Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2006
done BCECE Engineering Solved Paper-2006 Total Questions - 150
question_answer1) The length of a simple pendulum is about 100 cm known to an accuracy of 1mm. Its period of oscillation is 2s determined by measuring the time for 100 oscillations using a clock of 0.1 s resolution. What is the accuracy in the determined value of g?
question_answer2) Youngs modulus of the material of a wire is V. On pulling the wire by a force F, the increase in its length is x. The potential energy of the stretched wire is:
question_answer3) A charge situated at a certain distance along the axis of an electric dipole experiences a force F. If the distance of the charge from the dipole is doubled, the force acting on it will become:
question_answer4) Which of the following plots represents the variation of the electric field with distance from the centre of a uniformly charged non- conducting sphere of radius R?
question_answer5) A certain electrical conductor has a square cross-section, 2.0 mm on side, and is 12 m long. The resistance between its ends is 0.072\[\Omega .\] The resistivity of its material is equal to :
question_answer6) Figure shows three points A, B and C in a region of uniform electric field \[\mathbf{\vec{E}}\]. The line AB is perpendicular and BC is parallel to the field lines. Then which of the following holds good?
question_answer7) The (x, y, z) coordinates of two points A and B are given respectively as (0, 3,-1) and (-2, 6, 4). The displacement vector form A to B may be given by:
question_answer8) In the first second of its flight, rocket ejects 1/60 of its mass with a velocity of \[2400\,\,m{{s}^{-1}}\]. The acceleration of the rocket is:
question_answer9) In the given figure the pulley is assumed massless and frictionless. If the friction force on the object of mass m is \[f\], then its acceleration in terms of the force F will be equal to:
question_answer11) The magnetic field amplitude of an electromagnetic wave is \[2\times {{10}^{-7}}T\], Its electric field amplitude, if the wave is travelling in free space is:
question_answer12) A can is moving horizontally along a straight line with constant speed 30 m/s. A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moved 80 m. At what speed (relative to the can) must the projectile be fired? (Takes \[=10\,m/{{s}^{2}}\])
question_answer13) A boy begins to walk eastward along a street In front of his house, and the graph of his displacement from home is shown in the following figure. His average velocity for the whole time interval is equal to:
question_answer14) What is the potential drop between points A and C in the following circuit ?
Resistances 1\[\Omega \] and 2\[\Omega \] represent the internal resistances of the respective cells.
question_answer15) The escape velocity of a projectile on the earths surface is \[11.2\,\,km{{s}^{-1}}\]. A body is projected out with thrice this speed. The speed of the body far away from the earth will be:
question_answer16) A body moves along a circular pa-h of radius 10 m and the coefficient of friction is 0.5. What should be its angular speed in rad/s, if it is not to slip from the surface? \[(g=9.8\,m{{s}^{-2}})\]
question_answer17) One end of a string of length I is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v, the net force on the particle (directed towards the centre) is:
question_answer18) A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to:
question_answer19) In the adjacent figure is shown a closed path P. A long straight conductor carrying a current \[I\]passes through O and perpendicular to the plane of the paper. Then which of the following holds good?
question_answer21) The figure below shows the plot of \[\frac{PV}{nT}\] versus P for oxygen gas at two different temperatures.
Read the following statements concerning the above curves:
(i) The dotted line corresponds to the ideal gas behaviour.
(ii) \[{{T}_{1}}>{{T}_{2}}\]
(iii) The value of \[\frac{PV}{nT}\]at the point where the curves meet on the y-axis is the same for all gases.
question_answer22) The following figure represents the temperature versus time plot for a given amount of a substance when heat energy is supplied to it at a fixed rate and at a constant pressure.
