Solved papers for CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2009
done CEE Kerala Engineering Solved Paper-2009 Total Questions - 240
question_answer1) The percentage errors in the measurement of length and time period of a simple pendulum are 1% and 2% respectively. Then the maximum error in the measurement of acceleration due to gravity is
question_answer3) A body is falling freely under gravity. The distances covered by the body in first, second and third minute of its motion are in the ratio
question_answer4) A bullet fired into a fixed wooden block loses half of its velocity after penetrating 40 cm. It comes to rest after penetrating a further distance of
question_answer5) A ball A is thrown up vertically with a speed u and at the same instant another ball B is released from a height h. At time t, the speed of A relative to B is
question_answer6) A bullet is to be fired with a speed of 2000 \[m{{s}^{-1}}\]to hit a target 200 m away on a level ground. If\[g=10\text{ }m{{s}^{-2}},\]the gun should be aimed
question_answer7) The resultant of two vectors\[\overrightarrow{P}\]and\[\overrightarrow{Q}\]is\[\overrightarrow{R}\]. If the magnitude of\[\overrightarrow{Q}\]is doubled, the new resultant becomes perpendicular to\[\overrightarrow{P}\]. Then the magnitude of\[\overrightarrow{R}\]is
question_answer8) A motor car is moving with a speed of\[20\text{ }m{{s}^{-1}}\] on a circular track of radius 100 m. If its speed is increasing at the rate of\[3m{{s}^{-1}},\] its resultant acceleration is
question_answer9) A stationary body of mass 3 kg explodes into three equal pieces. Two of the pieces fly off in two mutually perpendicular directions, one with a velocity of\[3\hat{i}\,m{{s}^{-1}}\]and the other with a velocity of\[4\hat{j}\,m{{s}^{-1}}\]. If the explosion occurs in\[{{10}^{-4}}s,\]the average force acting on the third piece in newton is
question_answer10) A mass of 1 kg is just able to slide down the slope of an inclined rough surface when the angle of inclination is\[{{60}^{o}}\]. The minimum force necessary to pull the mass up the inclined plane\[(g=10m{{s}^{-2}})\]is
question_answer11) A block of mass m is resting on a smooth horizontal surface. One end of a uniform rope of mass\[\left( \frac{m}{3} \right)\]is fixed to the block, which is pulled in the horizontal direction by applying force F at the other end. The tension in the middle of the rope is
question_answer12) A particle is acted upon by a force F which varies with position\[x\]as shown in figure. If the particle at\[x=0\]has kinetic energy of \[25J,\] then the kinetic energy of the particle at \[x=16\text{ }m\]is
question_answer13) Two springs P and Q of force constants\[{{k}_{p}}\]and\[{{k}_{Q}}\] \[\left( {{k}_{Q}}=\frac{{{k}_{p}}}{2} \right)\]are stretched by applying forces of equal magnitude. If the energy stored in Q is E, then the energy stored in P is
question_answer14) A rod of mass m and length (is made to stand at an angle of\[{{60}^{o}}\]with the vertical. Potential energy of the rod in this position is
question_answer15) From a circular ring of mass M and radius R, an arc corresponding to a\[{{90}^{o}}\]sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is k times\[M{{R}^{2}}\]. Then the value of k is
question_answer16) A system consists of 3 particles each of mass m located at points (1, 1), (2, 2) and (3, 3). The coordinates of the centre of mass are
question_answer17) A wheel of moment of inertia\[2.5\text{ }kg-{{m}^{2}}\]has an initial angular velocity of\[40\text{ }rad\text{ }{{s}^{-1}}\]. A constant torque of 10 Nm acts on the wheel. The time during which the wheel is accelerated to\[60\text{ }rad\text{ }{{s}^{-1}}\] is
question_answer18) The ratio of radii of earth to another planet is\[\frac{2}{3}\]and the ratio of their mean densities is\[\frac{4}{5}\]. If an astronaut can jump to1 a maximum height of 1.5m on the earth, with the same effort, the maximum height he can jump on the planet is
question_answer21) A small spherical ball falling through a viscous medium of negligible density has terminal velocity v. Another ball of the same mass but of radius twice that of the earlier falling through the same viscous medium will have terminal velocity
question_answer23) In a capillary rise experiment, the water level rises to a height of 5 cm. If the same capillary tube is placed in water such that only 3 cm of the tube projects outside the water level, then
