The two vectors \[\vec{A}\] and \[\vec{B}\] are drawn from a common point and \[\overset{\to }{\mathop{C}}\,=\overset{\to }{\mathop{A}}\,+\overset{\to }{\mathop{B}}\,\] . Regarding the angle between \[\overset{\to }{\mathop{A}}\,\] and \[\overset{\to }{\mathop{B}}\,\],study the following statements,
A ball is projected from the floor of a long hall having a roof height of\[H=10m\]. The ball is projected with a velocity of \[u=25\text{ }m{{s}^{-1}}\]making an angle of \[\theta =37{}^\circ \] to the horizontal. On hitting the roof the ball loses its entire vertical component of velocity but there is no change in the horizontal component of its velocity. The ball was projected from point A and it hits the floor at B. Find the distance between AB.
A board is balanced on a rough horizontal semi-circular log. Equilibrium is obtained with the help of addition of a weight to one of the ends of the board when the board makes an angle 6 with the horizontal. Coefficient of friction between the log and the board is
Two particles of equal mass have velocities \[\overset{\to }{\mathop{{{v}_{1}}}}\,=2\hat{i}\,\,m/s\] and\[\overset{\to }{\mathop{{{v}_{2}}}}\,=2\hat{j}\,\,m/s\]. First particle has an acceleration \[\overset{\to }{\mathop{{{a}_{1}}}}\,=(3\hat{i}+3\hat{j})\,m/{{s}^{2}}\] while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a
A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r is made from an iron plate of thickness\[t/4\]. The relation between moments of inertia \[{{I}_{A}}\] and \[{{I}_{B}}\] is
A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius\[(1.01)R\]. The period of the second satellite is larger than that of the first one by approximately
A stream of water of density \[\rho ,\] cross-sectional area A, and speed v strikes a wall that is perpendicular to the direction of the stream, as shown in the figure. The water then flows sideways across the wall. The force exerted by the stream on the wall is
As part of an experiment to determine the latent heat of vaporisation of water, a student boils some water in a beaker using an electric heater as shown below. The student notes two sources of error.
Error 1: Thermal energy is lost from the sides of the beaker.
Error 2: As the water is boiling, water splashes out of the beaker.
Which of the following gives the correct effect of these two errors on the calculated value for the specific latent heat?
\[28\text{ }g\]of \[{{N}_{2}}\] gas is contained in a flask at a pressure of \[10\text{ }atm\]and at a temperature of\[57{}^\circ \]. It is found that due to leakage in the flask, the pressure is reduced to half and the temperature reduced to \[27{}^\circ C\]. The quantity of \[{{N}_{2}}\]gas that is leaked out is
A triangular rigid wire frame 'AOB' is made in which length of each wire is \[l\] and mass is m. The whole system is suspended from point O and free to perform SHM about x-axis or about z-axis. When it performs SHM about x-axis its time period of oscillation is \[{{T}_{1}}\] and when it performs SHM about z-axis, its time-period of oscillation is\[{{T}_{2}}\]. Then choose the CORRECT
In the figure shown, A is a fixed charge. B (of mass m) is given a velocity v perpendicular to the line AB. At this moment the radius of curvature of the resultant path of B is
Two infinite wires (fixed) carrying current \[{{I}_{0}}\] and a square loop with side 'a' also carrying the same current is placed in space as shown in the figure.
A)
The square frame starts moving parallel to line OX towards line OY
doneclear
B)
The square frame starts moving parallel to line OY towards line OX
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C)
The square frame starts moving along line OR away from point O
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D)
The square frame starts moving along line OR towards point O
In a two-slit experiment, with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by \[5\times {{10}^{-2}}m\]towards the slits, the change in fringe width is \[{{10}^{-3}}m\]. Then the wavelength of light used is (given that distance between the slits is\[0.03\text{ }mm\])
An ammeter A of finite resistance, and a resistor R are joined in series to an ideal cell C. A potentiometer P is joined in parallel to R. The ammeter reading is \[{{I}_{0}}\] and the potentiometer reading is \[{{V}_{0}}\]. P is now replaced by a voltmeter of finite resistance. The ammeter reading now is \[I\]and the voltmeter reading is V.
A metallic ring is dropped down, keeping its plane perpendicular to a constant and horizontal magnetic field. The ring enters the region of magnetic field at and completely emerges out at\[t=T\text{ }sec\]. The current in the ring varies as
A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are \[{{e}_{1}}\] and \[{{e}_{2}}\] respectively, the percentage error in the estimation of g is
A \[2\text{ }m\]wide truck is moving with a uniform speed \[{{v}_{0}}=8m/s\] along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v when the truck is 4 m away from him. What is the minimum value of v (in m/s) so that he can cross the road safely?
