For \[x\in \mathbf{R},\left| \left| x \right| \right|\] is defined as follows: \[\left\| x \right\|=\left\{ \begin{align} & x+1,0\le x<2 \\ & \left| x-4 \right|,x\ge 2 \\ \end{align} \right.\] Then the solution set of the equation \[{{\left\| x \right\|}^{2}}+x=\left\| x \right\|+{{x}^{2}}\]is
Consider a circle with its centre lying on the focus of the parabola \[{{y}^{2}}\text{ }=\text{ }2px\] such that it touches the directrix of the parabola. Then a point of intersection of the circle and the parabola is
A circle is given by \[{{x}^{2}}+{{(y-1)}^{2}}=\text{ }1,\] another circle C touches it externally and also the x-axis, then the locus of its centre is
If \[{{r}_{1}}\] and \[{{r}_{2}}\] are the distances from the origin of points on the curve \[10(z\bar{z})-3i\{{{z}^{2}}-{{(\bar{z})}^{2}}\}-6=0\]. Which are at maximum and minimum distance from the origin then the value of \[{{r}_{1}}+{{r}_{2}}\] is equal to
A hat contains a number of cards with 30% white on both sides, 50% black on one side and white on the other side, 20% black on both sides. The cards are mixed up, and a single card is drawn at random and placed on the table. Its upper side shows up black. The probability that it's other side is also black is
Let \[f(x)=a{{x}^{3}}+b{{x}^{2}}+cx+d,\,a>0,a,b,c,d\in R\] and \[f(x)=0\] has all roots of repeated nature. If \[g(x)=f'(x)-f''(x)+f'''(x)\] then \[\forall \,x\in R\]
Let \[{{z}_{1}},{{z}_{2}}\] be two complex numbers represented by points on the circles \[~\left| z \right|=1\] and \[\left| z \right|\text{=}2\] respectively, then which of the following is incorrect
Let \[P=\left[ \begin{matrix} 3 & -1 & -2 \\ 2 & 0 & \alpha \\ 3 & -5 & 0 \\ \end{matrix} \right]\] , where \[\alpha \in \mathbb{R}.\]suppose \[Q=[{{q}_{ij}}]\] is a matrix such that PQ=kI, where \[\operatorname{k}\in \mathbb{R}.\],\[\operatorname{k}\ne 0\]and I is the identity matrix of order 3. If \[{{\operatorname{q}}_{23}}=-\frac{k}{8}\] and \[\det (Q)=\frac{{{k}^{2}}}{2},\]then which of the following is incorrect
At a given instant, say \[t=0,\] two radioactive substances A and B have equal activates. The ratio \[\frac{{{R}_{B}}}{{{R}_{A}}}\] of their activates after time t itself decays with time t as \[{{e}^{-\,\,3t}},\] If the half-life of A is ln2, the half- life of B is:
A power transmission line feeds input power at 2300 V to a step down transformer with its primary winding- having 4000 turns. The output power is delivered ? 230 V by the transformer. If the current in the primary of the transformer is 5 A and its efficiency is 90%, the output current would be:
The energy associated with electric field is \[\text{(}{{\text{U}}_{\text{E}}}\text{)}\] and with magnetic field is \[\text{(}{{\text{U}}_{\text{B}}}\text{)}\] for an electromagnetic wave in free space. Then:
A particle having the same charge as of electron Moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric filed of 100 V/m makes it to move in a straight path, then particle is (given charge of electron \[=1.6\times {{10}^{-19}}C\])
Two point charge \[{{q}_{1}}\left( \sqrt{10}\mu C \right)\] and \[{{q}_{2}}(-25\mu C)\] are placed on the x-axis at \[x=1m\] and \[x=4m\] respectively. The electric filed (inV/m) at a point \[y=3m\] on y-axis is: \[\left[ \text{take}\frac{1}{4\pi {{\varepsilon }_{0}}}=9\times {{10}^{9}}N{{m}^{2}}{{C}^{-\,2}} \right]\]
Ge and Si diodes start conducting at 0.3 V and 0.7 V respectively. In the following figure if Ge diode connection are reversed, the value of \[{{\text{V}}_{o}}\] by : (assume that the Ge diode has large breakdown voltage)