Which parts of the above plot represent a phase change?
question_answer23) A bar magnet has a coercivity \[4\times {{10}^{3}}\,A{{m}^{-1}}\]. It is desired to demagnetise it by inserting it inside a solenoid 12 cm long and having 60 turns. The current carried by the solenoid should be:
question_answer24) In a series LCR circuit the frequency of a 10 VAC voltage source is adjusted in such a fashion that the reactance of the inductor measures 15 \[\Omega \] and that of capacitor 11\[\Omega \]. If R = 3 \[\Omega \] the potential difference across the series combination of L and C will be:
question_answer25) A circuit draws 330 W from a 110 V, 60 Hz AC line. The power factor is 0.6 and the current lags the voltage. The capacitance of a series capacitor that will result in a power factor of unity is equal to:
question_answer27) An open U-tube contains mercury. When 11.2 cm of water is poured into one of the arms of the tube, how high does the mercury rise in the other arm form its initial level?
question_answer28) The change in the entropy of a 1 mole of an ideal gas which went through an isothermal process from an initial state\[({{P}_{1}},{{V}_{1,}}T)\] to the final state \[({{P}_{2}},{{V}_{2,}}T)\] is equal to:
question_answer29) An unpolarized beam of light is incident on a glass surface at an angle of incidence equal to the polarizing angle of the glass. Read the following statements:
(i) The reflected beam is completely polarized.
(ii) The refracted beam is partially polarized.
(iii) The angle between the reflected and the refracted beams is \[90{}^\circ \].
question_answer30) The threshold frequency for certain metal is \[3.3\times {{10}^{14}}Hz\]. If light of frequency \[8.2\,\times {{10}^{14}}Hz\] is incident on the metal, the cut-off voltage of the photoelectric current will be:
question_answer31) Frequencies higher than 10 MHz were found not being reflected by the ionosphere on a particular day at a place. The maximum electron density of the ionosphere on the day was near to:
question_answer32) The de-Broglie wavelength of an electron, \[\alpha \]-particle and a proton all having the same kinetic energy is respectively given as \[{{\lambda }_{e,}}{{\lambda }_{\alpha }}\] and \[{{\lambda }_{P.}}\] Then which of the following is not true ?
question_answer35) Carbon, silicon and germanium have four valence electrons each. These are characterized by valence and conduction bands separated by energy band gap respectively equal to \[{{({{E}_{g}})}_{C}}\] \[{{({{E}_{g}})}_{Si}}\]and \[{{({{E}_{g}})}_{Ge.}}\]. Which of the following statements is true?
question_answer36) A particle executes SHM of amplitude 25 cm and time period 3 s. What is the minimum time required for the particle to move between two points 12.5 cm on either side of the mean position?
question_answer37) The speed of a wave on a string is 150 m/s when the tension is 120 N. The percentage increase the tension in order to raise the wave speed by 20% is:
question_answer38) A straight rod of length L has one of its ends at the origin and the other at x - L. If the mass per unit length of the rod is given by A x, where A is constant, where is its mass centre?
question_answer39) The image of a small electric bulb fixed on the wall of a room is to be obtained on the oppose wall 4 m away by means of a large convex lens. The maximum possible focal length of the lens required for this purpose will be:
question_answer41) In hydrogen atom, the electron is moving round the nucleus with velocity \[2.18\,\times {{10}^{6\,}}m/s\] in an orbit of radius \[0.528\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. The acceleration of the electron is:
