question_answer2) In Youngs experiment, the third bright band for light of wavelength coincides with the fourth bright band for another source of light in the same arrangement. Then the wavelength of second source is
question_answer3) If the angle of minimum deviation is of\[{{60}^{o}}\]for an equilateral prism, then the refractive index of the material of the prism is
question_answer4) The wavelength of red light from He-Ne laser is 633 nm in air but 474 nm in the aqueous humor inside the eye ball. Then the speed of red light through the aqueous humor is
question_answer5) The radius of curvature of the convex face of a planoconvex lens is 15 cm and the refractive index of the material is 1.4. Then the power of the lens in dioptre is
question_answer6) The threshold wavelength for photoelectric emission from a material is \[4800\overset{\text{o}}{\mathop{\text{A}}}\,\] . Photoelectrons will be emitted from the material, when it is illuminated with light from a
question_answer8) The nuclear radius of a certain nucleus is 7.2 fm and it has charge of\[1.28\times {{10}^{-17}}C\]. The number of neutrons inside the nucleus is
question_answer10) A common emitter amplifier gives an output of 3 V for an input of 0.01 V. If\[\beta \]of the transistor is 100 and the input resistance is \[1\text{ }k\Omega ,\]then the collector resistance is
question_answer13) The resonance frequency of the tank circuit of an oscillator when\[L=\frac{10}{{{\pi }^{2}}}mH\] and\[C=0.04\text{ }\mu F\]are connected in parallel is
question_answer17) A signal wave of frequency 12 kHZ is modulated with a carrier wave of frequency 2.51 MHz. The upper and lower side band frequencies are respectively
question_answer21) A particle starts from rest at\[t=0\]and moves in a straight line with an acceleration as shown in figure. The velocity of the particle at \[t=3\text{ }s\] is
question_answer22) Two cars A and B are moving with same speed of 45 km/h along same direction. If a third car C coming from the opposite direction with a speed of 36 km/h meets two cars in an interval of 5 min, the distance of separation of two cars A and B should be (in km)
question_answer23) Two particles A and B are projected with same speed so that the ratio of their maximum heights reached is 3:1. If the speed of A is doubled without altering other parameters, the ratio of the horizontal ranges attained by A and B is
question_answer24) An object of mass 5 kg is attached to the hook of a spring balance and the balance is suspended vertically from the roof of a lift. The reading on the spring balance when the lift is going up with an acceleration of 0.25 \[m{{s}^{-2}}\]is \[(g=10\text{ }m{{s}^{-2}})\]
question_answer25) A particle acted upon by constant forces \[4\hat{i}+\hat{j}-3\hat{k}\] and\[3\hat{i}+\hat{j}-\hat{k}\]is displaced from the point\[\hat{i}+2\hat{j}+3\hat{k}\]to the, point\[5\hat{i}+4\hat{j}+\hat{k}\]. The total work done by the forces in SI unit is
question_answer26) Two bodies A and B have masses 20 kg and 5 kg respectively. Each one is acted upon by a force of 4 kg-wt. If they acquire the same kinetic energy in times\[{{t}_{A}}\]and\[{{t}_{B}},\]then the ratio\[\frac{{{t}_{A}}}{{{t}_{B}}}\]is
question_answer27) A bullet of mass 0.05 kg moving with a speed of\[80\text{ }m{{s}^{-1}}\]enters a wooden block and is stopped after a distance of 0.40 m. The average resistive force exerted by the block on the bellow is
question_answer28) A particle of mass 2 kg is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below. The velocity of the particle after 10 s is
question_answer29) The height of the dam, in a hydroelectric power station is 10 m. In order to generate 1 MW of electric power, the mass of water (in kg) that must fall per second on the blades of the turbines is