The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 \[{{m}^{3}}\] water per minute through a circular opening of 2 cm radius in its wall. The depth of the opening from the level of water in the tank is close to:
The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth \[=6.4\times {{10}^{3}}\text{km}\]) is \[{{\text{E}}_{\text{1}}}\]and kinetic energy required for the satellite to be in a circular orbit at this height is \[{{\text{E}}_{\text{2}}}\] are The value of h for which \[{{\text{E}}_{\text{1}}}\] and \[{{\text{E}}_{\text{2}}}\]are equal is:
Two Carnot engines 'A and B are operated in series. The first one, A, receives heat at \[{{T}_{1}}\](= 600 K) and rejects to a reservoir at temperature\[{{T}_{2}}\]. The second engine B receives heat rejected by the first engine and, in turns, rejects to a heat reservoir at \[{{T}_{3}}\](= 400 K). Calculate the temperature\[{{T}_{2}}\] if the work outputs of the two engines are equal:
A series AC circuit containing an inductor (20 mH), a capacitor\[(120\mu F)\] and a resistor \[(60\,\Omega )\]is driven by an AC source of 24 V/50 Hz. The energy dissipated in the circuit in 60 s is:
A particle is executing simple harmonic motion (SHM) of amplitude A, along the \[x-\] axis, about \[x=0.\] When its potential energy (PE) equals kinetic energy (KE), the position of the particle will be:
A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of \[45{}^\circ \] at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is \[(g=10\text{m}{{\text{s}}^{-2}})\]
A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature \[27{}^\circ \text{C}\text{.}\] Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about: [Take \[R=8.3J/K\]mole]
In a Young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength \[\lambda =500\] is incident on the slits. The total number of bright fringes that are observed in the angular range \[-30{}^\circ \le \theta \le 30{}^\circ \] is:
Two plane mirrors are inclined to each other such that a ray of light incident to the first mirror \[({{M}_{1}})\] and parallel to the second mirror \[({{M}_{2}})\] is finally reflected from the second mirror\[({{M}_{2}})\] parallel to the first mirror \[({{M}_{1}})\]. The angle between the two mirrors will be:
A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of 30: from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal \[(\text{in}\,\text{rad}\,{{\text{s}}^{-\,1}})\]will \[(g=10\text{m}{{\text{s}}^{-\,2}}).\]
One of the two identical conducing wires of length L is bent in the form of a circular loop and the other one into a circular coil' of N identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop \[({{B}_{L}})\]to that at the centre of the coil \[({{B}_{C}}),\,ie.\frac{\text{BL}}{\text{BC}}\]will be:
(I) When copper ore is mixed with silica, in a reverberatory furnace copper matte is produced. The copper matte contains sulphides of copper (II) and iron (II).
(II) Zone refining is based on the principle that impurities are more soluble in molten metal than m solid metal.
(III) In the metallurgy of aluminium, graphite anode is oxidised to carbon monoxide and carbon dioxide.
Among the following statements which is INCORRECT:
A)
In the preparation of compounds of Xe, Bartlett had taken \[{{O}_{2}}Pt{{F}_{6}}\] as a base compound because both \[{{O}_{2}}\] and Xe have almost same. ionisation enthalpy.
doneclear
B)
Nitrogen does not show allotropy.
doneclear
C)
A brown ring is formed to the ring test for \[N{{O}_{3}}^{-}\] ion. It is due to the formation of \[{{[Fe\,{{({{H}_{2}}O)}_{5}}\,(NO)]}^{2+}}\]
doneclear
D)
On heating with concentrated NaOH solution in an inert atmosphere of \[C{{O}_{2}}\] red phosphorus gives \[P{{H}_{3}}\] gas.
