of lines $$y=m_1 x$$ and $$y=m_2 x$$ can be written as $$\left(y-m_1 x\right)\left(y-m_2 x\righ
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The distance of the point $$(3,4)$$ from the line $$3 x+2 y+7=0$$ measured along the line parallel to $$y-2 x+7=0$$ is e
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The slope of lines which makes an angle $$60^{\circ}$$ with the line $$y-3 x+18=0$$
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3 and 5 are intercepts of a line $$L=0$$, then the distance of $$L=0$$ from $$(3,7)$$ is
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The total number of terms in the expansion of $$(x+y)^{60}+(x-y)^{60}$$ is
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The coefficient of $$x^{29}$$ in the expansion of $$\left(1-3 x+3 x^2-x^3\right)^{15}$$ is
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In the expansion of $$\left(1+3 x+3 x^2+x^3\right)^{2 n}$$, the term which has greatest binomial coefficient, is
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Physics

The mean energy per molecule for a diatomic gas is
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The phase difference between displacement and velocity of a particle in simple harmonic motion is
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The mass density of a nucleus varies with mass number $$A$$ as
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A capacitor of capacity $$2 ~\mu \mathrm{F}$$ is charged upto a potential $$14 \mathrm{~V}$$ and then connected in paral
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The ratio of amplitude of magnetic field to the amplitude of electric field of an electromagnetic wave propagating in va
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A particle is projected at an angle $$30^{\circ}$$ with horizontal having kinetic energy $$K$$. The kinetic energy of th
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An air bubble in water $$\left(\mu=\frac{4}{3}\right)$$ is shown in figure. The apparent depth of the image of the bubbl
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A transistor is connected in CE configuration. The collector supply is $$10 \mathrm{~V}$$ and the voltage drop across a
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One end of the string of length $l$ is connected to a particle of mass $$m$$ and the other end is connected to a small p
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A thin circular ring of mass ,$$M$$ and radius $$R$$ rotates about an axis through its centre and perpendicular to its p
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Two wire of same material having radius in ratio 2 : 1 and lengths in ratio 1: 2. If same force is applied on them, then
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In the figure, pendulum bob on left side is pulled a side to a height $$h$$ from its initial position. After it is relea
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A gas is taken through the cycle $$A \rightarrow B \rightarrow C \rightarrow A$$, as shown in figure. What is the net wo
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The gases carbon monoxide $$(\mathrm{CO})$$ and nitrogen at the same temperature have kinetic energies $$E_1$$ and $$E_2
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Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $$A$$ and the
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Starting from the centre of the earth having radius $$R$$, the variation of $$g$$ (acceleration due to gravity) is shown
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A long spring, when stretched by a distance $$x$$, has potential energy $$U$$. On increasing the stretching to $$n x$$,
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With what velocity should an observer approach a stationary sound source, so that the apparent frequency of sound should
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A dielectric of dielectric constant $$K$$ is introduced such that half of its area of a capacitor of capacitance $$C$$ i
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Two very long straight parallel wires carry currents $$i$$ and $$2 i$$ in opposite directions. The distance between the
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The magnetic flux linked with a coil satisfies the relation $$\phi=\left(4 t^2+6 t+9\right) \mathrm{Wb}$$, where $$t$$ i
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The instantaneous values of alternating current and voltages in a circuit given as $$\begin{aligned} & i=\frac{1}{\sqrt{
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A car is moving towards a high cliff. The car driver sounds a horn of frequency $$f$$. The reflected sound heard by the
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If escape velocity on earth surface is $$11.1 \mathrm{~kmh}^{-1}$$, then find the escape velocity on moon surface. If ma
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An ideal gas goes from state $$A$$ to state $$B$$ via three different processes as indicated in the $$p$$-$$V$$ diagram.
