A massive platform of mass M is moving with speed \[v=6\,\,m{{s}^{-1}}\]. At \[t=0\] a body of mass\[m(m<<M)\]is gently placed on the platform. If coefficient of friction between body and platform is\[\mu =0.3\]and\[g=10\,\,m/{{s}^{2}}\]. Then,
A)
the body covers a distance 3 m on the platform in the direction of motion of the platform.
doneclear
B)
the body covers a distance 3 m on the platform opposite to the direction of motion of plat form before coming to rest.
doneclear
C)
the body covers a distance 6 m on the platform in the direction of motion of the platform.
doneclear
D)
the body covers a distance 6 m on the platform opposite to the direction of motion of plat form before coming to rest.
A given ray of light suffers minimum deviation in an equilateral prism P. Additional prism Q and R of identical shape and of the same material as Pare now added as shown in the figure. The ray will now suffer
Two coherent monochromatic light beams of intensities \[I\] and \[4I\] are superimposed. The maximum and minimum possible intensities in the resulting beam are
A ray incident at a point as an angle of incidence of \[60{}^\circ \], enters a glass sphere ofrefractiveindex, \[n=\sqrt{3}\] and is reflected and refracted at the further surface of the sphere. The angle between the reflected and refracted rays at this surface is
A rod of length \[l\] falls on two metal pads of same height from a height h. The coefficients of restitution of the metal pads are \[{{e}_{1}}\]and \[{{e}_{2}}({{e}_{1}}>{{e}_{2}})\]. The angular velocity of the rod after it recoils is
A uniform rod of length \[l\]and mass M is suspended on two vertical inextensible string as shown in the figure. Calculate tension T in left string at the instant, when right string snaps.
A particle with charge +q and mass m, moving under the influence of a uniform electric field \[Ei\] and a uniform magnetic field \[Bk,\] follows a trajectory from P to Q as shown. The velocities at P and Q are \[vi\]and \[-2vj\]. Which of the following is incorrect?
The average translational energy and the \[rms\]speed of molecules in a sample of oxygenate 300K are \[6.21\times {{10}^{-21}}J\] and 484 m/s, respectively. The corresponding values at 600Kare nearly (assuming ideal gas behavior).
In a room, where the temperature is \[30{}^\circ C\], a body cools from \[61{}^\circ C\] to \[59{}^\circ C\] is 4 min. The time taken by the body to cool from \[51{}^\circ C\] to \[49{}^\circ C\] will be
A planet has twice the density of earth but the acceleration due to gravity on its surface is exactly the same as that on the surface of earth. Its radius in terms of earth's radius R will be
A cube of mass m and density D is suspended from the point P by a spring of stiffness k. The system is kept inside a beaker filled with a liquid of density d. The elongation in the spring, assuming D > d, is
A small hole is made at a height of \[h'\left( =\frac{1}{\sqrt{2}} \right)m,\] from the bottom of a cylindrical water tank and at a depth of \[h=\sqrt{2}\,m,\]from the upper level of water in the tank. The distance where the water emerging from the hole strikes the ground is
A conducting loop is pulled with a constant velocity towards a region of constant (steady) magnetic field d induction B as shown in the figure. Then, the current involved in the loop is (d > r)
Two identical capacitors, have the same capacitance C. One of them is charged to potential \[{{V}_{1}}\]and the other to \[{{V}_{2}}\]. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is
A charge \[-q\] is placed at the axis of a charged ring of radius r at a distance of \[2\sqrt{2}\,r\] as shown in figure. If ring is fixed and carrying a charge Q, the kinetic energy of charge -q when it is released and reaches the centre of ring will be
A block Q of mass M is placed on a frictionless horizontal surface AB and a body P of mass m is released on its frictionless slope. As P slides by a length L on this slope of inclination \[\theta \], the block Q would slide by a distance
The de-Broglie wavelength of a particle moving with a velocity \[2.25\times {{10}^{8}}\] m/s is equal to the wavelength of photon. The ratio of kinetic energy of the particle to the energy of the photon is (velocity of light is \[3\times {{10}^{8}}\] m/s)
An insect crawls up a hemispherical surface very slowly (figure). The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre of hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of \[\alpha \]is given by
A rod of length \[l\] (laterally thermally insulated) of uniform cross-sectional area A consists of a material whose thermal conductivity varies with temperature as \[K=\frac{{{K}_{0}}}{a+bT},\]where \[{{K}_{0}}\], a and b are constants. \[{{T}_{1}}\]and\[{{T}_{2}}\,(<{{T}_{1}})\]are the temperature of two ends of rod. Then, rate of flow of heat across the rod is
Direction: According to the 6ohr model, the energy levels of a hydrogen atom can be found by making two assumptions.
