Given, \[HF+{{H}_{2}}O\xrightarrow{{{K}_{a}}}{{H}_{3}}{{O}^{+}}+{{F}^{-}};\] \[{{F}^{-}}+{{H}_{2}}O\xrightarrow{{{K}_{b}}}HF+O{{H}^{-}}.\] Which relation is correct
In an amino acid, the carboxyl group ionises at \[pK\,\,{{a}_{1}}=2.34\] and ammonium ion at \[pK\,\,{{a}_{2}}=9.60\]. The isoelectric point the amino acid is at pH
AB, \[{{A}_{2}}\] and \[{{B}_{2}}\]are diatomic molecules. If the bond enthalpies of \[{{A}_{2}},\]AB and \[{{B}_{2}}\]are in the ratio \[1:1\text{ }:0.5\] and enthalpy of formation of AB from \[{{A}_{2}}\] and \[{{B}_{2}}\]is \[-100kJ\,mo{{l}^{-1}}\]. What is the bond energy of \[{{A}_{2}}:\] :
If the following half cells have the \[E{}^\circ \] values as \[F{{e}^{+3}}+{{e}^{-}}\xrightarrow{{}}F{{e}^{+2}};\] \[{{E}^{o}}=+0.77V\] and \[F{{e}^{+2}}+2{{e}^{-}}\xrightarrow{{}}Fe;\]\[{{E}^{o}}=-0.44V.\]The \[{{E}^{o}}\] of the half cell \[F{{e}^{+3}}+3{{e}^{-}}\xrightarrow{{}}Fe\] will be
A metal which is not affected by cone. \[{{H}_{2}}S{{O}_{4}},HN{{O}_{3}}\] or alkalis forms a compound X. This compound X can be used to give a complex which finds its application for toning in photography? The metal is
An aqueous solution of colourless metal sulphate M gives a white precipitate with \[N{{H}_{4}}OH\]. This was soluble in excess of \[N{{H}_{4}}OH\]. On passing \[{{H}_{2}}S\] through this solution a white ppt. is formed. The metal M in the salt is
A laboratory reagent imparts green colour to the flame. heating with solid \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\] and cone. \[{{H}_{2}}S{{O}_{4}}\] it evolves a red gas. Identify the reagent
\[1\,mol\] of \[{{N}_{2}}\] and \[3\text{ }mol\] of \[{{H}_{2}}\] are placed in a closed container at a pressure of 4 atm. The pressure falls to 3 atm at the same temperature when the following equilibrium is attained \[{{N}_{2}}(g)+3{{H}_{2}}(g)2N{{H}_{3}}(g).\] The \[{{K}_{P}}\] for the dissociation of \[N{{H}_{3}}\] is
\[0.5\text{ }g\] mixture of \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\] and \[KMn{{O}_{4}}\] was treated with excess of \[KI\] in acidic medium. \[{{I}_{2}}\] liberated required \[100c{{m}^{3}}\] of \[0.15N\]. \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\] solution for titration. The percentage amount of \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\] in the mixture is
A d. c. supply of 120V is connected to a large resistance X. A voltmeter of resistance \[10\,k\Omega \] placed in series in the circuit reads 4V. What is the value of X?
An insect trapped in a circular groove of radius\[12\text{ }cm\]. Moves along the groove steadily and completes 7 revolutions in 100 sec. What is the linear speed of the motion
The period of the satellite of the earth orbiting very near to the surface of the earth is \[{{T}_{0}}\]. What is the period of the geostationary satellite in terms of \[{{T}_{0}}\]
An engine has an efficiency of \[1/6\]. When the temperature of sink is reduced by \[{{62}^{o}}C,\] its efficiency is doubled. Temperatures of source and sink are
The radius of curvature of a thin plano-convex lens is 10 cm (of curved surface) and the refractive index is\[1.5\]. If the plane surface is silvered, then it behaves like a concave mirror of focal length
The circular head of a screw gauge is divided into 200 divisions and move \[1\text{ }mm\] ahead in one revolution. If the same instrument has a zero error of- \[0.05\text{ }mm\] and the reading on the main scale in measuring diameter of a wire is \[6\text{ }mm\] and that on circular scale is 45. The diameter of the wire is
Ammeter and voltmeter readings were recorded as \[0.25\text{ }A\]and \[0.5\text{ }V\] during the experiment to determine the resistance of a given wire using Ohm's law. The correct value of the resistance is
The adjacent figure shows the position graph of one dimensional motion of a particle of mass 4 kg. The impulse at \[t=0\,s\] and \[t=4\]is given respectively as:
The following observations were taken while comparing the e.m.f s of two primary cells using a potentiometer. Balance point when \[{{E}_{1}}\] (Leclanche cell) in the circuit (\[{{\ell }_{1}}\]in cm) \[=350\] Balance point when \[{{E}_{2}}\] (Daniel cell) is the circuit (\[{{\ell }_{2}}\] in cm) \[=275\] The ratio \[({{E}_{1}}/{{E}_{2}})\] of emfs is approximately
A photon materializes into an electron-positron pair. The kinetic energy of the electron is found to be \[0.19\text{ }MeV\]. What was the energy of the photon?