question_answer30) A spring gun of spring constant 90 N/cm is compressed 12 cm by a ball of mass 16 g. If the trigger is pulled, the velocity of the ball is
question_answer31) A particle is moving under the influence of a force given by\[F=kx,\]where k is a constant and\[x\]is the distance moved. The energy (in joules) gained by the particle in moving from \[x=0\]to\[x=3\]is
question_answer32) A thin circular ring of mass M and radius R rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity cd. Four small spheres each of mass m (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be
question_answer34) Three identical spheres, each of mass 3 kg are placed touching each other with their centres lying on a straight line. The centres of the sphere are marked at P, Q and R respectively. The distance of centre of mass of system from P is
question_answer35) Infinite number of masses, each 1 kg, are placed along the x-axis at\[x=\pm \text{ }1\text{ }m,\pm 2m,\pm \text{ }4\] \[m,\pm \text{ }8\text{ }m,\pm \text{ }16m....\]The magnitude of the resultant gravitational potential in terms of gravitational constant G at the origin\[(x=0)\]is
question_answer36) Three identical bodies of mass M are located at the vertices of an equilateral triangle of side L. They revolve under the effect of mutual gravitational force in a circular orbit, circumscribing the triangle while preserving the equilateral triangle. Their orbital velocity is
question_answer37) A satellite is revolving around the earth with a kinetic energy E. The minimum addition of kinetic energy needed to make it escape from its orbit is
question_answer38) Eight drops of a liquid of density p and each of radius a are falling through air with a constant velocity\[3.75\,cm{{s}^{-1}}\]. When the eight drops coalesce to form a single drop the terminal velocity of the new drop will be
question_answer39) If the volume of a block of aluminium is decreased by 1%, the pressure (stress) on its surface is increased by (Bulk modulus of \[Al=7.5\times {{10}^{10}}N{{m}^{-2}})\]
question_answer40) The excess pressure inside one soap bubble is three times that inside a second soap bubble, then the ratio of their surface areas is
question_answer41) The area of cross-section of one limb of an U-tube is twice that of other. Both the limbs contain mercury at the same level. Water is poured in the wider tube so that mercury level in it goes down by 1 cm. The height of water column is (density of water\[={{10}^{3}}\,kg\,{{m}^{-3}},\]density of mercury \[=13.6\times {{10}^{3}}\] \[kg{{m}^{-3}}\])
question_answer42) A bubble of 8 mole of helium is submerged at a certain depth in water. The temperature of water increases by\[{{30}^{o}}C\]. How much heat is added approximately to helium during expansion?
question_answer43) The plots of intensity of radiation versus wavelength of three black bodies at temperatures\[{{T}_{1}},{{T}_{2}}\]and\[{{T}_{3}}\]are shown. Then,
question_answer44) Three rods made of same material and having same cross-section are joined as shown in the figure. Each rod is of same length. The temperature at the junction of the three rods is
question_answer45) The p-V diagram of a gas undergoing a cyclic process (ABCDA) is shown in the graph where P is in units of\[N{{m}^{-2}}\]and V in\[c{{m}^{3}}\]. Identify the incorrect statement.
A)
0.4 J of work is done by the gas from A to B.
doneclear
B)
0.2 J of work is done on the gas from C and D.
doneclear
C)
No work is done by the gas from B to C.
doneclear
D)
Net work done by the gas in one cycle is 0.2 J.
doneclear
E)
Work is done by the gas in going from B to C and on the gas from D to A.