question_answer42) When a spring is stretched by a distance x, it exerts a force given by \[F=(-5x-16{{x}^{3}})N\]The work done, when the spring is stretched from 0.1 m to 0.2 m is:
question_answer46) Two closed organ pipes A and B have the same length. A is wider than B. They resonate in the fundamental mode at frequencies \[{{n}_{A}}\] and \[{{n}_{B}}\] respectively, then:
A)
\[{{n}_{A}}={{n}_{B}}\]
doneclear
B)
\[{{n}_{A}}>{{n}_{B}}\]
doneclear
C)
\[{{n}_{A}}<{{n}_{B}}\]
doneclear
D)
either (b) or (c) depending on the ratio of their diameters
question_answer48) In double slit experiment, the distance between two slits is 0.6 mm and these are illuminated with light of wavelength \[4800\overset{\text{o}}{\mathop{\text{A}}}\,\]. The angular width of first dark fringe on the screen distant 120 cm from slits will be:
question_answer52) A cyclic hydrocarbon molecule has all the carbon and hydrogen is a single plane. All the carbon-carbon bonds are of same length, less than\[1.54\,\overset{\text{o}}{\mathop{\text{A}}}\,,\] but more than \[1.34\overset{\text{o}}{\mathop{\text{A}}}\,.\] The C-C bond angle will be:
question_answer54) Some chemists at ISRO wished to prepare a saturated solution of a silver compound and they wanted it to have the highest concentration of silver ion possible. Which of the following compounds, would they use? \[{{K}_{sp}}(AgCl)=1.8\times {{10}^{-10}},\] \[{{K}_{sp}}(AgBr)=5.0\times {{10}^{-13}},\] \[{{K}_{sp}}(A{{g}_{2}}Cr{{O}_{4}})=2.4\times {{10}^{-12}}\]
question_answer80) The decomposition of \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\]occurs as, \[\text{2}{{\text{N}}_{2}}{{O}_{5}}\xrightarrow{{}}4{{N}_{2}}+{{O}_{2}},\] and follows Ist order kinetics, hence:
question_answer83) When dilute aqueous solution of \[\text{AgN}{{\text{O}}_{\text{3}}}\](excess) is added to KI solution, positively charged sol of \[\text{AgI}\]is formed due to adsorption of:
question_answer88) The H-H bond energy is \[430\text{ }kJ\text{ }mo{{l}^{-1}}\] and \[ClCl\]bond energy is \[240\text{ }kJ\text{ }mo{{l}^{-1}},\]\[\Delta H\] for \[HCl\]is \[-\text{ }90\text{ }kJ.\] The \[HCl\]bond energy is about:
question_answer103) The value of \[x\] for which the equation \[1+r+{{r}^{2}}+...+{{r}^{x}}\] \[=(1+r)(1+{{r}^{2}})(1+{{r}^{4}})(1+{{r}^{8}})\] holds is:
question_answer105) The value of d for which the sum of the squares of the roots of the equation \[{{x}^{2}}-(a-2)x-a-1=0\] assumes the least value is:
question_answer106) A particle is dropped under gravity from rest from a height \[h(g=9.8\,m/{{s}^{2}})\]and it travels a distance \[\frac{9h}{25}\] in the last second the height \[h\]is:
question_answer112) If \[\omega \] and \[{{\omega }^{2}}\]are the two imaginary cube root unity, then the equation whose roots are \[a{{\omega }^{317}}\]and \[a{{\omega }^{382}}\]is:
question_answer114) If \[1,{{a}_{1}},{{a}_{2}},....,{{a}_{n-1}}\] are roots of unity, then the value of \[(1-{{a}_{1}})(1-{{a}_{2}})...(1-{{a}_{n-1}})\]is:
question_answer115) If \[\alpha ,\beta \]are the roots of \[a{{x}^{2}}+bx+c=0,\alpha +h,\beta +h\] are roots of \[p{{x}^{2}}+qx+r=0;\]and\[{{D}_{1}},{{D}_{2}}\]are the respective discriminants of the equations, then \[{{D}_{1}}:{{D}_{2}}\]is equal to:
question_answer118) Suppose a, b, c are in AP and | a|, | b|, | c| < 1. If \[x=1+a+{{a}^{2}}+....\,to\,\infty ,\] \[y=1+b+{{b}^{2}}+....\,\text{to}\,\infty ,\] \[z=-1+c+{{c}^{2}}+...\,\text{to}\,\infty \] then \[x,y,z\]are in
