A wooden block is dropped from the top of a cliff 100 m high. Simultaneously a bullet is fired from the foot of the cliff upward with a velocity of 100 m/s. The bullet hits the wooden block after - \[[Takeg=10\text{ }m/{{s}^{2}}]\]
A car of mass m is driven with acceleration a along a straight level road against a constant external resistive force F. When the velocity of car is v, the rate at which the engine of the car is doing work will be
A body is carrying a bucket of water in one hand & a wooden block in the other hand. After transferring the wooden block to the bucket the boy will carry
A simple pendulam of bob mass m & length (. Is oscillating in vertical plane, when string of pendulam is making an angle of \[37{}^\circ \] with the vertical its tangential and radial acceleration have same magnitude. The velocity of the bob when its crosses the mean position is
A boy of mass m is sliding down a vertical pole by pressing it with a horizontal force F. If u. is the coefficient of friction between his palm & the pole, the acceleration with which he slides down is
The wavelength of \[{{K}_{\alpha }}\] X-ray from an element of atomic number 41 is \[\lambda ,\] then the wavelength of \[{{K}_{\alpha }}\] X-ray from an element of atomic number 21 is
Two identical containers each of volume \[{{V}_{0}}\] are joined by a pipe of negligible volume. The containers contain identical gases at temperature. To and pressure Po. One container is heated to temperature \[2{{T}_{0}}\] while maintaining the other at the same temperature. The common pressure of the gas is P & n is the number of moles of gas in container at temperature\[2{{T}_{0}}\]. Mark the correct expression for this situation
In YDSE screen is kept 0.8 m from the slits. The coherent sources are 0.016 cm apart & fringes are observed on the screen. It is found that with a certain monochromatic source of light, the fourth bright fringe is situated at a distance of 1.06 cm from the central fringe. The wavelength of light used is
A light rod of length L is suspended from a support horizontally by means of two vertical wires A & B of equal lengths as shown. CSA of A is half of that of B, and Young's modulas of A is double to that of B. A weight W is hung on the rod as shown. The value of x so that stress in A is same as that in B is
\[{{E}_{O}}\And {{E}_{H}}\]respectively represent the average kinetic energy of a molecule of oxygen and hydrogen. If the two gases are at same temperature, which of the following statements is true?
A)
\[{{E}_{O}}>{{E}_{H}}\]
doneclear
B)
\[{{E}_{O}}={{E}_{H}}\]
doneclear
C)
\[{{E}_{O}}<{{E}_{H}}\]
doneclear
D)
nothing can be said about the magnitude of \[{{E}_{O}}\And {{E}_{H}}\]as the information given is insufficient.
A parallel beam of fast moving electrons is incident normally on a narrow slit. A screen is placed at a large distance from the slit. If the speed of the electrons in increased, then the correct statement is
A)
Diffraction pattern is not observed on the screen in the case of electrons
doneclear
B)
the angular width of the central maxima of the diffraction pattern will increase
doneclear
C)
the angular width of the central maxima will decrease
doneclear
D)
the angular width of the central maxima will remain same
From a conducting ring of radius R which carries a charge Q (uniformly distributed) along its periphery a small length \[d\ell \] is cut off. The electric field at the center due to the remaining wire is
Two particles of mass m & M are initially at rest and infinitely separated from each other. Due to mutual interaction (gravitational) they approach each other. Their relative velocity of approach when they are at a distance d is
An ac source has an internal resistance of\[{{10}^{4}}\Omega .\] The turn ratio of a transformer so as to match the source to a load of resistance \[10\Omega \] is
The poisson's ratio of a material is 0.4. If a force is applied to a bar of this material, there is a decrease of cross-sectional area by 2%. The percentage increase in its length is
A mass M is suspended from a light spring. An additional mass m added displaces the spring further by a distance x. Now the combined mass will oscillate on the spring with period
The ionisation energy of Hydrogen atom is 13.6 eV. Following Bohr's theory the energy corresponding to a transition between the 3rd and the 4th orbit is
The antenna current of an AM transmitter is 8A when only the carrier is sent, but it increases to 8 -93A when the carries is modulated by single sine wave. Find the modulation index.