A block A of mass 1 kg is placed on the rough surface of a trolley as shown in the figure. At \[t=0,\]the trolley starts moving from rest with an acceleration of\[5\text{ }m/{{s}^{2}}\]. What is the work done (in Joule) by friction on the block in ground reference frame till \[t=2\sec \]? (take \[{{\mu }_{s}}=0.5,\,{{\mu }_{k}}=0.4\] and \[g=10m/{{s}^{2}}\])
A rod of length 3 m and uniform cross-section area \[1\text{ }m{{m}^{2}}\]is subjected by four forces at different cross-section as shown in the figure. Young's modulus of the rod is \[2\times {{10}^{11}}\text{ }N/{{m}^{2}}\]. What is the total potential energy (in mJ) stored in the rod?
Two tuning forks, A and B, produce notes of frequencies \[258\text{ }Hz\]and\[262\text{ }Hz\]. An unknown note sounded with A produces certain beats. When the same note is sounded with B, the beat frequency gets doubled. What is the unknown frequency (in Hz)?
Magnification produced by an astronomical telescope for normal adjustment is 10 and length of telescope is\[1.1\text{ }m\]. What is the magnification when the image is formed at least distance of distinct vision\[(D=25\,cm)\]?
Consider the following transformations: \[{{\operatorname{CH}}_{3}}COOH\xrightarrow{CaC{{O}_{3}}}A\xrightarrow{heat}B\xrightarrow[NaOH]{{{I}_{2}}}C\] The molecular formula of C is
The values of \[\Delta H\,\,and\,\,\Delta S\] for the reaction, \[\operatorname{C}(graphite)+C{{O}_{2}}(g)\,\to \,\,2CO(g)\] are 170 kJ and \[170\,J{{K}^{-1}}\], respectively. This reaction will be spontaneous at
Containers A and B have same gases. Pressure, volume and temperature of A are all twice that of B, then the ratio of number of molecules of A and B are
A compound of formula \[{{A}_{2}}{{B}_{3}}\] has the hcp lattice. Which atom forms the hcp lattice and what fraction of tetrahedral voids is occupied by the other atoms:
A)
hcp lattice - A, \[\frac{2}{3}\] Tetrahedral voids - B
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B)
hcp lattice - A, \[\frac{1}{3}\] Tetrahedral voids - B
doneclear
C)
hcp lattice - B, \[\frac{2}{3}\] Tetrahedral voids - A
doneclear
D)
hcp lattice - B, \[\frac{1}{3}\] Tetrahedral voids - A
In the reaction of oxalate with permanganate in acidic medium, the number of electrons involved in producing one molecule of \[{{\operatorname{CO}}_{2}}\] is:
Find the total number of possible isomers for the complex compound \[\left[ C{{u}^{II}}{{\left( N{{H}_{3}} \right)}_{4}} \right] \left[ P{{t}^{II}}\,C{{l}_{4}} \right]\].
The mean and median of 100 items are 50 and 52 respectively The value of largest item is 100. It was later found that it is 110 and not 100. The true mean and median are
If \[{{m}_{1}}\]and \[{{m}_{2}}\]are the slopes of the pair of lines \[{{x}^{2}}(ta{{n}^{2}}\theta +co{{s}^{2}}\theta )-2xytan\]\[\theta +{{y}^{2}}{{\sin }^{2}}\theta =0\] then\[|{{m}_{1}}-{{m}_{2}}|\] is
If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+.....+{{C}_{n}}{{x}^{n}}\],then\[\frac{{{C}_{1}}}{{{C}_{0}}}+\frac{2{{C}_{2}}}{{{C}_{1}}}+\frac{3{{C}_{3}}}{{{C}_{2}}}+....+\frac{n{{C}_{n}}}{{{C}_{n-1}}}=\]
A circle which passes through the point (1, 1) and cuts orthogonally the two circles \[{{x}^{2}}+{{y}^{2}}-8x-2y+16=0\] and \[{{x}^{2}}+{{y}^{2}}-4x-4y+1=0\] . If its centre is (a, b), then a + b =
From a set of 40 cards numbered 1 to 40, 5 cards drawn at random and arranged in ascending order of magnitude \[{{x}_{1}}<{{x}_{2}}<{{x}_{3}}<{{x}_{4}}<{{x}_{5}}\]. The probability that \[{{x}_{3}}=24\] is