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In the series L-C-R circuit shown, the impedance is
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In Young's double slit interference experiment, using two coherent waves of different amplitudes, the intensities ratio
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The wavelength of the first line of Lyman series for $$\mathrm{H}$$ - atom is equal to that of the second line of Balmer
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If $$150 \mathrm{~J}$$ of heat is added to a system and the work done by the system is $$110 \mathrm{~J}$$, then change
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In the figure below, the capacitance of each capacitor is $$3 \mu \mathrm{F}$$. The effective capacitance between $$A$$
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The first emission of hydrogen atomic spectrum in Lyman series appears at a wavelength of
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In Young's double slit experiment, the ratio of maximum and minimum intensities in the fringe system is $$9: 1$$. The ra
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In the case of an inductor
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The height vertically above the earth's surface at which the acceleration due to gravity becomes $$1 \%$$ of its value a
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If $$C$$ be the capacitance and $$V$$ be the electric potential, then the dimensional formula of $$\mathrm{CV}^2$$ is
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Which logic gate is represented by the following combination logic gates?
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An LED is constructed from a $$p$$-$$n$$ junction diode using GaAsP. The energy gap is $$1.9 \mathrm{~eV}$$. The wavelen
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A body is projected vertically upwards. The times corresponding to height $$h$$ while ascending and while descending are
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When a certain metal surface is illuminated with light of frequency $$\nu$$, the stopping potential for photoelectric cu
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A fish in water (refractive index $$n$$ ) looks at a bird vertically above in the air. If $$y$$ is the height of the bir
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A car starts from rest and accelerates uniformly to a speed of $$180 \mathrm{~kmh}^{-1}$$ in $$10 \mathrm{~s}$$. The dis
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A plane electromagnetic wave of frequency $$20 \mathrm{~MHz}$$ travels through a space along $$x$$-direction. If the ele
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The sides of a parallelogram are represented by vectors $$\vec{p}=5 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+3 \hat{\mathbf{k
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If $$\theta_1$$ and $$\theta_2$$ be the apparent angles of dip observed in two vertical planes at right angles to each o
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Let $$K_1$$ be the maximum kinetic energy of photoelectrons emitted by light of wavelength $$\lambda_1$$ and $$K_2$$ cor
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A ball is projected horizontally with a velocity of $$5 \mathrm{~ms}^{-1}$$ from the top of a building $$19.6 \mathrm{~m
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A galvanometer having a resistance of $$8 \Omega$$ is shunted by a wire of resistance $$2 \Omega$$. If the total current
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In the diagram shown below, $$m_1$$ and $$m_2$$ are the masses of two particles and $$x_1$$ and $$x_2$$ are their respec
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A block of wood floats in water with $$(4 / 5)$$ th of its volume submerged. If the same block just floats in a liquid,
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A balloon with mass $m$ is descending down with an acceleration $$a$$ (where, $$a
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A straight wire of length $$2 \mathrm{~m}$$ carries a current of $$10 \mathrm{~A}$$. If this wire is placed in uniform m
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Two slabs are of the thicknesses $$d_1$$ and $$d_2$$. Their thermal conductivities are $$K_1$$ and $$K_2$$, respectively
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A square wire of each side l carries a current $$I$$. The magnetic field at the mid-point of the square
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A cylinder of radius $$r$$ and of thermal conductivity $$K_1$$ is surrounded by a cylindrical shell of inner radius $$r$
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The speeds of air-flow on the upper and lower surfaces of a wing of an aeroplane are $$v_1$$ and $$v_2$$, respectively.
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Two cells with the same emf $$E$$ and different internal resistances $$r_1$$ and $$r_2$$ are connected in series to an e
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A string vibrates with a frequency of $$200 \mathrm{~Hz}$$. When its length is doubled and tension is altered, it begins
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When $$10^{19}$$ electrons are removed from a neutral metal plate, the electric charge on it is
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In an electrical circuit $$R, L, C$$ and $$\mathrm{AC}$$ voltage source are all connected in series. When $$L$$ is remov
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