One mole of a non - ideal gas undergoes a change of state (2.0 atm, 3.0 L, 95 K) \[\to \] (4.0 atm, 5.0 L, 245 K) with a change in internal energy, \[\Delta E=30.0\text{ }L-atm.\]The change in enthalpy \[(\Delta E)\] of the process in L-atm is
For the complete combustion of ethanol amount of heat produced as measured in bomb calorimeter, is \[1364.47\text{ kJ }mo{{l}^{-1}}\] at \[25{}^\circ C\]. Assuming ideality the enthalpy of combustion, \[\Delta {{H}_{C}},\] for the reaction will be\[(R=8.314J{{K}^{-1}}mo{{l}^{-1}})\]
A solution contains a mixture of \[N{{a}_{2}}C{{O}_{3}}\] and NaOH. Using phenolphthalein as indicator, 25 mL of mixture required 19.5 mL of 0.995 N HCI for the end point. Whith methyl organge, 25 mL of solution required 24 mL of the same HCI for the end point. The grams per litre of \[N{{a}_{2}}C{{O}_{3}}\] in the mixture is
The enthalpies of formation of \[{{N}_{2}}O\] and NO are respectively 82 and \[90\,kJ\,mo{{l}^{-1}}.\] The enthalpy of reaction. \[2{{N}_{2}}{{O}_{(g)}}+{{O}_{2(g)}}\to 4N{{O}_{(g)}}\] is
Arrange the following compounds in the increasing order of their boiling points. [A] [B]\[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}Br\] [C] \[{{H}_{3}}C-\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\]
The expression to compute molar mass of a solute from the elevation of boiling point of a solvent is (where the various sybols have their usual meanings)
Trichloroacetaldehyde was subjected to Cannizaro's reaction by using NaOH. The mixture of the products contains sodium trichloroacetate and another compound. The other compound is
3.92 g of ferrous ammonium sulphate (Mohr's salt) react completely with \[50\,mL\frac{N}{10}KMn{{O}_{4}}\] solution. The percentage purity of the sample is
Let \[({{x}_{i}},{{y}_{i}})i=1,2,3,4\] are the integral solutions of equation \[2{{x}^{2}}{{y}^{2}}+{{y}^{2}}-6{{x}^{2}}-12=0.\] Then area of quadrilateral whose vertices are \[({{x}_{i}},{{y}_{i}})\]is
Passage: (Q. - 72) A triangle ABC is inscribed in a circle with AL, BM & CN as the diameters of circumcircle, then Sum of areas of triangles BLC, CMA & ANB is
Passage: (Q. - 73) A triangle ABC is inscribed in a circle with AL, BM & CN as the diameters of circumcircle, then If AL, BM & CN are angular bisectors of triangle, then if \[{{\Delta }_{1}}=\]area of \[\Delta ABC\And {{\Delta }_{2}}=Ar.\]of \[\Delta LMN,\]then
In ellipse\[{{E}_{1}}\], the normal at one end of the latus rectum passes through one end of minor axis. In ellipse \[{{E}_{2}}\], the latus rectum subtends a right angle at \[{{E}_{1}},{{E}_{2}}\] respectively, then
The first of the two samples has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 156 and standard deviation \[\sqrt{13.44},\] then the standard deviation of second group is
The area nearer to origin bounded by \[x={{x}_{1}},y={{y}_{1}}\] and \[y=-{{(x+1)}^{2}}\] where \[{{x}_{1}},{{y}_{1}}\] are the values of x, y satisfying the equation \[{{\sin }^{-1}}x+{{\sin }^{-1}}y=-\pi \] will be
If a is the common positive root of the equation \[{{x}^{2}}-ax+12=0,{{x}^{2}}-bx+15=0\]and\[{{x}^{2}}-(a+b)x+36=0\] and \[\cos x+\cos 2x+\cos 3x=\alpha ,\]then \[\sin x+\sin 2x+\sin 3x\]
Let a point R lies on the plane \[x-y+z-3=0\] and P be the point (1, 1,1). A point Q lies on PR such that \[P{{Q}^{2}}+\text{ }P{{R}^{2}}=k\] (constant), then the equation of locus of Q is
If \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{\sum\limits_{r=1}^{n}{\sqrt{r}}\sum\limits_{r=1}^{n}{\frac{1}{\sqrt{r}}}}{\sum\limits_{r=1}^{n}{r}}=\frac{k}{3},\] then the value of k is
One hundred identical coins, each with probability p, of showing up heads are tossed. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of the heads showing on 51 coins, then p =
Passage (Q. - 89) Let f(x) be a polynomial with positive leading coefficient satisfying \[f(0)=0\]and \[f(f(x))=\]\[x\int\limits_{0}^{x}{f(x)}dx\forall x\in R\] Two perpendicular tangents to the curve y = f(x) will intersect on the
Passage (Q. - 90) Let f(x) be a polynomial with positive leading coefficient satisfying \[f(0)=0\]and \[f(f(x))=\]\[x\int\limits_{0}^{x}{f(x)}dx\forall x\in R\] If tangents are drawn to the curve y = f(x) from any point on the line \[y+\sqrt{3}/4=0,\] then the chord of contacts will be concurrent at the point