(i) The electrons move in a circular orbit and (ii) the angular momentum of the electron in the n\[th\]energy level is quantized to have a value,\[n\frac{h}{2\pi }\]. The levels calculated with a nuclear charge \[Ze\] deals with a single electron in the orbit are called hydrogenic levels. Assume that the two electrons in the ground, state of a helium atom occupy the corresponding lowest hydrogenic level.
The minimum repulsive energy between the two electrons would then be
Direction: According to the 6ohr model, the energy levels of a hydrogen atom can be found by making two assumptions.
(i) The electrons move in a circular orbit and (ii) the angular momentum of the electron in the n\[th\]energy level is quantized to have a value,\[n\frac{h}{2\pi }\]. The levels calculated with a nuclear charge \[Ze\] deals with a single electron in the orbit are called hydrogenic levels. Assume that the two electrons in the ground, state of a helium atom occupy the corresponding lowest hydrogenic level.
If for a hydrogen atom ionization temperature is T, the temperature at which He atomsionize completely (both electrons having left off the atom) would be
Direction: A potentiometer is device used for measuring emf and internal resistance of a cell. It consists of two circuits one is main circuit in which there is a cell of given emf\[\varepsilon \] and given resistance R which is connected across a wire of length 100 cm having resistance r. Another circuit having unknown emf\[\varepsilon \]and galvanometer. For a given potentiometer if \[\varepsilon '=30\,V,\,\,r=1\Omega \] and resistance R varies with time t given by\[R=2t\]. The jockey can move on wire with constant velocity 10 cm/s and switch S is closed at\[t=0\].
If jockey starts moving from A at\[t=0\]and balancing point found a\[t=1s,\], then the value of \[\varepsilon \]is
Direction: A potentiometer is device used for measuring emf and internal resistance of a cell. It consists of two circuits one is main circuit in which there is a cell of given emf\[\varepsilon \] and given resistance R which is connected across a wire of length 100 cm having resistance r. Another circuit having unknown emf\[\varepsilon \]and galvanometer. For a given potentiometer if \[\varepsilon '=30\,V,\,\,r=1\Omega \] and resistance R varies with time t given by\[R=2t\]. The jockey can move on wire with constant velocity 10 cm/s and switch S is closed at\[t=0\].
If jockey starts moving from A at \[t=1\]s, then the balancing point will be obtained at
Direction: A potentiometer is device used for measuring emf and internal resistance of a cell. It consists of two circuits one is main circuit in which there is a cell of given emf\[\varepsilon \] and given resistance R which is connected across a wire of length 100 cm having resistance r. Another circuit having unknown emf\[\varepsilon \]and galvanometer. For a given potentiometer if \[\varepsilon '=30\,V,\,\,r=1\Omega \] and resistance R varies with time t given by\[R=2t\]. The jockey can move on wire with constant velocity 10 cm/s and switch S is closed at\[t=0\].
If balancing length is found to be 70 cm, then the time after which jockey starts moving from
Statement I Two non-ideal batteries are connected in parallel, the equivalent emf is smaller than either of the two emfs.
Statement II Two non-ideal batteries are connected in parallel, the equivalent internal resistance is smaller than either of the two internal resistances.
A)
Statement I is true, Statement II is also true and Statement II is the correct explanation of Statement I.
doneclear
B)
Statement I is true, Statement II is also true and Statement It is not the correct explanation of Statement I.
\[1\,M\,N{{H}_{4}}\,OH\]and 1 M HCI are mixed to make total volume of 300 mL. If pH of the mixture is 9.26 and \[p{{K}_{a}}\,(NH_{4}^{+})=9.26\] then volume ratio of \[N{{H}_{4}}OH\] and HCI will be
Apatite is a mineral that is found in tooth enamel. When fluoride toothpastes are used, this mineral is converted to fluoroapatite, which is more resistant to tooth decay. The formula of apatite is \[C{{a}_{5}}{{(P{{O}_{4}})}_{x}}F\]. What is the value of \[x\] if the compound contains 18.45% by weight of phosphorus? (Atomic weight of \[P=31,\,\,Ca=40,\,\,F=19\] and\[O=16\])
A white powder when strongly heated gives off brown fumes. A solution of this powder gives a yellow precipitate with a solution of Kl. When a solution of \[BaC{{l}_{2}}\]is added to a solution of powder, a white precipitate results. This white powder may be
Bond enthalpies of \[AB,\,\,{{A}_{2}}\] and \[{{B}_{2}}\] respectively are in the ratio 1:1:0.5. If \[\Delta H\] for the formation of AB is -200 kJ, bond enthalpy of \[{{A}_{2}}\] will be (in kJ/mol)
A certain quantity of ammonium chloride is boiled with 100 mL of 0.8 N NaOH till no further action occurs. Excess of NaOH required 40 mL of 0.75 N sulphuric acid to neutralise it. How much ammonium chloride was used?
