In a particular system, the unit of length, mass and time are chosen to be 10 cm, 10 g and 0.1 s respectively. The unit of force in this system will be equivalent to
A cyclotron is operated at an oscillator frequency of 24 MHz and has a dee radius R = 60 cm. What is magnitude of the magnetic field B (in tesla) to accelerate deuterons (mass\[=3.34\times {{10}^{-27}}kg\])?
The speed of a projectile at its maximum height is \[\frac{\sqrt{3}}{2}\]times its initial speed. If the range of the projectile is P times the maximum height attained by it, then P equals
A uniform solid cylinder has a radius R and length L. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through its centre and perpendicular to its length, then
A coil of inductance 300 mH and resistance \[2\Omega \]is connected to a source of voltage 2 V. The current reaches half of its steady state value in time t is
A body is projected up with a velocity equal to\[{{\left( \frac{3}{4} \right)}^{th}}\]of the escape velocity from the surface of the earth. The height it reaches is (Radius of the earth = R)
Radius of a circular ring is changing with time and the ring is placed in a uniform magnetic field perpendicular to its plane. The variation of r with time t as shown in the figure. The magnitude of induced emf \[(\varepsilon )\]is best represented by
A ray incident at a point at an angle of incidence of \[60{}^\circ \]enters a glass sphere of refractive index \[\mu =\sqrt{3}\] and is reflected and refracted at the further surface of the sphere. The angle between the reflected and refracted rays at this surface is
An air column in a pipe which is closed at one end, will be in resonance with the vibrating body of frequency 166 Hz, if the length of the air column is
Two coherent monochromatic light beams of intensities I and 4I are superimposed. The maximum and minimum possible intensities in the resulting beam are
If the work done in stretching a wire by 1 mm is 2 I, the work necessary for stretching another wire of same material but with double radius of cross-section and half the length by 1 mm is
The incident intensity on a horizontal surface at sea level from sun is about \[\text{1kW}\,{{\text{m}}^{-2}}\]. Assuming that 50 percent of this intensity is reflected and 50 percent is absorbed, the radiation pressure on this horizontal surface is
A parallel plate capacitor of capacity \[100\mu F\]is charged by a battery of 50 volts. The battery remains connected and if the plates of the capacitor are separated so that the distance between them becomes double the original distance, the additional energy given to the battery by the capacitor in joules is
Given that a photon of light of wavelength 10,000 A has an energy equal to 1.23 eV. When light of wavelength \[5000\overset{\text{o}}{\mathop{\text{A}}}\,\] and intensity \[{{I}_{0}}\] falls on a photoelectric cell, the surface current is \[0.40\times {{10}^{-6}}A\]and the stopping potential is 1.36 V, then the work function is
A glass capillary tube of inner diameter 0.28 mm is lowered vertically into water in a vessel. The pressure to be applied on the water in the capillary tube so that water level in the tube is same as that in the vessel in \[N{{m}^{-2}}\]is (Surface tension of water = 0.07 \[\text{N}\,{{\text{m}}^{-1}}\]and atmospheric pressure \[\text{=1}{{\text{0}}^{5}}\,\text{N}\,{{\text{m}}^{-2}}\])
The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is
Two masses of 10 kg and 20 kg respectively are connected by a massless spring. A force of 200 N is applied on the 20 kg mass as shown in the figure. At the instant shown, the 10 kg mass has acceleration \[12\text{m}\,{{\text{s}}^{-2}}\]. For 20 kg mass the acceleration is ___ \[\text{m}\,{{\text{s}}^{-2}}\].
One end of a spring of natural length \[{{l}_{0}}=0.1m\]and spring constant \[k=08\,\text{N}\,{{\text{m}}^{-1}}\]is fixed to the ground and the other end is fitted with a smooth ring of mass m = 2 g, which is allowed to slide on a horizontal rod fixed at a height h=0.1m. Initially the spring makes an angle of \[37{}^\circ \]with the vertical when the system is released from rest. When the spring becomes vertical, if the speed of ring is v, then the value of v is_______\[\text{m}\,{{\text{s}}^{-1}}\]. (Given \[\cos {{37}^{o}}=\frac{4}{5}\])
In brass, the velocity of longitudinal wave is 100 times the velocity of the transverse wave. If \[Y=1\times {{10}^{11}}\text{N}\,{{\text{m}}^{-2}}\], then stress in the wire is \[x\times {{10}^{7}}\text{N}\,{{\text{m}}^{-2}}\]. The value of x ___.
Which of the following statements is/are CORRECT about Ellingham diagram?
I. It represents the plots of \[{{\Delta }_{f}}{{G}^{\bigcirc -}}\]vs T for the formation of oxides of various elements. It predicts the feasibility of thermal reduction of an ore.
II. It explains that \[{{\Delta }_{f}}{{G}^{\bigcirc -}}\] has more \[+ve\]value at high temperatures for less reactive metals such as \[Ag\]and\[Hg\]. This implies that both \[A{{g}_{2}}O\] and \[{{H}_{2}}O\] are stable and does not decompose at high temperatures.
III. It explains that \[C{{r}_{2}}{{O}_{3}}\] can be reduced by \[Al\]metal.
IV. It explains that \[ZnO\]cannot be reduced by\[Si\]
Different forms of silica such as quartz, tridymite and cristobalite are as follows: \[\underset{(Si{{O}_{2}})}{\mathop{Quartz}}\,\xrightarrow{870{}^\circ C}\underset{(Si{{O}_{2}})}{\mathop{Tridymite}}\,\underset{(Si{{O}_{2}})}{\mathop{Cristobalite}}\,\]The structure possessed in them is
A certain transition in H spectrum from an excited state to the ground state in one or more steps gives rise to a total of 10 lines. How many of these belong to the UV spectrum?