question_answer121) If \[p=\cos {{55}^{o}},q=\cos {{65}^{o}}\] and \[r=\cos {{175}^{o}},\] then the value of\[\frac{1}{p}+\frac{1}{q}+\frac{r}{pq}\]is:
question_answer124) If the line \[\frac{x}{a}+\frac{y}{b}=1\] moves such that \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{c}^{2}}},\] where c is a constant, then the locus of the foot of the perpendicular from the origin to the line is:
question_answer125) The straight line whose sum of the intercepts on the axes is equal to half of the product of the intercepts, passes through the point:
question_answer126) If the circle \[{{x}^{2}}+{{y}^{2}}+4x+22y+c=0\]bisects the circumference of the circle \[{{x}^{2}}+{{y}^{2}}-2x+8y-d=0,\] then \[c+d\]is equal to :
question_answer129) If \[{{M}_{1}}\]and \[{{M}_{2}}\]are the feet of the perpendiculars from the foci \[{{S}_{1}}\]and \[{{S}_{2}}\]of the ellipse\[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{16}=1\] on the tangent at a point P on the ellipse, then \[({{S}_{1}}{{M}_{1}})({{S}_{2}}{{M}_{2}})\]is equal to:
question_answer130) If the chords of contact of tangents from two points \[({{x}_{1}},{{y}_{1}})\] and \[({{x}_{2}},{{y}_{2}})\] to the hyperbola \[4{{x}^{2}}-9y-36=0\] are at right angles, then \[\frac{{{x}_{1}}{{x}_{2}}}{{{y}_{1}}{{y}_{2}}}\] is equal to:
question_answer133) The solution set of the equation \[{{\left[ 4\left( 1-\frac{1}{3}+\frac{1}{9}-\frac{1}{27}+... \right) \right]}^{{{\log }_{2}}x}}\] \[={{\left[ 54\left( 1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+... \right) \right]}^{{{\log }_{x}}2}}\]is:
question_answer139) If \[\vec{a}+\vec{b}+\vec{c}=\vec{0}\]and \[|\vec{a}|=\sqrt{37},|\vec{b}|\]\[=3,|\vec{c}|=4,\] then angle between \[\vec{b}\]and \[\vec{c}\] is:
question_answer140) If \[\vec{a}=\hat{i}+\hat{j}-\hat{k},\,\vec{b}=-\hat{i}+\hat{k},\,\vec{c}=2\hat{i}+\hat{j}\]the value of \[\lambda \]such that \[\vec{a}+\lambda \,\vec{c}\]is perpendicular to \[\vec{b}\]is
question_answer141) The total work done by two forces \[{{\vec{F}}_{1}}=2\hat{i}-\hat{j}\]at \[{{\vec{F}}_{2}}=3\hat{i}+2\hat{j}-\hat{k}\]acting on a particle when it is displace from the point \[3\hat{i}+2\hat{j}+\hat{k}\]to \[5\hat{i}+5\hat{j}+3\hat{k}\]is:
question_answer142) Let \[\vec{a},\vec{b}\]and \[\vec{c}\]be three non-coplanar vectors, and let \[\vec{p}\]and \[\vec{r}\]be vectors defined by the relations \[\vec{P}=\frac{\vec{b}\times \vec{c}}{[\vec{a}\vec{b}\vec{c}]}.\vec{q}=\frac{\vec{c}\times \vec{a}}{[\vec{a}\vec{b}\vec{c}]}\]and \[\vec{r}=\frac{\vec{a}\times \vec{b}}{[\vec{a}\vec{b}\vec{c}]}\] Then, the value of the egression \[(\vec{a}+\vec{b}).\vec{p}+(\vec{b}+\vec{c}).\vec{q}+(\vec{c}+\vec{a}).\vec{r}\]is equal to:
question_answer144) If \[{{a}_{1}},{{a}_{2}},....,{{a}_{n}},...\] are in GP and \[{{a}_{1}}>0\]for each i, then determinant \[\Delta =\left| \begin{matrix} \log \,{{a}_{n}} & \log {{a}_{n+2}} & \log {{a}_{n+4}} \\ \log {{a}_{n+6}} & \log {{a}_{n+8}} & \log {{a}_{n+10}} \\ \log {{a}_{n+12}} & \log {{a}_{n+14}} & \log {{a}_{n+16}} \\ \end{matrix} \right|\] is equal to:
question_answer148) A and B are two events. Odds against A are 2 to Odds in favour of \[A\cup B\]are 3 to 1. If \[x\le P(B)\le y,\] then ordered pair \[(x,y)\] is:
question_answer149) In a series of three trials, the probability of exactly two successes in nine times is as large as the probability of three successes. Then, the probability of success in each trial is :
question_answer150) An integer is chosen at random from first two hundred numbers. Then, the probability that the integer chosen is divisible by 6 or 8 is: