question_answer2) If \[\text{A=3\hat{i}+4\hat{j}}\] and \[\text{B =7\hat{i}+24\hat{j},}\], then the vector having the same magnitude as Band parallel to A is
question_answer3) The gravitational, field due to a mass distribution is \[E=\frac{k}{{{x}^{3}}}\] in the \[x\] - direction, where k is a constant. The value of gravitational potential at a distance \[x\] is [Taking gravitational potential to be zero at infinity]
question_answer4) Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line. If velocity of flow of water in the pipe of 4 cm diameter is X, then velocity in 2 cm diameter is
question_answer5) Water rises to a height h in a capillary on the surface of the earth in stationary condition. Value of h increases, if this tube is taken
question_answer8) A small laboratory telescope has an objective lens of focal length 140 cm and an eye-piece of focal length 6 cm. Then, separation between the objective and eye-piece is
question_answer13) For an L-R circuit, the inductive reactance is equal to the resistance R of the circuit. An emf \[E={{E}_{0}}\cos (\omega t)\]is applied to the circuit. Then, the power consumed in the circuit is
question_answer16) Thermal conductivity of a material in CGS system is 0.4. In steady state, the rate of flow of heat is\[\text{1}0\text{ cal}/\text{s}-\text{c}{{\text{m}}^{\text{2}}}\].The thermal gradient will be
question_answer18) For a common emitter circuit amplifier, the load resistance of the output circuit is 500 times the resistance of the input circuit. If \[\alpha \text{ }=\text{ }0.\text{98}\], then, current gain is
question_answer19) A water pump of power 2kW is installed in a home. Then, the amount of water (in litres) it can raise in one minute to a height of 10m is [Take\[g=10m/{{s}^{2}}\]]
question_answer21) A man fires a large number of bullets in all directions with same speed \[\upsilon \]. The maximum area on the ground on which these bullets will spread is
question_answer24) The radii of two planets are respectively \[{{R}_{1}}\] and \[{{R}_{2}}\] and their densities are \[{{\rho }_{1}}\] and \[{{\rho }_{2}}\]. Ratio of the accelerations due to gravity at their surfaces is
question_answer25) A tank is filled with water. There is a hole in . the bottom. At the bottom total pressure is 3 aim, then, the velocity of water flowing from h\[\left( \text{1atm }=\text{1}{{0}^{5}}\text{ N}/{{\text{m}}^{\text{2}}} \right)\],then, the velocity of water flowing from hole is
question_answer26) A horizontal overhead power line carries a current of 90A in east to west direction. Magnitude of magnetic field due to the current 1.5 m below the line is
question_answer27) Find the difference of air pressure between the inside and outside of a soap bubble 5 mm in diameter, if the surface tension is 1.6 N/m.
question_answer30) An electron and a photon have equal energy. Then\[{{E}_{K}}\].the ratio of wavelengths of photon and electron is \[\left( \frac{{{\lambda }_{\text{photon}}}}{{{\lambda }_{\text{electron}}}} \right)\]
question_answer32) Light with an energy flux of \[\text{18W}/\text{c}{{\text{m}}^{\text{2}}}\]falls on a non-reflecting surface at normal incidence, The surface has an area of\[\text{2}0\text{ c}{{\text{m}}^{\text{2}}}\], then the total momentum delivered on the surface during a span of 30 mm is
question_answer33) The Young's modulus of a wire of length L and radius r is \[\text{YN}/{{\text{m}}^{\text{2}}}\]. The length and radius are reduced to \[\frac{L}{6}\] and \[\frac{r}{6},\] then its Young's modulus is
question_answer34) In a circular coil (1) of radius R, current \[I\] is flowing and in another coil (2) of radius 2R a current \[2I\] is flowing, then the ratio of the magnetic fields produced by the two coils is
question_answer37) In a semiconductor diode, the forward voltage is changed from 0.5 V to 0.7V, then the forward current changes by 1mA. The forward resistance of the diode junction is
question_answer38) Moment of inertia of wheel about the axis of 4 rotation is 3 MKS units. Its kinetic energy will be 600 J, if period of rotation is (in seconds)
question_answer39) A galvanometer has a coil resistance of 100 \[\Omega \] It gives a full scale deflection when a current of 1mA is passed through it. The value of resistance which can convert the galvanometer into an ammeter giving full scale deflection for a current of 10 A is
question_answer40) A siren emits sound of frequency 1000 Hz, it moves away from the observer towards a cliff with a speed of\[\text{1}0\text{ m}{{\text{s}}^{{{\text{-}}^{\text{1}}}}}\]. Then, the frequency of sound heard by observer coming directly from the siren is
question_answer41) One surface of a lens is convex and the other is concave. If the radii of curvatures are \[{{R}_{1}}\] and \[{{R}_{2}}\],then the lens will be convex, if
