Solved papers for RAJASTHAN PET Rajasthan PET Solved Paper-2011
done Rajasthan PET Solved Paper-2011 Total Questions - 120
question_answer1) The x and y coordinates of a particle at any time t are given\[x=7t+4{{t}^{2}}\]and\[y=5t,\]where\[x\]and y are in metre and t in second. The acceleration of particle at\[t=5s\]is
question_answer2) Find the velocity of the particle moving in a circular path having a centripetal force of 10 N whose mass is 100 g and radius of circular path is 50 cm
question_answer3) A small object placed on a rotating horizontal turn-table just slips when it is placed at a distance of 4 cm from the axis of rotation. If the angular velocity of the turn-table is doubled the object slips when its distance from the axis of rotation is
question_answer4) A bullet moving with speed 200 m/s is just able to pierce a wooden block of 6 cm thickness. What velocity is required to just pierce a block of 8 cm?
question_answer5) A bullet of 5 g is fired with a velocity of 800 m/s. The velocity of bullet becomes 200 m/s when it pierces a wooden block 2 m thick. What is the average resistance offered by the wooden block?
question_answer6) On a massless rod four masses are fixed as shown in figure. What is the moment of inertia about an axis passing through centre of rod
question_answer7) The two waves, whose intensities are\[9:16\]are made to interfere. The ratio of maximum and minimum intensities in the interference pattern is
question_answer9) A balloon contains\[500\text{ }{{m}^{3}}\]of helium at\[27{}^\circ C\]and 1 atmosphere pressure. The volume of the helium at\[-3{}^\circ C\]temperature and 0.5 atmosphere pressure will be
question_answer11) Two lamps of powers\[{{P}_{1}}\]and\[{{P}_{2}}\]are placed on either side of a paper having an oil spot. The lamps are at distances of 1 m and 2 m respectively on either side of the paper and the oil spot is invisible. What is the value of\[{{P}_{1}}/{{P}_{2}}\]?
question_answer12) A parallel plate capacitor of value 1.77 \[\mu \]F is to be designed using a dielectric material (dielectric constant = 200), breakdown strength of\[3\times {{10}^{6}}\] V/m. In order to make such a capacitor which can withstand a potential difference of 20 V across the plates, the separation between the plates d and area A of the plates respectively are
question_answer13) Mid way between the two equal and similar charges, we place the third equal and similar charge. Which of the following statements is correct?
A)
The third charge experiences a net force inclined to the line joining the charges
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B)
The third charge is in stable equilibrium
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C)
The third charge is in unstable equilibrium
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D)
The third charge experience a net force perpendicular to the line joining the charges
question_answer14) A magnetic field of 20 T is normal to a coil of 100 turns and area\[{{10}^{-2}}{{m}^{2}}\]. If the coil is removed from the magnetic field is 2 ms, what is the induced emf set up in the coil?
question_answer20) A charged particle with velocity\[2\times {{10}^{3}}\]m/s passes undeflected through electric and magnetic field is 1.5 T. The electric field intensity would be
question_answer22) What is the magnitude of the emf generated between the ends of the axle of a railway carriage 1 m in length when it is moving with a velocity of 30 km/h along horizontal track? Earth's horizontal magnetic field of induction\[=0.4\times {{10}^{-4}}T\]and angle of dip \[=60{}^\circ \]
question_answer23) Three identical charges placed at the vertices of an equilateral triangle. The force experienced by each charge \[\left( if\,k=\frac{1}{4}\pi {{\varepsilon }_{0}} \right)\] is
question_answer26) A magnet of magnetic moment M is freely suspended in a uniform magnetic field of strength B. The work done in rotating the magnet through \[60{}^\circ \]to\[90{}^\circ \]is
question_answer27) A 750 Hz, 20 V source is connected to a resistance of\[100\,\Omega ,\]an inductance of 0.1803 H and a capacitance of 10\[\mu \]F all in series. What is the time in which resistance (thermal capacity\[=2\text{ }J/{}^\circ C\]) will get heated by\[10{}^\circ C\]?
question_answer28) A capacitor discharges through an inductor of 0.02 H. If the frequency of discharge is 100 Hz then what is the capacitance of the capacitor?
question_answer30) A bomb of 12 kg explods into two pieces of masses 4 kg and 8 kg. The velocity of 8 kg mass is 6 m/s. The kinetic energy of the other mass is
question_answer31) The path difference between the two waves \[{{y}_{1}}={{a}_{1}}\sin \left( \omega t-\frac{2\pi x}{\lambda } \right)\] and \[{{y}_{2}}={{a}_{2}}\sin \left( \omega t-\frac{2\pi x}{\lambda }+\phi \right)is\]
question_answer34) Two spheres have identical masses and moment of inertia. One of them is solid and the other is hollow. The ratio of the radius of solid sphere to that of hollow sphere is
question_answer35) A body cools in 7 min from\[60{}^\circ C\]to\[40{}^\circ C\]. What time does it take to cool from\[40{}^\circ C\]to\[28{}^\circ C\]if the surrounding temperature is\[10{}^\circ C\]?
question_answer36) Two metal spheres of radii\[{{r}_{1}}\]and\[{{r}_{2}}\]are charged to the same potential. The ratio of the charge on the two spheres is
question_answer44) Elevation in boiling point of an aqueous urea solution is\[0.52{}^\circ C[{{K}_{b}}=0.52{}^\circ mo{{l}^{-1}}kg].\]Hence, mole fraction of urea in this solution is
question_answer46) For the reaction \[{{H}_{2}}(g)+C{{O}_{2}}(g)CO(g)+{{H}_{2}}O(g)\] If the initial concentration of \[[{{H}_{2}}]=[C{{O}_{2}}]\]and \[x\] mol/L of hydrogen is consumed at equilibrium, the correct expression of\[{{K}_{p}}\]is
question_answer48) A buffer solution with pH 9 is to be prepared by mixing\[N{{H}_{4}}Cl\]and\[N{{H}_{4}}OH\]. Calculate the number of moles of\[N{{H}_{4}}Cl\]that should be added to 1 L of\[1.0\text{ }M\text{ }N{{H}_{4}}OH\].
question_answer49) The emf of the cell involving following changes, \[Zn(s)+N{{i}^{2+}}(1M)\xrightarrow[{}]{{}}Z{{n}^{2+}}(1M)+Ni(s)\] is 0.5105 V. The standard emf of the cell is
question_answer54) Potassium permanganate acts as an oxidant in alkaline and acidic medium. The final products formed from\[KMn{{O}_{4}}\]in the two conditions are respectively
question_answer55) An alkene having the molecular formula \[{{C}_{9}}{{H}_{18}}\]on ozonolysis gives 2, 2-dimethyl propanal and butanone. The alkene is
question_answer59) Identify the compound Z in this reaction sequence \[C{{H}_{3}}C{{H}_{2}}COOH\xrightarrow[{}]{N{{H}_{3}}}X\xrightarrow[{}]{B{{r}_{2}}+KOH}Y\xrightarrow[{}]{HN{{O}_{2}}}Z\]
question_answer63) Four successive members of the first row of transition elements are listed below with their atomic numbers. Which one of them is expected to have the highest third ionization enthalpy?
question_answer69) Sulphide ores of metals are usually concentrated by froth floatation process. Which one of the following sulphide ores offers an exception and is concentrated by chemical leaching?
question_answer70) Soldiers of Napolean army which at Alps during freezing winter suffered a serious problem as regards to die tin buttons of their uniforms. White metallic tin buttons got covered to grey powder. This transformation is related to
A)
an interaction with nitrogen of the air at very low temperatures
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B)
a change in the partial pressure of oxygen in the air
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C)
a change in the crystalline structure of tin
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D)
an interaction with water vapour contained in the humid air
question_answer76) The enthalpy changes for the following processes are listed below \[C{{l}_{2}}(g)2Cl(g),242.3kJmo{{l}^{-1}}\] \[{{I}_{2}}(g)2I(g),151.0\,kJmo{{l}^{-1}}\] \[ICl(g)I(g)+Cl(g),211.3\,kJmo{{l}^{-1}}\] \[{{I}_{2}}(s){{I}_{2}}(g),62.76\,kJmo{{l}^{-1}}\] Given that the standard states for iodine and chlorine are\[{{I}_{2}}(s)\]and\[C{{l}_{2}}(g)\]the standard enthalpy of formation of\[ICI(g)\]is
question_answer79) \[2C{{H}_{3}}-\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}\,=O\xrightarrow[Reduction]{Mg-Hg+{{H}_{2}}O}A\xrightarrow[{}]{{{H}^{+}}}B\] Identify the B in the above sequence
question_answer81) If a plane meets the coordinate axes at A, B and C, in such a way that the centroid of \[\Delta ABC\]is at the point (1, 2, 3), the equation of the plane is
question_answer87) The value of b for which the function \[f(x)=\left\{ \begin{matrix} 5x-4, & 0<x\le 1 \\ 4{{x}^{2}}+3bx, & 1<x<2 \\ \end{matrix} \right.\]is continuous at every point of its domain is
question_answer88) The area bounded by the x-axis, the curve\[y=f(x)\]and the lines\[x=1\]and\[x=b\]is equal to\[\sqrt{{{b}^{2}}+1}-\sqrt{2}\]for all\[b>1,\]then\[f(x)\]is
question_answer92) Let\[p(x)={{a}^{2}}+bx,\]\[q(x)=l{{x}^{2}}+mx+n,\]if \[p(1)-q(1)=0,\]\[p(2)-q(2)=1\]and \[p(3)-q(3)=4,\]then\[p(2)-q(2)=1\]equals to
question_answer95) The integral \[\int_{-1/2}^{1/2}{\left\{ [x]+\log \left( \frac{1+x}{1-x} \right) \right\}dx}=?\] Where\[[.]\]is the greatest integer function.
question_answer97) Let\[f:R\to R,\text{ }g:R\to R,\]be two functions such that\[f(x)=2x-3,\text{ }g(x)={{x}^{3}}+5\]the function\[{{(fog)}^{-1}}(x)\]is equal to
question_answer98) If\[(a\text{ }sec\,\theta ,\text{ b }tan\,\theta )\]and\[(a\text{ }sec\phi ,\text{ b }tan\,\phi )\]are the ends of a focal chord of\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]then \[\tan \theta /2\tan \phi /2\]is equal to
question_answer101) A variable line drawn through the point (1, 3) meets the\[x-\]axis at A and y-axis at B. If the rectangle OAPB is completed, where 0 is the origin, then locus of y is
question_answer108) Let\[{{z}_{1}}\]and\[{{z}_{2}}\]be complex numbers such that \[{{z}_{1}}\ne {{z}_{2}}\]and\[|{{z}_{1}}|=|{{z}_{2}}|.\]If\[{{z}_{1}}\]has positive real part and\[{{z}_{2}}\]has negative imaginary part, then\[\frac{{{z}_{1}}+{{z}_{2}}}{{{z}_{1}}-{{z}_{2}}}\]may be
question_answer114) If A and B are square matrices of the same order and A is non-singular, then for a positive integer n,\[{{({{A}^{-1}}BA)}^{n}}\]is equal to