A)
water will begin to overflow through the capillary
question_answer24) The Youngs modulus of the material of a wire is\[2\times {{10}^{10}}N{{m}^{-2}}\].If the elongation strain is 1%, then the energy stored in the wire per unit: volume in\[J{{m}^{-3}}\]is
question_answer25) The change in internal energy of a given mass of gas, when its volume changes from V to 2V at constant pressure p is(\[\frac{{{C}_{P}}}{{{C}_{V}}}=\gamma ,\]universal gas constant =R)
question_answer26) In a Carnot engine, the temperature of reservoir is\[{{927}^{o}}C\]and that of sink is\[{{27}^{o}}C\]. If the work done by the engine when it transfers heat from reservoir to sink is\[12.6\times {{10}^{,}}^{6}J,\]the quantity of heat absorbed by the engine from the reservoir is
question_answer27) In the given\[p-V\]diagram, I is the initial state and F is the final state. The gas goes from\[I\]to F by (i) \[IAF\] (ii) \[IBF\] (iii) \[ICF\] The heat absorbed by gas is
question_answer28) Hot water cools from\[60{}^\circ C\]to\[50{}^\circ C\]in the first 10 min and to\[42{}^\circ C\]in the next 10 min. The temperature of the surroundings is
question_answer29) In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.14 s. The frequency of the wave is
question_answer30) An electric motor of mass 40. kg is mounted on four vertical springs each having a spring constant of\[4000\text{ }N{{m}^{-1}}\]. The period with which the motor vibrates vertically is
question_answer31) Two simple harmonic motions are represented by\[{{y}_{1}}=4\sin (4\pi t+\pi /2)\]and\[{{y}_{2}}=3\cos (4\pi t)\]. The resultant amplitude is
question_answer32) An observer is approaching a stationary source with a velocity\[\frac{1}{4}\]th of the velocity of sound. Then the ratio of the apparent frequency to actual frequency of source is
question_answer33) When a wave travels in a medium, the particle displacement is given by the equation\[y=a\sin 2\pi (bt-cx)\]where a, b and c are constants. The maximum particle velocity will be twice the wave velocity, if
question_answer35) Which one of the following graphs represents the variation of electric field with distance r from the centre of a charged spherical conductor of radius R?
question_answer36) Two conducting spheres A and B of radius a and b respectively are at the same potential. The ratio of the surface charge densities of A and B is
question_answer38) A particle of mass m carrying charge q is kept at rest in a uniform electric field E and then released. The kinetic energy gained by the particle, when it moves through a distance y is.
question_answer39) C, V, U and Q are capacitance, potential difference, energy stored and charge of a parallel plate capacitor respectively. The quantities that, increase when a dielectric slab is introduced between the plates without disconnecting the battery are
question_answer40) A heater of 220 V heats a volume of water in 5 min. The same heater when connected to 110 V heats the same volume of water in (minute)
question_answer42) Two different conductors have same resistance at\[{{0}^{o}}C\]. It is found that the resistance of the first conductor at\[{{t}_{1}}^{o}C\]is equal to the resistance of the second conductor at\[{{t}_{2}}^{o}C\]. The ratio of the temperature coefficients of resistance of the conductors,\[\frac{{{\alpha }_{1}}}{{{\alpha }_{2}}}\]is
question_answer44) A potentiometer wire of length 10 m and resistance\[20\,\Omega \]is connected in series with a 15 V battery and an external resistance\[40\,\Omega \]. A secondary cell of emf£ in the secondary circuit is balanced by 240 cm long potentiometer wire. The emf E of the cell is
question_answer45) A current I enters a circular coil of radius R branches into two parts and then recombines as shown in the circuit diagram. The resultant magnetic field at the centre of the coil is
question_answer46) The resistance of a galvanometer is\[50\,\Omega \]. and it shows full scale deflection for a current of 1 mA. To convert it into a voltmeter to measure 1 V and as well as 10 V (Refer circuit diagram) the resistances\[{{R}_{1}}\]and\[{{R}_{2}}\]respectively are
question_answer47) Two long parallel wires carry currents\[{{i}_{1}}\]and\[{{i}_{2}}\]such that\[{{i}_{1}}>{{i}_{2}}\]. When the currents are in the same direction, the magnetic field at a point midway between the wires is\[6\times {{10}^{-6}}T\]. If the direction of\[{{i}_{2}}\]is reversed, the field becomes\[3\times {{10}^{-5}}T.\]The ratio\[\frac{{{i}_{1}}}{{{i}_{2}}}\]is
question_answer48) A coil of 100 turns and area\[2\times {{10}^{-2}}{{m}^{2}},\]pivoted about a vertical diameter in a uniform magnetic field carries a current of 5A. When the coil is held with its plane in North-South direction, it experiences a torque of 0.3 Nm. When the plane is in East-West direction the torque is 0.4 Nm. The value of magnetic induction is (Neglect earths magnetic field)
question_answer49) The angle of dip at a place is\[{{37}^{o}}\]and the vertical component of the earths magnetic field is\[6\times {{10}^{-5}}T.\]The earths magnetic field at this place is\[(tan\text{ }{{37}^{o}}=3/4)\]
question_answer50) The impedance of a\[R-C\]circuit is\[{{Z}_{1}}\]for frequency\[f\]and\[{{Z}_{2}}\]for frequency\[2f\]. Then, \[{{Z}_{1}}/{{Z}_{2}}\]is
question_answer51) In an L-C-R series AC circuit the voltage across L, C and R is 10 V each. If the inductor is short circuited, the voltage across the capacitor would become on
question_answer52) A transformer of efficiency 90% draws an input power of 4 kW. An electrical appliance connected across the secondary draws a current of 6 A. The impedance of the device is
question_answer53) The inductance of a coil in which a current of 0.1 A increasing at the rate of\[0.5\text{ }A{{s}^{-1}}\]represents a power flow of\[\frac{1}{2}W,\]is
question_answer54) A point source of electromagnetic radiation has an average power output of 1500 W. The maximum value of electric field at a distance of 3 m from this source in\[V{{m}^{-1}}\]is
question_answer55) The refractive index and the permeability of a medium are respectively 1.5 and\[5\times {{10}^{-7}}H{{M}^{-1}}\]. The relative permittivity of the medium is nearly
question_answer56) A square wire of side 1 cm is placed perpendicular to the principal axis of a concave mirror of focal length 15 cm at a distance of 20 cm. The area enclosed by the image of the wire is
question_answer57) A thin prism P of refracting angle\[{{3}^{o}}\]and refractive index 1.5 is combined with another thin prism Q of refractive index 1.6 to produce dispersion without deviation. Then the angle of prism Q is
question_answer58) Light of wavelength \[6000\,\overset{\text{o}}{\mathop{\text{A}}}\,\] falls on a single slit of width 0.1 mm. The second minimum will be formed for the angle of diffraction of
question_answer59) In a double slit experiment, the screen is placed at a distance of 1.25 m from the slits. When the apparatus is immersed in water\[({{\mu }_{w}}=4/3)\], the angular width of a fringe is found to be\[{{0.2}^{o}}\]. When the experiment is performed in air with same set up, the angular width of the fringe is
question_answer60) Two plano-concave lenses (1 and 2) of) glass of refractive index 1.5 have radii of curvature 25 cm and 20 cm. They are placed in contact with their curved surfaces towards each other and the space between them is filled with liquid of refractive index\[\frac{4}{3}\]. Then the combination is
question_answer61) When a metallic surface is illuminated by a light of wavelength\[\lambda ,\]the stopping potential for the photoelectric current is 3 V. When the same surface is illuminated by light of wavelength\[2\lambda ,\]the stopping potential is 1 V, the threshold wavelength for this surface is
question_answer62) The temperature at which protons in proton gas would have enough energy to overcome Coulomb barrier of\[4.14\times {{10}^{-14}}J\]is (Boltzmann constant\[=1.38\,\times {{10}^{-23}}\,J{{K}^{-1}}\])
question_answer63) The activity of a radioactive element decreases to one-third of the original activity \[{{A}_{0}}\]in a period of 69 yr. After a further lapes of 9 yr, its activity will
question_answer64) Two nucleons are at a separation of 1 fermi The net force between them is\[{{F}_{1}}\]if both are neutrons\[{{F}_{2}}\]if both are protons and\[{{F}_{3}}\]if one is proton and the other is a neutron. Then
question_answer69) Electromagnetic waves of frequencies higher than\[9\sqrt{2}\]MHz are found to be reflected by the ionosphere on a particular day at a place. The maximum electron density in the ionosphere is
question_answer70) Which one of the following statements is wrong ?
A)
Radio waves in the frequency range 30 MHz to 60 MHz are called sky waves
doneclear
B)
Radio horizon of the transmitting antenna for space wave is\[{{d}_{T}}=\sqrt{(2R{{h}_{T}})}\] (R = radius of earth,\[{{h}_{T}}=\]height of transmitting antenna)
doneclear
C)
Within the skip distance neither the ground waves nor the sky waves are received
doneclear
D)
The principle of fibre optical communication is total internal reflection
doneclear
E)
Fibre optical communication is free from electrical disturbances
question_answer71) A diode AM detector with the output circuit consisting of\[R=1\text{ k}\Omega \]and\[C=1\text{ }\mu \text{F}\]would be more suitable for detecting a carrier signal of
question_answer72) In optical communication system operating at 1200 nm, only 2% of the source frequency is available for TV transmission having a bandwidth of 5 MHz. The number of TV channels that can be transmitted is
question_answer74) The number of photons emitted per second by a 60 W source of monochromatic light of wavelength 663 nm is \[(h=6.63\times {{10}^{-34}}Js)\]
question_answer77) When a sample of gas is compressed at constant temperature from 15 atm to 60 atm, its volume changes from\[76\,c{{m}^{3}}\text{ }to\text{ }20.50\text{ }{{m}^{3}}\]. Which of the following statements are possible explanations of this behaviour?
question_answer78) The vapour pressure of two liquids X and Y are 80 and 60 Torr respectively. The total vapour pressure of the ideal solution obtained by mixing 3 moles of X and 2 moles of Y would be
question_answer85) A compound in which a metal ion \[{{M}^{x+}}(Z=25)\]has a spin only magnetic moment of\[\sqrt{24}\]BM. The number of unpaired electrons in the compound and the oxidation state of the metal ion are respectively
question_answer86) To an aqueous solution containing anions a few drops of acidified\[KMn{{O}_{4}}\]are added. Which one of the following anions, if present will not decolourise the\[KMn{{O}_{4}}\]solution?
question_answer87) Lead is the final product formed by a series of changes in which the rate determining stage is the radioactive decay of uranium\[-238\]with a half-life of\[4.5\times {{10}^{9}}yr\]. What would be the age of a rock sample originally lead free in which the molar proportion of uranium to lead is now 1 : 3?
question_answer88) Energy released when one atom of uranium undergoes nuclear fission according to the following reaction is (atomic mass of U= 235.060; n= 1.009; Ba = 143.881 and Kr= 89.947) about \[_{92}{{U}^{235}}{{+}_{0}}{{n}^{1}}{{\to }_{56}}B{{a}^{144}}{{+}_{36}}K{{r}^{90}}+{{2}_{0}}{{n}^{1}}\]
question_answer89) When 0.2 g of 1-butanol was burnt in a suitable apparatus, the heat evolved was sufficient to raise the temperature of 200 g water by\[5{}^\circ C\]. The enthalpy of combustion of 1-butanol in kcal\[mo{{l}^{-1}}\]will be
question_answer91) When 200 mL of aqueous solution of\[HCl\] (pH = 2) is mixed with 300 mL of an aqueous solution of NaOH (pH = 12), the pH of the resulting mixture is
question_answer92) At a certain temperature, the dissociation constants of formic acid and acetic acid are \[1.8\times {{10}^{-4}}\]and\[1.8\times {{10}^{-5}}\]respectively. The concentration of acetic acid solution in which the hydrogen ion has the same concentration as in 0.001 M formic acid solution is equal to
question_answer93) An 1% solution of\[KCl\](I),\[NaCl\](II),\[BaC{{l}_{2}}\](III) and urea (IV) have their osmotic pressure at thesame temperature in the ascending order (molar masses of\[NaCl,KCl,BaC{{l}_{2}}\]and urea are respectively 58.5, 74.5, 208.4 and 60 g. \[mo{{l}^{-1}})\].Assume 100% ionization of the electrolytes at this temperature
question_answer94) The difference between the boiling point and freezing point of an aqueous solution containing sucrose (molecular wt = 342 g\[mo{{l}^{-1}}\]) in 100 g of water is\[105.0{}^\circ C\]. If\[{{k}_{f}}\]and\[{{k}_{b}}\]of water are 1.86 and\[0.51\text{ }K\text{ }kg\text{ }mo{{l}^{-1}}\] espectively, the weight of sucrose in the solution is about
question_answer95) In the following reaction, \[{{M}^{x+}}+MnO_{4}^{-}\xrightarrow{{}}MO_{3}^{-}+M{{n}^{2+}}+\frac{1}{2}{{O}_{2}},\] If one mole of\[MnO_{4}^{-}\]oxidizes 2.5 moles of\[{{M}^{x+}},\]then the value of\[x\]is
question_answer96) In acid medium Zn reduces nitrate ion to\[NH_{4}^{+}\] ion according to the reaction\[Zn+NO_{3}^{-}\to Z{{n}^{2+}}\]\[+NH_{4}^{+}+{{H}_{2}}O\](unbalanced) How many moles of\[HCl\]are required to reduce half a mole of\[NaN{{O}_{3}}\] completely? Assume the availability of sufficient\[Zn\]
question_answer97) The activation energies of two reactions are \[{{E}_{1}}\]and\[{{E}_{2}}({{E}_{1}}>{{E}_{2}})\]If the temperature of the system is increased from\[{{T}_{1}}\]to\[{{T}_{2}},\]he rate constant of the reactions changes from\[{{k}_{1}}\]to \[k{{}_{1}}\] in the first reaction and \[{{k}_{2}}\] to \[k{{}_{2}}\] in the second reaction. Predict which of the following expression is correct?
question_answer98) A reaction was observed for 15 days and the percentage of the reactant remaining after the days indicated was recorded in the following table
Time (days)
% Reactant remaining
0
100
2
50
4
39
6
25
8
21
10
18
12
15
14
12.5
15
10
Which one of the following best describes the order and the half-life of the reaction?
question_answer102) What is the overall formation equilibrium constant for the ion\[{{[M{{L}_{4}}]}^{2-}}\]ion, given that\[{{\beta }_{4}}\]for this complex is\[2.5\times {{10}^{13}}\]?
question_answer103) 0.25 g of an organic compound on Kjeldahls analysis gave enough ammonia to just neutralize \[10\text{ }c{{m}^{3}}\]of\[0.5\text{ }M\text{ }{{H}_{2}}S{{O}_{4}}\]. The percentage of nitrogen in the compound is
question_answer113) A compound A having the molecular formula \[{{C}_{5}}{{H}_{12}}O,\]on oxidation give a compound B with molecular formula\[{{C}_{5}}{{H}_{10}}O.\] Compound B gave a 2, 4-dinitrophenylhydrazine derivative but did not answer haloform test or silver mirror test. The structure of compound A is
question_answer121) If \[\alpha ,\,\beta ,\,\gamma \] are the cube roots of unity, then the value of the determinant\[\left| \begin{matrix} {{e}^{\alpha }} & {{e}^{2\alpha }} & ({{e}^{3\alpha }}-1) \\ {{e}^{\beta }} & {{e}^{2\beta }} & ({{e}^{2\beta }}-1) \\ {{e}^{\gamma }} & {{e}^{2\gamma }} & ({{e}^{3\gamma }}-1) \\ \end{matrix} \right|\]is equal to
question_answer124) If the three linear equations \[x+4ay+az=0\] \[x+3by+bz=0\] \[x+2cy+cz=0\] have a non-trivial solution, where\[a\ne 0,b\ne 0,\] \[c\ne 0,\]then \[ab+bc\]is equal to
question_answer126) If\[A=\left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right],\]then the value of the determinant\[|{{A}^{2009}}-5{{A}^{2008}}|\]is
question_answer134) If a and b are positive numbers such that\[a>b,\]then the minimum value of\[a\sec \theta -b\tan \theta \left( 0<\theta <\frac{\pi }{2} \right)\]is
question_answer139) If tan A and tan B are the roots of \[ab{{x}^{2}}-{{c}^{2}}x+\]\[ab=0\] where a, b, c are the sides of the triangle ABC, then the value of \[si{{n}^{2}}A+si{{n}^{2}}B+si{{n}^{2}}C\text{ }is\]
question_answer143) From the top of a tower, the angle of depression of a point on the ground is\[60{}^\circ \]. If the distance of this point from the tower is\[\frac{1}{\sqrt{3}+1}m,\]then the height of the tower is
question_answer144) The vertices of a family of triangles have integer coordinates. If two of the vertices of all the triangles are (0, 0) and (6, 8), then the least value of areas of the triangles is
question_answer146) One side of length 3a of a triangle of area\[{{a}^{2}}\]square unit lies on the line\[x=a\]. Then, one of the lines on which the third vertex lies, is
question_answer149) Triangle ABC has vertices (0, 0), (11, 60) and (91, 0). If the line\[y=kx\]cuts the triangle into 2 two triangles of equal area, then k is equal to
question_answer150) If the lines\[y=3x+1\]and\[2y=x+3\]are equally inclined to the line\[y=mx+4,\left( \frac{1}{2}<m<3 \right),\]then the values of m are
question_answer154) If two chords having lengths\[{{a}^{2}}-1\]and\[3(a+1),\]where a is a constant of a circle bisect each other, then the radius of the circle is