Lights of two different frequencies, whose photons have energies \[1\text{ }eV\] and \[2.5\text{ }eV\] respectively successively illuminate a metal whose work function is \[0.5\text{ }eV\] The ratio of the maximum speeds of the emitted electrons will be
DIRECTIONS (Qs 51): Read the following passage and answer the questions that follows
A block of mass \[15\text{ }kg\] is placed over a frictionless horizontal surface. Another block of mass \[10\text{ }kg\] is placed over it, that is connected with a light string passing over two pulleys fastened to the \[15\text{ }kg\] block. A force \[F=80N\]is applied horizontally to the free end of the string. Friction coefficient between two blocks is\[0.6\]. The portion of the string between \[10kg\] block and the upper pulley is horizontal. Pulley string and connecting rods are massless. (Take \[g=10\text{ }m/{{s}^{2}}\])
The magnitude of acceleration of the \[10\text{ }kg\] block is
DIRECTIONS (Qs 52): Read the following passage and answer the questions that follows
A block of mass \[15\text{ }kg\] is placed over a frictionless horizontal surface. Another block of mass \[10\text{ }kg\] is placed over it, that is connected with a light string passing over two pulleys fastened to the \[15\text{ }kg\] block. A force \[F=80N\]is applied horizontally to the free end of the string. Friction coefficient between two blocks is\[0.6\]. The portion of the string between \[10kg\] block and the upper pulley is horizontal. Pulley string and connecting rods are massless. (Take \[g=10\text{ }m/{{s}^{2}}\])
If applied force \[F=120\text{ }N,\]then magnitude of acceleration of \[15\text{ }kg\] block will be-
DIRECTIONS (Qs. 53): Each of these questions contains two statements: Statements -1 (Assertion) and Statement -2 (Reason). Choose the correct answer (ONLY ONE option correct) from the following.
Statement-1: When two semiconductor of p and n type are brought in contact, they form p-n junction which act like a rectifier.
Statement-2: A rectifier is used to convert alternating current into direct current.
A)
Statement-1 is false, Statement - 2 is true.
doneclear
B)
Statement-1 is false, Statement - 2 is true. Statement-2 is a correct explanation for Statement-1.
doneclear
C)
Statement-1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1
DIRECTIONS (Qs. 54): Each of these questions contains two statements: Statements -1 (Assertion) and Statement -2 (Reason). Choose the correct answer (ONLY ONE option correct) from the following.
Statement 1: A nucleus at rest splits into two nuclear parts having radii in the ratio\[1:2\]. Their velocities will be in the ratio \[8:1\].
Statement 2: The radius of a nucleus is proportional to the cube root of its mass number.
A)
Statement-1 is false, Statement - 2 is true.
doneclear
B)
Statement-1 is false, Statement - 2 is true. Statement-2 is a correct explanation for Statement-1.