In a hexagonal closed packed system of crystals, assume that \[C=2\times \]distance between two close packed layers, and (r) is the radius of every sphere. The number of effective atoms and \[\left( \frac{C}{r} \right)\] ratio in this hcp unit cell are, respectively,
The concentration of \[C{{O}_{2}}\] in atmosphere is 88 ppm. If all of the \[C{{O}_{2}}\] present in \[{{10}^{5}}\text{ }mL\]of air is dissolved in \[1\text{ }d{{m}^{3}}\]water, then approximate \[pOH\]of solution at \[27{}^\circ C\]will be [\[{{K}_{a1}}={{10}^{-7}},\,{{K}_{a2}}={{10}^{-11}}\] for \[{{H}_{2}}C{{O}_{3}}\]]
For the reaction \[A\xrightarrow{{}}\]Product. It is found that the rate of reaction increases by a factor of \[6.25\]when concentration of A increases by a factor of\[2.5\]. Calculate the order of reaction with respect to A.
In the following reaction given, select the CORRECT product. \[Hexane-2,5-dione\xrightarrow[(ii)\,\Delta ]{(i)\,\overset{\bigcirc -}{\mathop{O}}\,H}?\]
Three samples of \[{{H}_{2}}{{O}_{2}}\]labelled as \[11.2\] volume, \[16.8\]volume and \[22.4\] volume. If one litre of each sample is mixed, then volume strength of resultant solution is______.
\[{{\Delta }_{f}}{{H}^{\bigcirc -}}\] of Cyclohexene and benzene at \[25{}^\circ C\]is \[-156\] and \[+49\,kJ\,mo{{l}^{-1}},\] respectively. \[{{\Delta }_{f}}{{H}^{\bigcirc -}}{{\Delta }_{hydrogenation}}{{H}^{\bigcirc -}}\]cyclohexene at \[25{}^\circ C\]is \[-199\,kJ\,\,mo{{l}^{-1}}\] (Resonance energy of benzene is found to be\[-38x\,\,kJ\text{ }mo{{l}^{-1}}.\]) Find the value of x.
Marshall's acid \[({{H}_{2}}{{S}_{2}}{{O}_{8}})\] or peroxo disulphuric acid is prepared by the electrolytic oxidation \[{{H}_{2}}S{{O}_{4}}\] as: \[2{{H}_{2}}S{{O}_{4}}\xrightarrow{{}}{{H}_{2}}{{S}_{2}}{{O}_{8}}+2{{H}^{\oplus }}+2{{e}^{\bigcirc -}}\] \[{{O}_{2}}(g)\] and \[{{H}_{2}}(g)\] are obtained as byproducts. In such electrolysis \[4.48\text{ }L\]of \[{{H}_{2}}(g)\] and \[1.12\text{ }L\]or \[{{O}_{2}}(g)\] were produced at STP. The weight of \[{{H}_{2}}{{S}_{2}}{{O}_{8}}\] formed is
The vapour density of the equilibrium mixture of the reaction: \[S{{O}_{2}}C{{l}_{2}}(g)S{{O}_{2}}(g)+C{{l}_{2}}(g)\] is 50. The percent dissociation of \[S{{O}_{2}}C{{l}_{2}}\] is ______.
Let f and g be functions from the interval \[[0,\infty )\]to the interval \[[0,\infty )\] f being an increasing and g being a decreasing function. If \[f\{g(0)\}=0\] then
In a certain twon, \[40%\]of the people have brown hair, \[25%\]have brown eyes and \[15%\]have both brown hair and brown eyes. If a person selected at random from the town, has brown hair, the probability that he also has brown eyes, is
If the relation between sub-normal SN and sub-tangent ST at any point S on the curve; \[b{{y}^{2}}={{(x+a)}^{3}}\] is \[p(SN)=q{{(ST)}^{2}},\]then the value of \[p/q\]is
Consider a family of circles which are passing through the point \[(-1,1)\] and are tangent to x-axis. If (h, k) are the coordinate of the centre of the circles, then the set of values of k is given by the interval
If the combined mean of two groups is \[\frac{40}{3}\]and if the mean of one group with 10 observations is 15, then the mean of the other group with 8 observations is equal to
The distance between the line \[\vec{r}=(2\hat{i}-2\hat{j}+3\hat{k})+\lambda (\hat{i}-\hat{j}+4\hat{k})\]and the plane \[\vec{r}.(\hat{i}+5\hat{j}+\hat{k})=5\] is
If [x] stands for the greatest integer functions, then the value of \[\left[ \frac{1}{2}+\frac{1}{1000} \right]+\left[ \frac{1}{2}+\frac{2}{1000} \right]+......+\left[ \frac{1}{2}+\frac{999}{1000} \right]\]is
Let the equation of the plane containing line \[x-y-z-4=0,\] \[x+y+2z-4=0\]and parallel to the line of intersection of the planes \[2x+3y+z=1=0\] and \[x+3y+2z=2\]be\[x+Ay+Bz+C=0\]. Then the value of \[\left| A+B+C-4 \right|\]is
In a plane there are 37 straight lines of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no line passes through both points A and B, and no two are parallel. Then the number of intersection points the lines have is