question_answer42) A convex mirror of radius of curvature 1.6 m has an object placed at a distance of 1m from it. The image is formed at a distance of 1
question_answer43) When a radioactive isotope \[_{88}{{R}^{228}}\]decays in 5 series by the emission of \[3\alpha \]-particles and P--\[\beta \]-particles, the mass number of the isotope finally formed is
question_answer44) As shown in the experimental setup, two cells with the same emf E and different internal resistance \[{{r}_{1}}\] and \[{{r}_{2}}\] are connected in series to an external resistance R Value of R so that the potential difference across the first cell be zero, is
question_answer45) Two radioactive sources X and Y of half lives 1h and 2 h respectively initially contain the same number of radioactive atoms. At the end of 2 h, their rates of disintegration are in the ratio of
question_answer47) The current gain of a transistor in a common base arrangement is 0.98. The change in collector current corresponding to a change of 5 mA in emitter current is
question_answer48) B. A plano-convex lens has a curved surface of radius of curvature R and refractive index \[\mu \]. If its plane surface is silvered, then, it behaves as a
question_answer52) The wave number of the spectral line in the emission spectrum of hydrogen will be equal to \[\frac{8}{9}\] times the Rydberg's constant if the electron jumps from
question_answer54) Nitrobenzene on reduction using zinc in alkaline medium results in X. The number of sigma (\[\sigma \]) and pi (\[\pi \]) bonds in X is
question_answer55) Peroxide ion............ (i) has five completely filled anti bonding molecular orbitals (ii) is diamagnetic (iii) has bond order one (iv) is isoelectronic with neon Which one of these is correct?
question_answer59) Compound A \[({{C}_{3}}{{H}_{6}}O)\]undergoes following reactions to form B and C. Identify A, 5 and C. \[\underset{A}{\mathop{C\xleftarrow{Zn-Hg/HCl}{{C}_{3}}}}\,\underset{B}{\mathop{\underset{A}{\mathop{{{H}_{6}}}}\,O}}\,\xrightarrow{{{I}_{2}}/NaOH}\underset{C}{\mathop{B}}\,\]
question_answer62) Given that \[\text{dE }=\text{ TdS }-\text{ pdV}\] and \[\text{H }=\text{ E }+\text{ pV}\]. Which one of the following relations is true?
question_answer64) A system is allowed to move from state A to B following path ACB by absorbing 80 J of heat energy. The work done by the system is 30 J. The work done by the system in reaching state B from A is 10 J through path ADB. Which statements are correct? (i) Increase in internal energy from state A tc state B is 50 J. (ii) If path ADB is followed to reach state B, \[\Delta E=50J\]. (iii) If work done by the system in path AB is 20J,the heat absorbed during path AB = 70 J. (iv) The value \[{{E}_{C}}-{{E}_{A}}\]is equal to \[{{E}_{D}}-{{E}_{B}}\]. (v) Heat absorbed by the system to reach B from A through path ADD is 60 J.
question_answer65) Identify the order in which the spin only magnetic moment (in BM) increases for the following four ions \[\text{I}.\text{ F}{{\text{e}}^{\text{2+}}}\] \[\text{II}\text{.T}{{\text{i}}^{\text{2+}}}\] \[\text{III}\text{.C}{{\text{u}}^{\text{2+}}}\] \[\text{IV}\text{.}{{\text{V}}^{\text{2+}}}\]
question_answer67) In photoelectric effect, if the energy required to overcome the attractive forces on the electron, (work functions) of Li, Na and Rb are\[\text{2}.\text{41 eV}\], \[\text{2}.\text{3}0\text{ eV}\] and \[\text{2}.0\text{9 eV}\] respectively, the work function of 'K' could approximately be in eV.
question_answer71) An oxygen containing organic compound upon oxidation forms a carboxylic acid as the only organic product with its molecular mass higher by 14 units. The organic compound is
question_answer72) A buffer solution contains 0.1 mole of sodium acetate in \[\text{1}000\text{ c}{{\text{m}}^{\text{3}}}\]of 0.1 M acetic acid. To the above buffer solution, 0.1 mole of sodium acetate is further added and dissolved. The pH of the resulting buffer is equal to
question_answer74) The activation energy for a reaction at the temperature T K was found to be 2. 303 RT J \[\text{mo}{{\text{l}}^{\text{-1}}}\]. The ratio of the rate constant to Arrhenius factor is
question_answer77) g of silver gets distributed between \[\text{1}0\text{ c}{{\text{m}}^{\text{3}}}\]of molten zinc and \[\text{1}00\text{ c}{{\text{m}}^{\text{3}}}\]of molten lead at\[\text{8}00{}^\circ \text{ C}\]. The percentage of silver in the zinc layer is approximately
question_answer79) Which one of the following is the ratio of the lowering of vapour pressure of 0.1 M aqueous solutions of \[\text{BaC}{{\text{l}}_{2}}\], \[\text{NaCl}\] and \[\text{A}{{\text{l}}_{2}}{{(S{{O}_{4}})}_{3}}\] respectively?