question_answer46) The period of a simple pendulum inside a stationary lift is T. The lift accelerates upwards with an acceleration of g/3. The time period of pendulum will be
question_answer50) A glass tube of length 1.0 m is completely filled with water. A vibrating tuning fork of frequency 500 Hz is kept over the mouth of the tube and the water is drained out slowly at the bottom of the tube. If velocity of sound in air is \[330\,m{{s}^{-1}},\] then the total number of resonances that occur will be
question_answer51) A bus is moving with a velocity of 5 ms towards a huge wall. The driver sounds a horn of frequency 165 Hz. If the speed of sound in air is\[335\text{ }m{{s}^{-1}},\] the number of beats heard per second by a passenger inside the bus will be
question_answer52) Two identical conducting spheres carrying different charges attract each other with a force F when placed in air medium at a distance d apart. The spheres are brought into contact and then taken to their original positions. Now the two spheres repel each other with a force whose magnitude is equal to that of the initial attractive force-The ratio between initial charges on the spheres is
question_answer53) Small drops of the same size are charged to V volt each. If n such drops coalesce to form a single large drop, its potential will be
question_answer54) A capacitor of capacitance value\[1\,\mu F\]is charged to 30 V and the battery is then disconnected. If the remaining circuit is connected across a\[2\,\mu F\]capacitor, the energy lost by the system is
question_answer55) An electric dipole of length 1 cm is placed with the axis making an angle of\[{{30}^{o}}\]to an electric field of strength\[{{10}^{4}}N{{C}^{-1}}\]. If it experiences a torque of\[10\sqrt{2}Nm,\]the potential energy of the dipole is
question_answer56) Three charges\[{{Q}_{0}},-q\]and\[-q\]are placed at the vertices of an isosceles right angle triangle as in the figure. The net electrostatic potential energy is zero if\[{{Q}_{0}}\]is equal to
question_answer58) The drift velocity of the electrons in a copper wire of length 2 m under the application of a potential difference of 220 V is\[0.5\text{ }m{{s}^{-1}}\]. Their mobility (in\[{{m}^{2}}{{V}^{-1}}{{s}^{-1}}\])
question_answer59) When two resistances \[{{R}_{1}}\] and \[{{R}_{2}}\] are connected in series, they consume 12 W power. When they are connected in parallel, they consume 50 W power. What the ratio of the powers of\[{{R}_{1}}\]and\[{{R}_{2}}\]?
question_answer60) In the circuit shown, if the resistance\[5\,\Omega \]develops a heat of 42 J per second, heat developed in 20 must be about (in\[J{{s}^{-1}}\])
question_answer61) When a Daniel cell is connected in the secondary circuit of a potentiometer, the balancing length is found to be 540 cm. If the balancing length becomes 500 cm when the cell is short circuited with \[1\,\Omega ,\] the internal of the cell is
question_answer62) Two particles of equal charges after being accelerated through the same potential difference enter a uniform transverse magnetic field and describe circular path of radii\[{{R}_{1}}\]and\[{{R}_{2}}\]respectively. Then the ratio of their masses\[({{M}_{1}}/{{M}_{2}})\]is
question_answer65) The oscillating frequency of a cyclotron is 10 MHz. If the radius of its dees is 0.5 m, the kinetic energy of a proton, which is accelerated by the cyclotron is
question_answer66) In a certain place, die horizontal component of magnetic field is\[\frac{1}{\sqrt{3}}\]times to vertical component. The angle of dip at this place is
question_answer67) An alternating voltage\[e=200\text{ }sin\text{ }100t\]is applied to a series combination\[R=30\,\Omega \]and an inductor of 400 mH. The power factor of the circuit is
question_answer68) The flux linked with a circuit is given by \[\phi ={{t}^{3}}+3t-7\]. The graph between time (\[x-\]axis) and induced emf (y-axis) will be a
question_answer70) A resistor \[30\,\Omega ,\] inductor of reactance \[10\,\Omega \] and capacitor of reactance \[10\,\Omega \] are connected in series to an AC voltage source\[e=300\sqrt{2}\,sin(\omega t)\]. The current in the circuit is
question_answer71) A plane electromagnetic wave travelling along the\[X-\]direction has a wavelength of 3 mm. The variation in the electric field occurs in the \[Y-\]direction with an amplitude\[66\,V{{m}^{-1}}\]. The equations for the electric and magnetic fields as a function of\[x\]and t are respectively.