question_answer158) If\[{{e}_{1}}\]is the eccentricity of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{7}=1\]and\[{{e}_{2}}\]is the eccentricity of the hyperbola\[\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{7}=1,\]then\[{{e}_{1}}+{{e}_{2}}\]is equal to
question_answer160) Vectors\[\overrightarrow{a}\]and\[\overrightarrow{b}\]are inclined at an angle\[\theta =120{}^\circ \].If\[|\overrightarrow{a}|=1,|\overrightarrow{b}|=2,\]then \[{{[(\overrightarrow{a}+3\overrightarrow{b})\times (3\overrightarrow{a}+\overrightarrow{b})]}^{2}}\]is equal to
question_answer161) If the projection of the vector a on b is\[\overrightarrow{a}\]on\[\overrightarrow{b}\]is \[|\overrightarrow{a}\times \overrightarrow{b}|\]and if\[3\overrightarrow{b}=\hat{i}+\hat{j}+\hat{k},\] then the angle between \[\vec{a}\] and \[\vec{b}\] is
question_answer162) If\[\overrightarrow{x}=\overrightarrow{a}+\overrightarrow{b},\overrightarrow{y}=\overrightarrow{a}-\overrightarrow{b},|\overrightarrow{a}|=2,|\overrightarrow{b}|=3\]and the angle between\[\overrightarrow{a}\]and\[\overrightarrow{b}\]is\[\frac{\pi }{3}\],then\[|\overrightarrow{x}\times \overrightarrow{y}|\]is equal to
question_answer163) If the position vectors of three consecutive vertices, of a parallelogram are\[\hat{i}+\hat{j}+\hat{k},\] \[\hat{i}+3\hat{j}+5\hat{k}\] and\[7\hat{i}+9\hat{j}+11\hat{k},\] then the coordinates of the fourth vertex are
question_answer164) The two variable vectors\[3x\hat{i}+y\hat{j}-3\hat{k}\]and\[x\hat{i}-4y\hat{j}+4\hat{k}\]are orthogonal to each other, then the locus of\[(x,\text{ }y)\]is
question_answer165) If\[\overrightarrow{a},\text{ }\overrightarrow{b},\text{ }\overrightarrow{c}\] are non-coplanar and \[(\overrightarrow{a}+\lambda \overrightarrow{b}).[(\overrightarrow{b}+3\overrightarrow{c})\times (\overrightarrow{c}\times 4\overrightarrow{a})]=0,\] then the value of\[\lambda \]is equal to
question_answer167) The angle between the straight lines\[\overrightarrow{r}=(2-3t)\hat{i}+(1+2t)\hat{j}+(2+6t)\hat{k}\]and\[\overrightarrow{r}=(1+4s)\hat{i}+(2-s)\hat{j}+(8s-1)\hat{k}\]is
question_answer169) The distance of the point of intersection of the line\[\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}\]and me plane \[x-y+z=5\]from the point\[(-1,-5,-10)\]is
question_answer172) If the lines\[\frac{1-x}{3}=\frac{y-2}{2\alpha }=\frac{z-3}{2}\]and\[\frac{x-1}{3\alpha }\]\[=y-1=\frac{6-z}{5}\]are perpendicular, then the value of\[\alpha \]is
question_answer173) The distance between the lines\[\overrightarrow{r}=(4\hat{i}-7\hat{j}-9\hat{k})+t(3\hat{i}-7\hat{j}+4\hat{k})\]and\[\overrightarrow{r}=(7\hat{i}-14\hat{j}-5\hat{k})+s(3\hat{i}+7\hat{j}-4\hat{k})\]is equal to
question_answer175) The mean of the values 0, 1, 2, 3, ..., n with the corresponding weights\[^{n}{{C}_{0}}{{,}^{n}}{{C}_{1}},....{{,}^{n}}{{C}_{n}}\]respectively, is
question_answer176) A complete cycle of a traffic light takes 60 s. During each cycle the light is green for 25 s, yellow for 5 s and red for 30 s. At a randomly chosen time, the probability that the light will not be green, is
question_answer177) If the random variable X takes the values\[{{x}_{1}},{{x}_{2}},{{x}_{3}},....,{{x}_{10}}\]with probabilities\[p(X={{x}_{i}})=ki,\]then the value of k is equal to