question_answer80) In which one of the following, does the given amount of chlorine exert the least pressure in a vessel of capacity \[\text{1 d}{{\text{m}}^{\text{3}}}\]at 273 K?
question_answer81) 19 g of a mixture containing \[\text{NaHC}{{\text{O}}_{\text{3}}}\]and \[N{{a}_{2}}C{{O}_{3}}\]on complete heating liberated 1.12 L of \[C{{O}_{2}}\] at STP. The weight of the remaining solid was 15.9 g. What is the weight (in g) of \[N{{a}_{2}}C{{O}_{3}}\]in the mixture before heating?
question_answer86) What is Z in the following reactions? \[\text{BC}{{\text{l}}_{\text{3}}}\text{+}{{\text{H}}_{\text{2}}}\xrightarrow[\text{45}{{\text{0}}^{\text{o}}}\text{-C}]{\text{Cu-Al}}\text{X+HCl}\] \[\text{X}\xrightarrow{\text{methylation}}Z\]
question_answer87) The empirical formula of a non-electrolyte is\[\text{C}{{\text{H}}_{\text{2}}}\text{O}\]. A solution containing 6g of the compound exerts the same osmotic pressure as that of 0.05 M glucose solution at the same temperature. The molecular formula of the compound is
question_answer88) \[{{E}_{1}},{{E}_{2}},{{E}_{3}}\]are the emf values of the three galvanic cells respectively. (i) \[\text{Zn }\!\!|\!\!\text{ Zn}_{\text{1M}}^{\text{2+}}\text{ }\!\!|\!\!\text{ }\!\!|\!\!\text{ Cu}_{\text{0}\text{.1M}}^{\text{2+}}\text{ }\!\!|\!\!\text{ Cu}\] (ii) \[Zn|Zn_{1M}^{2+}||Cu_{1M}^{2+}|Cu\] (iii) \[Zn|Zn_{0.1M}^{2+}||Cu_{1M}^{2+}|Cu\] Which one of the following is true?
question_answer89) In Kjeldahl's method, ammonia from 5 got food neutralizes \[\text{3}0\text{ c}{{\text{m}}^{\text{3}}}\] of 0.1 N acid. The percentage of nitrogen in the food is
question_answer92) The enthalpy changes for the following processes are listed below \[\text{C}{{\text{l}}_{\text{2}}}\text{(g)}\to \text{2Cl(g),242}\text{.3 kJ mo}{{\text{l}}^{\text{-1}}}\] \[{{\text{I}}_{\text{2}}}\text{(g)}\to \text{2I(g),151}\text{.0 kJ mo}{{\text{l}}^{\text{-1}}}\] \[\text{ICl(g)}\to \text{I(g)+Cl(g),211}\text{.3 kJ mo}{{\text{l}}^{\text{-1}}}\] \[{{\text{I}}_{\text{2}}}\text{(g)}\to {{\text{I}}_{\text{2}}}\text{(g),62}\text{.76 kJ mo}{{\text{l}}^{\text{-1}}}\] Given that the standard states for iodine and chlorine are\[{{I}_{2}}(s)\] and \[C{{l}_{2}}(g),\] the standard enthalpy for the formation of \[ICl(g)\] is
question_answer93) \[\text{2}.\text{5 mL}\] of \[\frac{2}{5}M\] weak monoacidic base\[({{K}_{b}}=1\times {{10}^{-12}}\text{ at 2}{{\text{5}}^{\circ }}C)\] is titrated with \[\frac{2}{15}M\] \[\text{HCl}\] in water at\[\text{25}{}^\circ \text{C}\]. The concentration of \[{{\text{H}}^{\text{+}}}\] at equivalence point is\[({{K}_{\omega }}=1\times {{10}^{-14}}\text{ at 2}{{\text{5}}^{\circ }}C)\]
question_answer94) Three reactions involving \[{{\text{H}}_{\text{2}}}\text{PO}_{\text{4}}^{\text{-}}\] are given below \[\text{I}\text{.}\] \[{{\text{H}}_{\text{3}}}\text{P}{{\text{O}}_{\text{4}}}\text{+}{{\text{H}}_{\text{2}}}\text{O}\to {{\text{H}}_{\text{3}}}{{\text{O}}^{\text{+}}}\text{+}{{\text{H}}_{\text{2}}}\text{PO}_{\text{4}}^{\text{-}}\] \[\text{II}\text{. }{{\text{H}}_{2}}\text{PO}_{4}^{-}\text{+}{{\text{H}}_{\text{2}}}\text{O}\to \text{HPO}_{4}^{2-}\text{+}{{\text{H}}_{3}}{{\text{O}}^{+}}\] \[\text{III}\text{. }{{\text{H}}_{\text{2}}}\text{PO}_{\text{4}}^{\text{-}}\text{+O}{{\text{H}}^{\text{-}}}\to {{\text{H}}_{\text{3}}}\text{P}{{\text{O}}_{\text{4}}}\text{+}{{\text{O}}^{\text{2-}}}\] In which of the above does H^O^ act as an acid?