question_answer72) A plane electromagnetic wave travels in free space along \[x-\]axis. At a particular point in space, the electric field along y-axis is\[9.3\text{ }V{{m}^{-1}}\]. The magnetic induction is
question_answer74) The dihalogen derivative X of a hydrocarbon with three carbon atoms reacts with alcoholic KOH and produces another hydrocarbon which forms a red precipitate with ammoniacal\[C{{u}_{2}}C{{l}_{2}}\]. X gives an aldehyde on reaction with aqueous KOH. The compound Jf is
question_answer75) An organic compound X with molecular formula,\[{{C}_{7}}{{H}_{8}}O\]is insoluble in aqueous \[NaHC{{O}_{3}}\]but dissolves in NaOH. When treated with bromine water X rapidly gives\[Y,{{C}_{7}}{{H}_{5}}OB{{r}_{3}}\]. The compounds X and V respectively, are
A)
benzyl alcohol and 2, 4, 6-tribromo-3- methoxy benzene
doneclear
B)
benzyl alcohol and 2, 4, 6-tribromo-3-methyl phenol
doneclear
C)
o-cresol and 3, 4, 5-tribromo-2-methyl phenol
doneclear
D)
methoxybenzene and 2, 4, 6-tribromo-3- methoxy benzene
question_answer83) \[MnO_{4}^{-}\] ions are reduced in acidic condition to \[M{{n}^{2+}}\]ions whereas they are reduced in neutral condition to\[Mn{{O}_{2}}\]. The oxidation of 25 mL of a solution X containing \[F{{e}^{2+}}\]ions required in acidic condition 20 mL of a solution Y containing\[Mn{{O}_{4}}\]ions. What volume of solution Y would be required to oxidise 25 mL of a solution X containing \[F{{e}^{2+}}\] ions in neutral condition?
question_answer87) A solid compound contains X, Y and Z atoms in a cubic lattice with X atom occupying the comers. Y atoms in the body centred positions and Z atoms at the centres of faces of the unit cell. What is the empirical formula of the compound?
question_answer88) \[KCl\]crystallises in the same type of lattice as does\[NaCl\]. Given that\[{{r}_{Na}}+/{{r}_{C{{l}^{-}}}}=0.55\]and\[{{r}_{{{K}^{+}}}}/{{r}_{C{{l}^{-}}}}=0.74\]. Calculate the ratio of the side of the unit cell for\[KCl\]to that of\[NaCl\].
question_answer89) The first ionisation energy of oxygen is less than that of nitrogen. Which of the following is the correct reason for this observation?
A)
Lesser effective nuclear charge of oxygen than nitrogen
doneclear
B)
Lesser atomic size of oxygen than nitrogen
doneclear
C)
Greater interelectron repulsion between two electrons in the same p-orbital counter balances the increase in effective nuclear charge on moving from nitrogen to oxygen
doneclear
D)
Greater effective nuclear charge of oxygen than nitrogen
question_answer98) Two radioactive elements X and Fhave half-lives of 6 min and 15 min respectively. An experiment starts with 8 times as many atoms of X as Y. How long it takes for the number of atoms of X left equals the number of atoms of Y left?
question_answer99) Using the following thermochemical equations (i) \[S(rh)+3/2{{O}_{2}}(g)\xrightarrow[{}]{{}}S{{O}_{3}}(g)\] \[\Delta H=-2x\,kJ\,mo{{l}^{-1}}\] (ii) \[S{{O}_{2}}(g)+1/2{{O}_{2}}(g)\xrightarrow{{}}S{{O}_{3}}(g)\] \[\Delta H=-y\,kJ\,mo{{l}^{-1}}\] Find out the heat of formation of\[S{{O}_{2}}(g)\]in kJ\[mo{{l}^{-1}}\].
question_answer101) 1.6 moles of\[PC{{l}_{5}}(g)\]is placed in\[4\text{ }d{{m}^{3}}\]closed vessel. When the temperature is raised to 500 K, it decomposes and at equilibrium 1.2 moles of\[PC{{l}_{5}}(g)\]remains. What is the\[{{K}_{c}}\]value for the decomposition of\[PC{{l}_{5}}(g)\]to\[PC{{l}_{3}}(g)\]and\[C{{l}_{2}}(g)\]at 500 K?
