VITEEE 2021
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Chemistry

What is the total number of electrons that can have the values $$n=2, l=1, s=1 / 2$$ in the electronic configuration $$1
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Calculate the wavelength associated with an electron moving with a velocity of $$10^6 \mathrm{~m} / \mathrm{s}$$ (mass o
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Which of the following pairs is not correctly matched?
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The orbital diagram in which Aufbau principle is violated is
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How does electron affinity change when we move from left to right in a period in the Periodic Table?
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Which of the following statements is not correct?
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Which of the following statements is correct?
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Which of the following oxides of group 16 has the highest boiling point?
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Specify the coordination number of cobalt in $$\left[\mathrm{Co}(\mathrm{CN})\left(\mathrm{H}_2 \mathrm{O}\right)(\mathr
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Which of the following complexes is square planar and diamagnetic?
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Which type of isomerism is exhibited by $$\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_2 \mathrm{Cl}_2\right]$$ ?
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When a cation leaves its normal position in the crystal and moves to some interstitial space, the defect in the crystal
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In thermodynamics, a quantity whose value simply depends upon the initial and final state of the system is called
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If $$\Delta H$$ and $$\Delta S$$ are positive for a reaction, the reaction will be spontaneous only when
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A catalyst is a substance which
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Consider the reaction, $$2 \mathrm{~N}_2 \mathrm{O}_5(g) \longrightarrow 4 \mathrm{NO}_2(g)+\mathrm{O}_2(g)$$ The rate l
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The $$[\mathrm{OH}]^{-}$$ in a solution is $$1 \mathrm{~mol} \mathrm{~L}^{-1}$$. The $$\mathrm{pH}$$ of the solution is
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The solubility of $$\mathrm{Fe}(\mathrm{OH})_3$$ is $$x \mathrm{~mol} \mathrm{~L}^{-1}$$. Its $$K_{\mathrm{sp}}$$ would
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When an electrolytic solution conducts electricity, the current is carried by
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An electrochemical cell has two half cell reactions as, $$\begin{aligned} A^{2+}+2 e^{-} & \longrightarrow A ; E_{A^{2+}
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The number of optical isomers of the compound $$\mathrm{CH}_3 \mathrm{CHBrCHBrCOOH}$$ is
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Which of the following compounds will exhibit cis-trans (geometrical) isomerism?
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The hybridization of carbon atoms in $$\mathrm{C}-\mathrm{C}$$ single bond of $$\mathrm{HC} \equiv \mathrm{C}-\mathrm{CH
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Which of the following groups is ortho and para directing?
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Phenol on treatment with conc. $$\mathrm{HNO}_3$$ gives
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Which of the following compounds will be formed when methoxy benzene is reacted with $$\mathrm{HBr}$$ ?
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When ethanol and $$\mathrm{I}_2$$ are heated in the presence of $$\mathrm{Na}_2 \mathrm{CO}_3$$, the yellow crystals obt
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Identify B in the following series of reaction $$\mathrm{CH}_3 \mathrm{CHO} \xrightarrow{\mathrm{CH}_3 \mathrm{MgX}} A \
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Among the following, the least reactive aldehyde is
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Propanal on reaction with lithium aluminium hydride gives
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Identify Z in the following sequence $$\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{I} \xrightarrow{\mathrm{KCN}} X \xrightarrow{
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Treatment of aniline with bromine water produces
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Which of the following compounds has maximum acidic character?
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$$\mathrm{C}_6 \mathrm{H}_5 \mathrm{COCl} \xrightarrow{\mathrm{NH}_3} X \xrightarrow{\mathrm{P}_2 \mathrm{O}_5} Y \xrigh
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Chlorobenzene can be prepared by reacting aniline with
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Electrolysis of an aqueous solution of sodium ethanoate gives
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The reaction given below is an example of which of the following? $$2 \mathrm{CH}_3 \mathrm{Br}+2 \mathrm{Na} \xrightarr
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Which of the following is least reactive to nitration?
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Nucleic acids are polymers of
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Which of the following enzymes helps in digestion of proteins?
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English

I can write with .............. hand.
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Your friend ............. too much.
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We bought ............. books.
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Select the antonym for the word 'Bane'.
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Pick out the correct synonym of the word 'Treason'.
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Mathematics

The value of $$\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left\{\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+
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If $$\theta=\frac{\pi}{2^n+1}$$, then the value of $$2^n \cos \theta \cos 2 \theta \cos 2^2 \theta \ldots \cos 2^{n-1} \
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Using the principal values, the value of $$\sin ^{-1}\left\{\sin \frac{5 \pi}{6}\right\}+\tan ^{-1}\left\{\tan \frac{\pi
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Find the value of $$\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{3}{5}\right)$$.