doneclear
C)
Statement-1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1
A plate of mass (M) is placed on a horizontal frictionless surface and a body of mass (m) is placed on this plate. The coefficient of dynamic friction between this body and the plate is \[\mu \]. If a force \[3\mu mg\] is applied to the body of mass (m) along the horizontal, the acceleration of the plate will be
Two rods of length \[{{d}_{1}}\]and \[{{d}_{2}}\] and coefficients of thermal conductivities \[{{K}_{1}}\]and \[{{K}_{2}}\] are kept touching each other. Both have the same area of cross-section the equivalent of thermal conductivity is
Two masses A and B of \[10\text{ }kg\] and \[5\text{ }kg\] respectively are connected with a string passing over a frictionless pulley fixed at the corner of a table (as shown in figure). The coefficient of friction between the table and the block is\[0.2\]. The minimum mass of C that may be placed on A to prevent it from moving is equal to
A particle starts S.H.M. from the mean position. Its amplitude is a and total energy E. At one instant5 its kinetic energy is \[3\text{ }E/4,\] its displacement at this instant is
Two long parallel wires P and Q are both perpendicular to the plane of the paper with distance of 5 m between them. If P and Q carry current of \[2.5\] amp and 5 amp respectively in the same direction, then the magnetic field at a point half-way between the wires is
In a circuit L, C and R are connected in series with an alternating voltage source of frequency f The current leads the voltage by \[{{45}^{o}}\]. The value of C is
\[\lambda \]for which \[\frac{x-2}{-3}=\frac{y-4}{7}=\frac{z-8}{\lambda }\] and\[\frac{x-1}{\lambda }=\frac{y-2}{-3}=\frac{z-3}{6}\] are perpendicular equals
If \[a,\,\,\,b,\,\,\,c\] are in \[A.P.,\,\,\,b,\,\,\,c,\,\,\,d\] are in \[GP.\] and \[c,\,\,\,d,\,\,\,e\] are in \[H.P.\] then \[a,\,\,\,c,\,\,\,e\] are in
DIRECTION (Qs. 80): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct answer (ONLY ONE option is correct) from the following-
DIRECTION (Qs. 81): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct answer (ONLY ONE option is correct) from the following-
Statement-1: Range of\[f(x)=\sqrt{4-{{x}^{2}}}\]is\[[0,\,\,2]\].
Statement-2: \[f(x)\] is increasing for \[0\le x\le 2\] and decreasing for\[-2\le x\le 0\].
A)
Statement-1 is false, Statement-2 is true.
doneclear
B)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
doneclear
C)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
DIRECTION (Qs. 82): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct answer (ONLY ONE option is correct) from the following-
Let \[x,\,\,\,y,\,\,\,z\] are three integers lying between \[1\] and \[9\] such that \[x\,51,\,\,\,y\,41\] and \[z\,31\] are three digit numbers.
Statement-1: The value of the determinant\[\left| \begin{matrix} 5 & 4 & 3 \\ x\,51 & y\,41 & z\,31 \\ x & y & z \\ \end{matrix} \right|is\,\,zero\].
Statement-2: The value of a determinant is zero if the entries in any two rows (or columns) of the determinant are correspondingly proportional.
A)
Statement-1 is false, Statement-2 is true.
doneclear
B)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
doneclear
C)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
DIRECTION (Qs. 83): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct answer (ONLY ONE option is correct) from the following-
Statement-1: Slope of tangents drawn from \[(4,\,\,10)\]) to parabola\[{{y}^{2}}=9x\]are\[\frac{1}{4},\,\,\frac{9}{4}\]
Statement-2: Every parabola is symmetric about its directrix
A)
Statement-1 is false, Statement-2 is true.
doneclear
B)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
doneclear
C)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
DIRECTION (Qs. 84): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct answer (ONLY ONE option is correct) from the following-
Statement-1 : If \[{{x}^{2}}+x+1=0\] then the value of\[{{\left( x+\frac{1}{x} \right)}^{2}}+{{\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)}^{2}}+...+\left( {{x}^{27}}+\frac{1}{{{x}^{27}}} \right)\,\,\text{is}\,\,54.\]
Statement-2: \[\omega ,\,\,\,{{\omega }^{2}}\] are the roots of given equation and\[x+\frac{1}{x}=-1,\,\,{{x}^{2}}+\frac{1}{{{x}^{2}}}=-1,\,\,{{x}^{3}}+\frac{1}{{{x}^{3}}}=2\]
A)
Statement-1 is false, Statement-2 is true.
doneclear
B)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
doneclear
C)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
An inverted cone is 10 cm in diameter and \[10\,\,cm\] deep. Water is poured into it at the rate of \[4c{{m}^{3}}/\min \]. When the depth of water level is \[6\,\,cm\], then it is rising at the rate