question_answer102) For a concentrated solution of a weak electrolyte\[{{A}_{x}}{{B}_{y}}\]By of concentration C, the degree of dissociation\[\alpha \]is given as
question_answer103) The relative lowering of vapour pressure of an aqueous solution containing non-volatile solute is 0.0125. The molality of the solution is
question_answer104) Two liquids X and Y form an ideal solution. The mixture has a vapour pressure of 400 mm at 300 K when mixed in the molar ratio of\[1:1\]and a vapour pressure of 350 mm when mixed in the molar ratio of\[1:2\]at the same temperature. The vapour pressures of the two pure liquids X and Y respectively are
question_answer106) The pH of a solution obtained by mixing 50 mL of\[1\text{ }N\text{ }HCl\]and 30 mL of\[1\text{ }N\text{ }NaOH\]is [log 2.5 = 0.3979]
question_answer108) For the two gaseous reactions, following data are given \[A\xrightarrow{{}}B;{{k}_{1}}={{10}^{10}}{{e}^{-20,000/T}}\] \[C\xrightarrow{{}}D;{{k}_{2}}={{10}^{12}}{{e}^{-24,606/T}}\] the temperature at which\[{{k}_{1}}\]becomes equal to \[{{k}_{2}}\]is
question_answer109) Plot of\[log\text{ }x/m\]against log p is a straight line inclined at an angle of\[45{}^\circ \]. When the pressure is 0.5 arm and Freundlich parameter. \[k\]is 10, the amount of solute adsorbed per gram of adsorbent will be\[(log\text{ }5=0.6990)\]
question_answer112) The two isomers X and Y with the formula \[Cr{{({{H}_{2}}O)}_{5}}ClB{{r}_{2}}\]were taken for experiment on depression in freezing point. It was found that one mole of X gave depression corresponding to 2 moles of particles and one mole of Y gave depression due to 3 moles of particles. The structural formulae of X and Y respectively are
question_answer118) An organic compound with molecular formula \[{{C}_{6}}{{H}_{12}}\]upon ozonolysis give only acetone as the product. The compound is
question_answer120) Acyclic stereoisomer having the molecular formula\[{{C}_{4}}{{H}_{7}}Cl\]are classified and tabulated. Find out the correct set of numbers.
question_answer124) In a certain town 25% families own a cell phone, 15% families own a scooter and 65% families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is
question_answer126) Let\[{{a}_{n}}={{i}^{{{(n+1)}^{2}}}},\]where\[i=\sqrt{-1}\]and\[n=1,2,3.....\]. Then the value of\[{{a}_{1}}+{{a}_{3}}+{{a}_{5}}+...+{{a}_{25}}\]is
question_answer127) If\[\frac{5{{z}_{2}}}{11{{z}_{1}}}\]is purely imaginary, then the value of\[\left[ \frac{2{{z}_{1}}+3{{z}_{2}}}{2{{z}_{1}}-3{{z}_{2}}} \right]\]is
question_answer131) If a is positive and if A and G are the arithmetic mean and the geometric mean of the roots of\[{{x}^{2}}-2ax+{{a}^{2}}=0\]respectively, then
question_answer132) Suppose that two persons A and B solve the equation\[{{x}^{2}}+ax+b=0\]. While solving A commits a mistake in the coefficient of\[x\]was taken as 15 in place of-9 and finds the roots as \[-7\]and\[-2\]. Then, the equation is
question_answer134) If\[\alpha ,\beta \]are the roots of the equation\[{{x}^{2}}+x+1=0,\]then the equation whose roots are\[{{\alpha }^{22}}\]and\[{{\beta }^{19}}\]is
question_answer135) If\[\sec \theta \]and\[\tan \theta \]are the roots of \[a{{x}^{2}}+bx+c=0;\]\[(a,b\ne 0)\]then the value of\[\sec \theta -\tan \theta \]is