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If $$A=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right]$$, then $$\left(A-A^{\prime}\right)$$ is equal to (wher
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If $$A^{-1}=\left[\begin{array}{rr}5 & -2 \\ -7 & 3\end{array}\right]$$ and $$B^{-1}=\frac{1}{2}\left[\begin{array}{rr}9
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$$\lim _\limits{x \rightarrow 0}\left\{\tan \left(\frac{\pi}{4}+x\right)\right\}^{1 / x}$$ is equal to
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The value of $$\lim _\limits{n \rightarrow \infty}\left\{\frac{1+2+3+\ldots+n}{n+2}-\frac{n}{2}\right\}$$ is
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If $$y=1+\frac{x}{1 !}+\frac{x^2}{2 !}+\frac{x^3}{3 !} \ldots$$, then $$\frac{d y}{d x}$$ is equal to
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The value of $$\frac{d}{d x}\left(x^n \log _a x e^x\right)$$ is
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The interval in which the function $$f(x)=\sin x-\cos x, 0 \leq x \leq 2 \pi$$ is strictly decreasing, is
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The slope of normal to the curve $$y=x^3+2 x+6$$ which is parallel to line $$x+14 y+4=0$$ is
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If $$f(x)=\left\{\begin{array}{cc}\frac{(1-\cos 4 x)}{x^2}, & \text { if } x 0\end{array}\right.$$ then $$f(x)$$ is con
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The value of $$\int\limits_0^{\pi / 2} \frac{d x}{1+\tan x}$$ is
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Evaluate $$\int \frac{3 x-2}{(x+3)(x+1)^2} d x$$.
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The general solution of the linear differential equation $$\frac{d y}{d x}+\sec x \cdot y=\tan x\left(0 \leq x \leq \fra
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On solving the differential equation $$x^2 y d x-\left(x^3+y^3\right) d y=0$$, the value of $$\log y$$ is
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The particular solution of the differential equation $$\frac{d y}{d x}+y \cot x=2 x+x^2 \cot x$$, such that $$y(\pi / 2)
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The area bounded by the circle $$x^2+y^2=16$$ and the line $$y=x$$ in the first quadrant is
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The focal distance of the point $$(x, y)$$ from the ellipse $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$$ is
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The equation of a straight line which cuts off intercept on $$X$$-axis which is twice that on $$Y$$-axis and is at a uni
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The equation of a straight line upon which the length of the perpendicular from the origin is 5 and slope of this perpen
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The radius of the circle $$(x \cos \theta+y \sin \theta-a)^2+(x \sin \theta-y \cos \theta-b)^2=k^2$$ is
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The locus of a point which moves in a plane such that its distance from a fixed point in the plane is always equal to it
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The eccentricity of the ellipse $$25 x^2+9 y^2-150 x-90 y+225=0$$ is
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A bag contains 50 tickets numbered $$1,2,3, ..., 50$$ of which five are drawn at random and arranged in ascending order
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Five persons entered the lift cabin on the ground floor of an eight floor house. Suppose that each of them independently
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If $$(3,4,-1)$$ and $$(-1,2,3)$$ be end points of the diameter of a sphere, then the radius of the sphere is
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The following lines are $$\begin{aligned} \mathbf{r} & =(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\lambda^{\prime}(\hat{\mathb
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The position vector of a point $$R$$ which divides the line joining $$P(6,3,-2)$$ and $$Q(3,1,-4)$$ in the ratio $$2 : 1
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The angle between the lines $$\frac{x-5}{-3}=\frac{y+3}{-4}=\frac{z-7}{0}, \frac{x}{1}=\frac{y-1}{-2}=\frac{z-6}{2}$$ is
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The cartesian product $$A \times A$$ has 9 elements among which are found $$(-1,0)$$ and $$(0,1)$$, then set $$A$$ is eq
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If $$S=\{(a, b): b=|a-1|, a \in Z$$ and $$|a|
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The quotient of the identity function by the reciprocal function is given by
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Which of the following is not a function?
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If $$(1+i)(2 i+1)(1+3 i) \ldots(1+n i)=x+i y$$, then $$2 \cdot 5 \cdot 10 \ldots\left(1+n^2\right)$$ is equal to
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The non-zero solutions of the equation $$z^2+|z|=0$$, where $$z$$ is a complex number, are
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The coefficient of the term independent of $$x$$ in the expansion $$\left(\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x
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Which of the following is the correct principle of Mathematical induction?