question_answer98) 48. Consider the following statements. I. \[\text{La}{{\left( \text{OH} \right)}_{\text{3}}}\]is the least basic among hydroxides of lanthanides. II. \[Z{{r}^{4+}}\]and \[\text{H}{{\text{f}}^{\text{4+}}}\]possess almost the same ionic radii. III. \[C{{e}^{4+}}\] can act as an oxidising agent. Which of the above is/are true?
question_answer99) Concentrated hydrochloric acid when kept in open air sometimes produces a cloud of white fumes. The explanation for it is that
A)
concentrated hydrochloric acid emits strongly smelling HC1 gas all the time
doneclear
B)
oxygen in air reacts with the emitted HCl gas to form a could of chlorine gas
doneclear
C)
strong affinity of HCl gas for moisture in air results in forming of droplets of liquid solution which appears like a cloudy smoke
doneclear
D)
due to strong affinity for water, concentrated hydrochloric acid pulls moisture of air towards itself. This moisture forms droplets of water and hence, the cloud.
question_answer100) Compartments A and B have the following combinations solution
Column 1
Column II
I. \[\text{0}\text{.1M KCl}\] II. \[\text{0}\text{.1 }\!\!%\!\!\text{ (m/V)NaCl}\] III. \[\text{18g}{{\text{L}}^{-1}}\] glucose IV. \[\text{20 }\!\!%\!\!\text{ (m/V)}\]
\[\text{0}\text{.2 M KCl}\] \[\text{10 }\!\!%\!\!\text{ (m/V)NaCl}\] \[34.2g{{L}^{-1}}\]sucrose \[\text{10 }\!\!%\!\!\text{ (m/V)}\]glucose
Indicate the number of solutions which is/are isotonic
question_answer101) The value of \[\int_{{}}^{{}}{\frac{dx}{(1+{{x}^{2}})\sqrt{1-{{x}^{2}}}}}\] is *-correct-answer-description-* Let \[\int_{{}}^{{}}{\frac{dx}{(1+{{x}^{2}})\sqrt{1-{{x}^{2}}}}}\] Put \[x=\frac{1}{t}\Rightarrow dx=-\frac{1}{{{t}^{2}}}dt\] Then, \[l=\int_{{}}^{{}}{\frac{-dt}{{{t}^{2}}\left( 1+\frac{1}{{{t}^{2}}} \right)\sqrt{1-{{\left( \frac{1}{t} \right)}^{2}}}}}\] \[=-\int_{{}}^{{}}{\frac{tdt}{({{t}^{2}}+1)\sqrt{{{t}^{2}}-1}}}\] Again put \[{{\text{t}}^{\text{2}}}\text{-1 = }{{\text{z}}^{\text{2 }}}\Rightarrow \text{t dt = z dz}\] Then , \[\text{l = -}\int_{{}}^{{}}{\frac{\text{z dz}}{\text{(}{{\text{z}}^{\text{2}}}\text{+2) z}}}\] \[=-\int_{{}}^{{}}{\frac{1}{{{z}^{2}}+2}}dz\] \[=-\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{z}{\sqrt{2}} \right)+C\] \[=-\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{\sqrt{{{t}^{2}}-1}}{\sqrt{2}} \right)+C\] \[=-\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{\sqrt{1-{{x}^{2}}}}{\sqrt{2}x} \right)+C\]
question_answer105) Let a, b and c be non-zero vectors such that no two are collinear and \[(a\times b)\times c=\frac{1}{3}\]\[b||c|\]\[|a.\] If \[\theta \] is the acute angle between the vectors b and c, then sin \[\theta \] is equal to
question_answer107) The sides of an equilateral triangle are increasing at the rate of 2 cm/s. The rate at which the area increases when the side is 10 cm, is
question_answer110) The equation of the plane meets the axes in A, and C such that the centroid of the \[\Delta \]ABC is\[\left( \frac{1}{3},\frac{1}{3},\frac{1}{3} \right),\] is given by
question_answer111) The probability that a student get success in a competition is \[\frac{3}{4}\]. The probability that exactly 2 out of 4 students get success, is