question_answer138) Let a, b, c be in AP. If \[0<a,b,c<1,x=\sum\limits_{n=0}^{\infty }{{{a}^{n}}},\] \[y=\sum\limits_{n=0}^{\infty }{{{b}^{n}}}\]and\[z=\sum\limits_{n=0}^{\infty }{{{c}^{n}}},\]then
question_answer139) The sum of the first n terms of the series \[\frac{1}{\sqrt{2}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{11}}+.....\]is
question_answer145) The number of four-letter words that can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R, is
question_answer146) All the words that can be formed using alphabets A, H, L, U, R are written as in a dictionary (no alphabet is repeated). Then, the rank of the word RAHUL is
question_answer148) The value\[{{(}^{7}}{{C}_{0}}{{+}^{7}}{{C}_{1}})+{{(}^{7}}{{C}_{1}}{{+}^{7}}{{C}_{2}})+....\]\[+{{(}^{7}}{{C}_{6}}{{+}^{7}}{{C}_{7}})\]is
question_answer149) If the expansion of\[{{\left( \frac{3\sqrt{x}}{7}-\frac{5}{2x\sqrt{x}} \right)}^{13n}}\]contains a term independent of\[x\]in the 14th term, then n should be
question_answer150) If the matrix M, is given by \[{{M}_{r}}=\left[ \begin{matrix} r & r-1 \\ r-1 & r \\ \end{matrix} \right],r=1,2,3,....,\]then the value of\[\det ({{M}_{1}})+\det ({{M}_{2}})+....+\det ({{M}_{2008}})\] is
question_answer158) Let p be the statement Ravi races and let q be the statement Ravi wins. Then, the verbal translation of\[\tilde{\ }(p\vee (\tilde{\ }q))\]is
A)
Ravi does not race and Ravi does not win
doneclear
B)
It is not true that Ravi races and that Ravi does not win
doneclear
C)
Ravi does not race of Ravi wins
doneclear
D)
It is not true that Ravi races or that Ravi does not win
doneclear
E)
It is not true that Ravi does not race and Ravi does not win
question_answer169) In a triangle ABC,\[\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}.\]If\[a=\frac{1}{\sqrt{6}},\]then the area of the triangle (in square units) is
question_answer172) A flagpole stands on a building of height 450 ft and an observer on a level ground is 300 ft from the base of the building. The angle of elevation of the bottom of the flagpole is\[30{}^\circ \]and the height of the flagpole is 50 ft. If\[\theta \]is the angle of elevation of the top of the flagpole, then\[\tan \theta \]is equal to
question_answer174) If the line segment joining the points P (a, b) and Q (c, d) subtends an angle \[\theta \] at the origin, then the value of\[\cos \theta \]is
question_answer179) A line passes through the point of intersection of the lines\[100x+50y-1=0\]and\[75x+25y+\] \[3=0\]and makes equal intercepts on the axes. Its equation is
question_answer185) If the foci of the ellipse\[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{16}=1\]are\[(0,\sqrt{7})\]and\[(0,-\sqrt{7}),\]then the foci of the ellipse\[\frac{{{x}^{2}}}{9+{{t}^{2}}}+\frac{{{y}^{2}}}{16+{{t}^{2}}}=1\,t\in R,\]
question_answer186) If the lines joining the foci of the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}\,+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\] where\[a>b,\]and an extremly of its minor axis are inclined at an angle\[60{}^\circ ,\]then the eccentricity of the ellipse is