question_answer180) If\[f(x)=\left\{ \begin{matrix} \frac{3\sin \pi x}{5x} & ,x\ne 0 \\ 2k & ,x=0 \\ \end{matrix} \right.\]is continuous at\[x=0,\]then the value of k is equal to
question_answer189) If the curves\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{12}=1\]and\[{{y}^{3}}=8x\]intersect at right angle, then the value of\[{{a}^{2}}\]is equal to
question_answer190) If the function \[f(x)={{x}^{3}}-12a{{x}^{2}}+36{{a}^{2}}x\] \[-4(a>0)\]attains its maximum and minimum at\[x=p\]and\[x=g\]respectively and if\[3p={{q}^{2}},\]then a is equal to
question_answer192) The diagonal of a square is changing at the rate of\[0.5\text{ }cm{{s}^{-1}}\]. Then, the rate of change of area, when the area is\[400\text{ }c{{m}^{2}},\]is equal to
question_answer195) Let\[f(x)={{(x-7)}^{2}}{{(x-2)}^{7}}{{(x-2)}^{7}},x\in [2,7]\]. The value of\[\theta \in (2,7)\]such that\[f(\theta )=0\]is equal to
question_answer206) The figure shows a triangle AOB and the parabola\[y={{x}^{2}}\]. The ratio of the area of the triangle AOB to the area of the region AOB of the parabola\[y={{x}^{2}}\]is equal to
question_answer209) The order and degree of the differential equation \[{{\left( 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right)}^{\frac{3}{4}}}={{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{\frac{1}{3}}}\]is
question_answer214) Two finite sets A and B have m and n elements respectively. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m is
question_answer221) The centre of a regular hexagon is at the point\[z=i\]. If one of its vertices is at\[2+i,\]then the adjacent vertices of\[2+i\]are at the points
question_answer222) If the roots of the equation\[\frac{1}{x+p}+\frac{1}{x+q}=\frac{1}{r},\] \[(x\ne -p,x\ne -q,r\ne 0)\]are equal in magnitude but opposite in sign, then\[p+q\]is equal to
question_answer225) If one root of the equation\[l{{x}^{2}}+mx+n=0\]is \[\frac{9}{2}\] \[(l,m\]and n are positive integers) and \[\frac{m}{4n}=\frac{l}{m},\]then\[\frac{1}{x}+\frac{1}{y}\]is equal to
question_answer228) A student read common difference of an AP as\[-3\]instead of 3 and obtained the sum of first 10 terms as\[-30\]. Then, the actual sum of first 10 terms is equal to
question_answer230) If\[{{a}_{1}},{{a}_{2}},.....,{{a}_{n}}\]are in AP with common difference\[d\ne 0,\]then\[(\sin d)\]\[[\sec {{a}_{1}}\sec {{a}_{2}}+\] \[\sec {{a}_{2}}\sec {{a}_{3}}+...+\sec {{a}_{n-1}}\sec {{a}_{n}}]\]is equal to
question_answer233) The sum of the infinite series\[\frac{1}{2}\left( \frac{1}{3}+\frac{1}{4} \right)-\frac{1}{4}\left( \frac{1}{{{3}^{2}}}+\frac{1}{{{4}^{2}}} \right)+\frac{1}{6}\left( \frac{1}{{{3}^{3}}}+\frac{1}{{{4}^{3}}} \right)-....\]is equal to
question_answer236) \[^{15}{{C}_{0}}{{,}^{5}}{{C}_{5}}{{+}^{15}}{{C}_{1}}{{.}^{5}}{{C}_{4}}{{+}^{15}}{{C}_{2}}{{.}^{5}}{{C}_{3}}{{+}^{15}}{{C}_{3}}{{.}^{5}}{{C}_{2}}\]\[{{+}^{15}}{{C}_{4}}{{.}^{5}}{{C}_{1}}\]is equal to
question_answer240) Let\[{{T}_{n}}\]denote the number of triangles which can be formed by using the vertices of a regular polygon of n sides. If \[{{T}_{n+1}}-{{T}_{n}}=28,\]then\[n\]equals