The coolant usually contains a solution of antifreeze prepared by mixing equal volumes of ethylene giycol, \[{{C}_{2}}{{H}_{4}}{{(OH)}_{2}}\] and water. The density of ethylene glycol is\[1.113\,\,g\,\,c{{m}^{-3}}\]. The freezing point of the mixture is (\[{{K}_{f}}\] for water \[=1.86\,kg\,\,mo{{l}^{-1}}\,{{K}^{-1}}\])
Reactants of reaction \[I\]are \[C{{H}_{3}}CON{{H}_{2}},\,\,KOH,\,B{{r}_{2}}\]. Reactants of reaction II are \[C{{H}_{3}}N{{H}_{2}},\]\[C{{H}_{3}}C{{l}_{3}},\,\,KOH\].The intermediate species of reaction I and reaction II are respectively
The reaction given below shows the peptisation of \[Sn{{O}_{2}}\] precipitate by KOH\[Sn{{O}_{2}}+KOH\xrightarrow{\,}X\] (negatively charged sol). The sol X has formula,
Consider the following reduction reaction \[C{{H}_{3}}C{{H}_{2}}-\overset{\begin{matrix} O \\ || \\ \end{matrix}}{\mathop{C}}\,-C{{H}_{3}}+LiAl{{H}_{4}}\xrightarrow{O{{H}_{2}}}Alcohol\] the correct statement is
A)
racemic mixture of products is obtained
doneclear
B)
acerbation reactive intermediate is involved
doneclear
C)
if hydrolysis is done with \[{{D}_{2}}O\] in place of \[{{H}_{2}}O,\] the product remains the same
doneclear
D)
if\[LiAl{{D}_{4}}\] is used in place of \[LiAl{{H}_{4}},\,C{{H}_{3}}C{{H}_{2}}(OD)C{{H}_{3}}\] is obtained
Hydrogen sulphide reacts with lead acetate forming a black compound which reacts with\[{{H}_{2}}{{O}_{2}}\] to form another compound. The colour of the compound is
Direction: A waxy crystalline solid [a] with garlic odour is obtained by burning a white solid [e] in the steam of air. [a] reacts vigorously with hot water forming a gas [b] and an acid [c]. Gas [b] has unpleasant odour of rotten fish and is neutral towards litmus. Wizen gas [b] is passed through a blue solution of a compound [f], it produces a black precipitate [d]. Compound [f] gives chocolate colored precipitate [g] with \[{{K}_{4}}[Fe{{(CN)}_{6}}]\].
Direction: A waxy crystalline solid [a] with garlic odour is obtained by burning a white solid [e] in the steam of air. [a] reacts vigorously with hot water forming a gas [b] and an acid [c]. Gas [b] has unpleasant odour of rotten fish and is neutral towards litmus. Wizen gas [b] is passed through a blue solution of a compound [f], it produces a black precipitate [d]. Compound [f] gives chocolate colored precipitate [g] with \[{{K}_{4}}[Fe{{(CN)}_{6}}]\].
Direction: A waxy crystalline solid [a] with garlic odour is obtained by burning a white solid [e] in the steam of air. [a] reacts vigorously with hot water forming a gas [b] and an acid [c]. Gas [b] has unpleasant odour of rotten fish and is neutral towards litmus. Wizen gas [b] is passed through a blue solution of a compound [f], it produces a black precipitate [d]. Compound [f] gives chocolate colored precipitate [g] with \[{{K}_{4}}[Fe{{(CN)}_{6}}]\].