For a given reaction A\[\to \]Product, rate is \[1\times {{10}^{-\,4}}M{{s}^{-1}}\] when \[[A]=0.01\,\,M\]and rate is \[1.41\times {{10}^{-\,4}}M{{s}^{-1}}\]when \[[A]=0.02\,\,M.\] Hence, rate law is:
The electrode potentials for \[C{{u}^{2\,+}}_{(aq)}+{{e}^{-}}\xrightarrow{{}}C{{u}^{+}}_{(aq)}\] and \[C{{u}^{+}}_{(aq)}+{{e}^{-}}\xrightarrow{{}}C{{u}^{+}}_{(s)}\] are \[+\,0.15\,V\] and \[+\,0.50\,V\] respectively The value of \[E{{{}^\circ }_{C{{u}^{2\,+}}/Cu}}\]will be:
\[{{H}_{2}}S\] reacts with lead acetate forming a black compound which reacts with \[{{H}_{2}}{{O}_{2}}\] to form another compound. The colour of the compound is:
In FCC lattice A, B, C, D atoms, are arranged at comers, face centres, octahedral voids and tetrahedral voids respectively, then the body diagonal contains:
The enantiomeric excess and observed specific rotation of a mixture containing 6 gm of \[(+)-2-\]butanol and 4 (gm) of \[(-)-2-\]butanol are respectively (If the specific rotation of enantiomerically pure \[(+)-2-\]butanol is\[+\,13.5\,\text{unit}\]).
Given below is a diagrammatic sketch of a portion of human male reproductive system. Select the correct set of the names of the parts labelled A, B, C, D
\[P(a,b)\]is a points in the first quadrant. Circles are drawn through P touching the coordinate axes, such that the length of common chord of these circle is maximum. The possible values of \[a/b\]is
If \[f(x)\] be a real valued function defined by \[2f(\tan x)+f(\cot \,x)=x;x\in R-\left\{ \frac{n\pi }{2},n\in I \right\}\] then \[\int\limits_{0}^{1}{f(x)}dx+\frac{1}{2}\ell n\,2\] is equal to
A certain polynomial \[P(x),\text{ }x~\in R\] when divided by \[x-a,\,x-b,\,x-c\] leaves remainders \[a,\text{ }b,\text{ }c\] respectively. The remainder when P(x) is divided by \[(x-a)(x-b)(x-c)\,\]is (a, b, c are distinct)
The point of intersection of two tangents to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], the product of whose slopes is \[{{c}^{2}},\]lies on the curve.
A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance ?L/2? from its centre on both sides, it reduces the oscillation frequency by 20%. The value of ratio m/M is close to:
Charge is distributed within a sphere of radius R with a volume charge density \[\rho (r)=\frac{A}{{{r}^{2}}}{{e}^{-2r/a}},\]where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:
A parallel palate capacitor with square plates is filled with four dielectrics of dielectric constants \[{{K}_{1,}}\]\[{{K}_{2,}}\]\[{{K}_{3,}}\] \[{{K}_{4,}}\] arranged as shown in the figure. The effective dielectric constant K will be:
The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 1" respectively. When the screw gauge is fully tightene. without any object, the zero of its circular scale lie 3 divisions below the mean line. The readings of the main scale and the circular scale for a thin sheet, are 5.5 mm and 48 respectively, the thickness of this sheet is:
A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to:
In a car race on straight road, car A takes a time 't' less than car B at the finish and passes finishing point with a speed V more than that of car B. Both the cars from rest from rest and travel with constant acceleration \[a{{ }_{1}}\] and \[a{{ }_{2}}\] respectively. Then 'v' is equal to:
The magnetic filed associated with a light wave is given, at b by \[B={{B}_{0}}[\sin (3.14\times {{10}^{7}})ct+\sin \,(6.28\times {{10}^{7}})ct]\]. If this light falls on a silver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the photo electrons?