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The negation of $$\sim s \vee(\sim r \wedge s)$$ is equivalent to
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Physics

The Young's modulus of a rope of $$10 \mathrm{~m}$$ length and having diameter of $$2 \mathrm{~cm}$$ is $$200 \times 10^
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The zeroth law of thermodynamics for three systems $$A, B$$ and $$C$$ in contact demands that
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The velocity of sound in a gas is $$1300 \mathrm{~m} / \mathrm{s}$$ at STP and specific heat at constant pressure is $$6
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The net electric force on a charge of $$+3 \mu \mathrm{C}$$ at the mid-point on the line joining two charges of magnitud
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A parallel plate capacitor of capacitance $$5 \mu \mathrm{F}$$ is charged to $$120 \mathrm{~V}$$ and then connected to a
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24 cells of emf $$1.5 \mathrm{~V}$$ each having internal resistance of $$1 \mathrm{~ohm}$$ are connected to an external
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Two straight wires each $$10 \mathrm{~cm}$$ long are parallel to one another and separated by $$2 \mathrm{~cm}$$. When t
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The alternating current in a circuit is given by $$I=50 \sin 314 t$$. The peak value and frequency of the current are
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A bar magnet of pole strength $$10 \mathrm{~Am}$$ is cut into two equal parts breadthwise. The pole strength of each mag
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A $$50 \mathrm{~Hz}$$ $$\mathrm{AC}$$ signal is applied in a circuit of inductance of $$(1 / \pi) \mathrm{H}$$ and resis
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The magnetic field at a point on the axis of a long solenoid having 5 turns per $$\mathrm{cm}$$ length when a current of
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An object is $$8 \mathrm{~cm}$$ high. It is desired to form a real image $$4 \mathrm{~cm}$$ high at $$60 \mathrm{~cm}$$
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When an object is placed $$40 \mathrm{~cm}$$ from a diverging lens, its virtual image is formed $$20 \mathrm{~cm}$$ from
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Polonium has a half-life of 140 days. If we take $$20 \mathrm{~g}$$ of polonium initially then the amount of it that rem
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According to Bohr model of hydrogen atom, only those orbits are permissible which satisfy the condition
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Einstein's photoelectric equation is
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The Brewster's law is given by the expression
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If two slits in Young's experiment are $$0.4 \mathrm{~mm}$$ apart and fringe width on a screen $$200 \mathrm{~cm}$$ away
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The distance of moon form the earth is $$3.8 \times 10^5 \mathrm{~km}$$. Supposing that the eye is most sensitive to the
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Which of the following logic gates are also known as the Universal gates?
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Based on the band theory of conductors, insulators and semi-conductors, the forbidden gap is smallest in
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The demodulator or detector circuit consists of a
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The power $$(P)$$ of an engine lifting a mass of $$100 \mathrm{~kg}$$ upto a height of $$10 \mathrm{~m}$$ in $$1 \mathrm
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A silver wire of radius $$0.1 \mathrm{~cm}$$ carries a current of $$2 \mathrm{~A}$$. If the charge density in silver is
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An electron revolves in a circle at the rate of $$10^{19}$$ rounds per second. The equivalent current is $$\left(e=1.6 \
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A hollow sphere of radius $$0.1 \mathrm{~m}$$ has a charge of $$5 \times 10^{-8} \mathrm{C}$$. The potential at a distan
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The efficiency of a Carnot engine kept at the temperatures of $$27^{\circ} \mathrm{C}$$ and $$127^{\circ} \mathrm{C}$$ i
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According to equipartition law of energy each particle in a system of particles have thermal energy $$E$$ equal to
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An electric charge does not have which of the following properties?
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Two identical capacitors are first connected in series and then in parallel. The ratio of equivalent capacitance is
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The horizontal and vertical components of earth's magnetic field at a place are $$0.3 \mathrm{G}$$ and $$0.52 \mathrm{G}
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A long straight wire is carrying a current of $$12 \mathrm{~A}$$. The magnetic field at a distance of $$8 \mathrm{~cm}$$
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The temperature coefficient of the resistance of a wire is 0.00125 per $${ }^{\circ} \mathrm{C}$$. At $$300 \mathrm{~K}$
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Which component of electromagnetic spectrum have maximum wavelength?
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The induced emf in a coil of $$10 \mathrm{H}$$ inductance in which current varies from $$9 \mathrm{~A}$$ to $$4 \mathrm{
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If the alternating current $$I=I_1 \cos \omega t+ I_2 \sin \omega t$$ then the rms current is given by
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A conductor of length $$5 \mathrm{~cm}$$ is moved parallel to itself with a speed of $$2 \mathrm{~m} / \mathrm{s}$$, per
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The Rutherford scattering experiment proves that an atom consists of
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Unpolarised light falls on two polarising sheets placed one on top of other. If the intensity of transmitted light is on
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A person has a minimum distance of distinct vision as $$50 \mathrm{~cm}$$. The power of lenses required to read a book a
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