question_answer188) If\[\overrightarrow{a},\overrightarrow{b}\]and\[\overrightarrow{c}\]are position vectors of the vertices of the triangle ABC, then\[\frac{\left| \left( \overrightarrow{a}-\overrightarrow{c} \right)\times \left( \overrightarrow{b}-\overrightarrow{a} \right) \right|}{\left( \overrightarrow{c}-\overrightarrow{a} \right).\left( \overrightarrow{b}-\overrightarrow{a} \right)}\]is equal to
question_answer189) If\[\overrightarrow{a}\]is a vector of magnitude 50, collinear with the vector\[\overrightarrow{b}=6\hat{i}-8\hat{j}-\frac{15}{2}\hat{k}\]and makes an acute angle with the positive direction of\[z-\]axis, then a is equal to
question_answer190) If the volume of a parallelepiped with \[\overrightarrow{a}\times \overrightarrow{b},\text{ }\overrightarrow{b}\times \overrightarrow{c},\text{ }\overrightarrow{c}\times \overrightarrow{a}\] as cotermmus edges is\[9\text{ }cu\]units, then the volume of the parallelepiped with \[(a\times b)\times (b\times c),(b\times c)\times (c\times a),\] \[(c\times a)\times (a\times b)\]as coterminus edges is
question_answer191) If the constant forces\[2\hat{i}-5\hat{j}+6\hat{k}\]and \[-\hat{i}+2\hat{j}-\hat{k}\]act on a particle due to which it is displaced from a point\[A(4,-3,-2)\]to a point B \[(6,1,-3),\]then the work done by the forces is
question_answer193) A unit vector in\[xy-\]plane makes an angle of \[45{}^\circ \]with the vector\[\hat{i}+\hat{j}\]and an angle of\[60{}^\circ \]with the vector\[3\hat{i}-4\hat{j},\]is
question_answer194) Let a, b, c be distinct non-negative numbers. If the vector\[a\hat{i}+a\hat{j}+c\hat{k},\text{ }\hat{i}+\hat{k}\]and\[c\hat{i}+c\hat{j}+b\hat{k}\] lies in a plane, then c is
question_answer195) The equation of the plane perpendicular to the line\[\frac{x-1}{1}=\frac{y-2}{-1}=\frac{z+1}{2}\]and passing through the point (2, 3, 1) is
question_answer196) The coordinates of the foot of the perpendicular drawn from the point A (1, 0, 3) to the join of the points B (4, 7, 1) and C (3, 5, 3) are
question_answer197) If a line makes angles\[\alpha ,\beta ,\gamma \]and \[\delta \] with four diagonals of a cube, then the value of \[si{{n}^{2}}\alpha +si{{n}^{2}}\beta +si{{n}^{2}}\gamma +si{{n}^{2}}\delta \]is
question_answer198) If the planes\[\overrightarrow{r}.(2\hat{i}-\lambda \hat{j}+3\hat{k})=0\]and\[\overrightarrow{r}.(\lambda \hat{i}+5\hat{j}-\hat{k})=0\]are perpendicular to each other, then the value of\[{{\lambda }^{2}}+\lambda \]is
question_answer206) The standard deviation for the scores 1, 2, 3, 4, 5, 6 and 7 is 2. Then, the standard deviation of 12, 23, 34, 45, 56, 67 and 78 is
question_answer215) If\[f(x)=\frac{x-1}{4}+\frac{{{(x-1)}^{3}}}{12}+\frac{{{(x-1)}^{5}}}{20}\]\[+\frac{{{(x-1)}^{7}}}{28}+....,\]where\[0<x<2,\]then\[f(x)\]is equal to
question_answer218) Gas is being pumped into a spherical balloon at the rate of\[30\text{ }f{{t}^{3}}/min\]. Then, the rate at which the radius increases when it reaches the value 15ft is
question_answer221) A spherical iron ball of radius 10 cm, coated with a layer of ice of uniform thickness, melts at a rate of\[100\,\pi \,c{{m}^{3}}/min\]. The rate at which the thickness of decreases when the thickness of ice is 5 cm, is
question_answer224) Let\[g(x)=\left\{ \begin{matrix} 2e, & if\,x\le 1 \\ \log (x-1), & if\,x>1 \\ \end{matrix} \right..\]The equation of the normal to\[y=g(x)\]at the point ( 3, log 2), is