In the given internal resistance of the 18 V cell is negligible .If \[{{R}_{1}}=400\] \[\Omega ,\] \[{{R}_{3}}=100\Omega \] and \[{{R}_{4}}=500\Omega \]and the reading of an ideal voltmeter Across \[{{R}_{4}}\]is 5 V, then the value of \[{{R}_{2}}\] will be:
In a communication system operating at wavelength 800 nm, only one percent of source frequency is available as signal bandwidth. The number of channels accommodated for transmitting TV signals of band width 6 MHz are (Take velocity of light \[c=3\times {{10}^{8}}\] m/s, \[h=6.6\times {{10}^{-34}}\] J-s)
The position co-ordinates of a particle moving in a 3-D coordinates system is given by \[x=a\,\cos \,\omega t\], \[y=a\,\sin \,\omega t\] and \[z=\,a\omega t\] The speed of the" particle is:
Electrode potential for Zn electrode varies according to the equation.\[{{E}_{Z{{n}^{2+}}|Zn}}=E_{Z{{n}^{2+}}|Zn}^{^{{}^\circ }}-\frac{0.059}{2}\log \frac{1}{\left[ Z{{n}^{2+}} \right]}.\] The graph of \[{{E}_{Z{{n}^{2+}}|Zn}}\,vs\,\,\log \left[ Z{{n}^{2+}} \right]\]is
Graph between \[log\text{ }K\] and \[\frac{1}{T}\] [Where K is rate constant \[\left( {{S}^{^{-1}}} \right)\] and T is temperature (K)] is a straight line with \[OX=5,\,\theta ={{\tan }^{-1}}\left[ -\frac{1}{2.303} \right]\]
Hence \[{{E}_{a}}\] and log A respectively will be:
(I) \[{{\left[ MnC{{l}_{6}} \right]}^{3-}},\,{{\left[ Fe{{F}_{6}} \right]}^{3-}}\] and \[{{\left[ Co{{F}_{6}} \right]}^{3-}}\] are paramagnetic having four, five and four unpaired electrons respectively.
(II) Valence bond theory gives a quantitative interpretation of the thermodynamic stabilities of coordination compounds.
(III) The crystal field splitting \[{{\Delta }_{{}^\circ }},\] depends upon the field produced by the ligand and charge on the metal ion. Amongs the following correct statements are:
\[1\,mol\,C{{H}_{3}}COOH\] is added in \[250\text{ }g\] benzene. Acetic acid dimerises in benzene due to hydrogen bond. \[{{K}_{b}}\]of benzene Is \[2\,\,K\,\,kgmo{{l}^{-1}}.\] The boiling point has increased by \[6.4K.\text{ }%\] dimerisation of acetic acid is :
\[{{S}_{1}}:\] Trans-But-2-ene has higher boiling point than cis-But-2-ene. \[{{S}_{2}}:\,\,1,\,\]4-Dichiorobenzene has zero dipole moment. \[{{S}_{3}}:\,\] Trans cyclodecene is more stable as compare to cis-cyclodecene. \[{{S}_{4}}:\,\]Trans 1, 2-Dibromoethene is more soluble in water than cis-1, 2-Dibromoethene.
Compound \[X\left( {{C}_{3}}{{H}_{6}}O \right)\] gives negative tests with the following reagents, [a] \[B{{r}_{2}}\] [b)]\[2,\,\,4\]Dinitrophenylhydrazine [c] Na metal. It gives two monochloro structural isomers. Identify \['X'.\]
[a] The female of many primates, including humans have ............... (i).............. Cycle, in which the ................ (ii).............. is shed. [b] Whereas other animals have........... (iii) Cycle. [c] During the first 14 days of the menstrual cycle growth of the follicle is promoted by........... (iv)
A married couple adopted a male child. A few years later twin boys were born to them. The blood group of the couple is AB positive and O negative. The blood group of the three sons is A positive, B positive and O positive. The blood group of the adopted son is -
A)
O positive
doneclear
B)
A positive
doneclear
C)
B positive
doneclear
D)
Cannot be determined on the basis of the given data
Match the names of disease listed under column-I with meanings given under column-II, choose the answer which give the correct combination of the alphabets of the columns.
ABC dominant genes are required for production of purple colour of flower in a plant. A purple plant with genotype AABBCC crossed with a colourless plant with genotype aabbcc produces purple colour in \[{{F}_{1}}\]hybrid. On selfing of \[{{F}_{1}}\]- what proportion of coloured offspring in \[{{F}_{2}}.\]