If the total number of m elements subsets of the set \[A=\{{{a}_{1}},\,{{a}_{2}},\,{{a}_{3}},...,{{a}_{n}}\}\] is \[\lambda \] times the number of 3 elements subsets containing \[{{a}_{4}},\] then \[n\] is
If \[{{D}_{k}}=\left| \begin{matrix} 1 & n & n \\ 2k & {{n}^{2}}+n+1 & {{n}^{2}}+n \\ 2k-1 & {{n}^{2}} & {{n}^{2}}+n+1 \\ \end{matrix} \right|\] and \[\sum\limits_{k\,=\,1}^{n}{{{D}_{k}}=56,}\] then \[n\] is equal to
A box contains 15 transistors, 5 of which are defective. An inspectors takes out one transistor at random, examines it for defects and replaces it. After it has been replaced another inspector does the same thing and then so does a third inspector. The probability at least one of the inspectors, finds a defective transistor is equal to
Range of the function f defined by \[f(x)\,=\left[ \frac{1}{\sin \,\{x\}} \right],\], (where, [.] and {.} respectively, denotes the greatest integer and the fractional part function) is
Let \[f(x)=\left\{ \begin{matrix} |{{x}^{3}}+{{x}^{2}}+3x+\sin \,x| & x\ne 0 \\ 0 & x=0 \\ \end{matrix}, \right.\] then number of points [where \[f(x)\] attains its minimum value] is
Suppose \[{{A}_{1}},\,{{A}_{2}},\,...,{{A}_{30}}\] are thirty sets each with five elements and \[{{B}_{1}},\,{{B}_{2}},\,...,{{B}_{n}}\] are n set each with three elements. Let \[\bigcup\limits_{i\,=\,1}^{30}{{{A}_{i}}=}\,\bigcup\limits_{j\,=\,1}^{n}{{{B}_{j}}=S}\]. Assume that each element of S belongs to exactly 10 of the \[{{A}_{i}}'s\] and exactly 9 of \[{{B}_{j}}'s\]. The value of n must be
If\[\overline{X}\] and \[{{\overline{X}}_{2}}\] are the means of two distributions such that \[{{\overline{X}}_{1}}<{{\overline{X}}_{2}}\] and \[\overline{X}\] is the mean of the combined distribution, then
Direction: Let a, b and c be three vectors such that \[|a|\,=\,|b|\,=\,|\,c|\,=4\]and the angle between a and b is \[\pi /3,\] the angle between b and c is \[\pi /3,\] and angle between c and a is \[\pi /3,\]. Then,
The volume of the parallelepiped whose adjacent edges are represented by the vectorsa, band c is
Direction: Let a, b and c be three vectors such that \[|a|\,=\,|b|\,=\,|\,c|\,=4\]and the angle between a and b is \[\pi /3,\] the angle between b and c is \[\pi /3,\] and angle between c and a is \[\pi /3,\]. Then,
The height of the parallelepiped whose adjacent edges are represented by the vectors a, b and c is
Direction: If \[\cos \,\frac{\pi }{7},\,\,\cos \,\frac{3\pi }{7}\]and \[\cos \,\frac{5\pi }{7}\] are the roots of the equations \[8{{x}^{3}}-4{{x}^{2}}-4x+1=0\] then,
The value of \[\sec \,\frac{\pi }{7}+\sec \,\frac{3\pi }{7}+\sec \,\frac{5\pi }{7}\] is
Direction: If \[\cos \,\frac{\pi }{7},\,\,\cos \,\frac{3\pi }{7}\]and \[\cos \,\frac{5\pi }{7}\] are the roots of the equations \[8{{x}^{3}}-4{{x}^{2}}-4x+1=0\] then,
The value of \[\frac{\pi }{14}\,\sin \,\frac{3\pi }{14}\,\sin \,\frac{5\pi }{14}\] is
Direction: For the following questions. Choose the correct answer from the codes [a], [b], [c] and [d] defined as follows.
For each of the following questions, one out of given options is correct.
Statement I lf\[\frac{x}{a}+\frac{y}{b}=1\] and \[\frac{x}{c}+\frac{y}{d}=-1\] cut \[x\] and \[y-\] axes at four concyclic points, A, B, C and D respectively, then the orthocentre of \[\Delta ABC\]is \[\left( 0,\,\frac{ac}{b} \right)\].
Statement II If chords AC and BD of a circle intersect at origin O, then\[OA\cdot OC=OB\cdot OD\].
A)
Statement I is true, Statement II is also true and Statement II is the correct explanation of Statement I.
doneclear
B)
Statement I is true. Statement II is also true and Statement II is not the correct explanation of Statement I.