question_answer112) 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_answer113) The function \[f:R\to R\] is defined by \[f\left( x \right)={{3}^{-x}}\]. Observe the following statements I. \[f\] is one-one. II. \[f\] is onto. III.\[f\] s a decreasing function. Out of these, true statements are
question_answer116) If\[x={{\log }_{\alpha }}bc,\] \[y={{\log }_{b}}ca\]and \[z={{\log }_{c}}ab\], then the value of\[\frac{1}{1+x}+\frac{1}{1+y}+\frac{1}{1+z}\] will be
question_answer117) If\[\alpha \] and \[\beta \]are the roots of \[{{x}^{\text{2}}}+5x+\text{ 4 }=\text{ }0,\] then equation whose roots are \[\frac{\alpha +2}{3}\] and \[\frac{\beta +2}{3}\], is
question_answer118) If one of the roots of equation \[{{x}^{2}}+ax\text{ }+\text{3 }=\text{ }0\] is 3 and one of the roots of the equation \[~{{x}^{2}}+ax+\text{ }b=0\] is three times the other root, then the value of b is
question_answer119) If sum of the series \[\sum\limits_{n=0}^{\infty }{{{r}^{n}}=S}\]for \[|r|<1,\] then sum of the series \[\sum\limits_{n=0}^{\infty }{{{r}^{2n}}}\]is
question_answer126) The number of values of \[x\] in \[[0,2\pi ]\]satisfying the equation \[3\text{ }\cos \text{ }2x-10\text{ }\cos \text{ }x\text{ }+\text{ }7\text{ }=\text{ }0\] is
question_answer128) If in a \[\Delta \text{ABC}\], the altitudes from the vertices A, B and C on opposite sides are in HP, then sin A, sin B, sin C are in
question_answer130) The base of a cliff is circular. From the extremities of a diameter of the base, angles of elevation of the top of the cliff are \[\text{3}0{}^\circ \] and\[\text{6}0{}^\circ \]. If the height of the cliff be 500 m, then diameter of the base of the cliff is
question_answer132) Let A (2, -3) and B (-2,1) be vertices of a \[\Delta \text{ABC}\]. If the centroid of this triangle moves on the line\[2x\text{ }+\text{ }3y\text{ }=\text{1}\], then the locus of the vertex C is the line
question_answer133) A straight line through the point (2, 2) intersects the lines \[\sqrt{3}x+y=0\] and \[\sqrt{3x}-y=0\]at the points A and B. The equation of the line AB, so that the \[\Delta \text{OAB}\] is equilateral, is
question_answer135) The locus of a point which moves so that the ratio of the length of the tangents to the circles \[{{x}^{2}}+{{y}^{2}}+4x+3=0\]and \[{{x}^{2}}{{y}^{2}}-6x\]\[+5=0\] is 2 : 3, is
question_answer136) The circles \[{{x}^{2}}+{{y}^{2}}-\text{ }5x+6y+\text{ 15 }=\text{ }0\] and \[{{x}^{2}}+{{y}^{2}}-2x+6y+\text{6}=0\]touch each other
question_answer137) An ellipse has OB as semi-minor axis, F and F' are its foci and the\[\angle FBF'\]is a right angle. Then, the eccentricity of the ellipse is
question_answer139) The locus of a point \[P(\alpha ,\beta )\] moving under the condition that the line \[y=ax+\beta \] is a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], is
question_answer145) If \[f'(2)=6,f'(1)=4,\], then \[\underset{h\to 0}{\mathop{\lim }}\,\frac{f(2h+2+{{h}^{2}})-f(2)}{f(h-{{h}^{2}}+1)-f(1)}\] is equal to
question_answer146) The value of k for which the function\[f(x)\left\{ \underset{k,}{\mathop{\frac{1-\cos 4x}{8{{x}^{2}}}}}\, \right.,\begin{matrix} x\ne 0 \\ x=0 \\ \end{matrix}\]is continuous at \[x=\text{ }0\], is
question_answer148) Suppose p points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is