Statement I \[{{I}_{S}}\] and \[{{I}_{H}}\] are the moments of inertia about the diameters of a solid and thin walled hollow sphere respectively. If the radii and the masses of the above spheres are equal, \[{{I}_{H}}>{{I}_{S}}\].
Statement II In solid sphere, the mass is continuously and regularly distributed about the centre whereas the mass, to a large extent, is concentrated on the surface of hollow sphere.
A)
Both Statement I and Statement II are true and the Statement II is the correct explanation of the Statement I.
doneclear
B)
Both Statement I and Statement II are true but the Statement II is not the correct explanation of the Statement II.
Statement I Water in a U-tube executes SHM, the time period for mercury filled up to the same height in the U-tube be greater than that in case of water.
Statement II The amplitude of an oscillating pendulum goes on increasing.
A)
Both Statement I and Statement II are true and the Statement II is the correct explanation of the Statement I.
doneclear
B)
Both Statement I and Statement II are true but the Statement II is not the correct explanation of the Statement II.
Direction (Q. Nos. 20) A solid ball of mass M and radius R is sliding on a smooth horizontal surface with velocity of shown in figure solely and smoothly it comes on the inclined plane of inclination \[30{}^\circ \]. Based on the above information answer the following questions:
If incline is smooth, then
A)
ball will perform pure rolling motion
doneclear
B)
ball will perform impure rolling motion on incline
doneclear
C)
ball will slide down on incline
doneclear
D)
ball will perform pure rolling motion on incline if it was initially in pure rolling motion on the horizontal surface
Direction (Q. Nos. 21) A solid ball of mass M and radius R is sliding on a smooth horizontal surface with velocity of shown in figure solely and smoothly it comes on the inclined plane of inclination \[30{}^\circ \]. Based on the above information answer the following questions:
If incline is rough, then
A)
ball can perform pure rolling motion for some time
doneclear
B)
ball can perform impure rolling motion for some time
Direction (Q. Nos. 22) A solid ball of mass M and radius R is sliding on a smooth horizontal surface with velocity of shown in figure solely and smoothly it comes on the inclined plane of inclination \[30{}^\circ \]. Based on the above information answer the following questions:
Mark out the correct statement(s).
A)
If incline is smooth, then the maximum height attained by the ball is \[\frac{v_{0}^{2}}{2g}\].
doneclear
B)
If initially ball is performing pure rolling motion on horizontal surface and Incline is rough enough to prevent any slipping, then the maximum height attained by the ball is \[\frac{7v_{0}^{2}}{10g}\].
doneclear
C)
If initially ball is performing pure rolling motion on horizontal surface and the incline is smooth, then maximum height attained by the ball is \[\frac{v_{0}^{2}}{2g}\].
Direction (Q. Nos. 23) A parallel plate capacitor is as shown in figure. Half of the region in between the plates of the capacitor is filled with a dielectric material of dielectric constant K and in the remaining half air is present. The capacitor is given a charge Q with the help of a battery. Some surfaces are marked on the figure.
Surface I is the right half inner surface of the upper plate of capacitor in tire region in which air is present.
Surface II is the left half inner surface of the upper plate of capacitor.
Surface III is the surface of the dielectric slab which is near to the upper plate of capacitor.
Based on above information answer the following questions:
Mark out the correct statement(s).
A)
The electric field in region with dielectric is greater than that of electric field in the air-filled region.
doneclear
B)
The electric field in the region with dielectric is less than that of electric field in the air-filled region.
doneclear
C)
The electric field in the region with dielectric is equal to that of electric field in the air-filled region.
doneclear
D)
Nothing can be predicted about electric field from the given information.
Direction (Q. Nos. 24) A parallel plate capacitor is as shown in figure. Half of the region in between the plates of the capacitor is filled with a dielectric material of dielectric constant K and in the remaining half air is present. The capacitor is given a charge Q with the help of a battery. Some surfaces are marked on the figure.
Surface I is the right half inner surface of the upper plate of capacitor in tire region in which air is present.
Surface II is the left half inner surface of the upper plate of capacitor.
Surface III is the surface of the dielectric slab which is near to the upper plate of capacitor.
Based on above information answer the following questions:
Direction (Q. Nos. 25) A parallel plate capacitor is as shown in figure. Half of the region in between the plates of the capacitor is filled with a dielectric material of dielectric constant K and in the remaining half air is present. The capacitor is given a charge Q with the help of a battery. Some surfaces are marked on the figure.
Surface I is the right half inner surface of the upper plate of capacitor in tire region in which air is present.
Surface II is the left half inner surface of the upper plate of capacitor.
Surface III is the surface of the dielectric slab which is near to the upper plate of capacitor.
Based on above information answer the following questions:
Directions (Q. Nos. 27): For the following questions. Choose the correct answers from the codes [a], [b], [c] and [d] defined as follows.
Statement I If we consider an inertial frame S in which two identical charges move towards each other with same speed, then it is impossible to find another inertial frame S' in which only one of the fields either electric or magnetic would be observed.
Statement II For above described situation, it is impossible to have an inertial frame S' in which both the charges are at rest.
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.
Directions (Q. Nos. 28): For the following questions. Choose the correct answers from the codes [a], [b], [c] and [d] defined as follows.
Statement I In Doppler effect, if the detector is stationary and the source is moving with constant velocity, then the apparent frequency as received by detector must be constant.
Statement II In Doppler effect expression, \[{{f}_{AP}}=f\,\left[ \frac{v-{{v}_{d}}}{v-{{v}_{s}}} \right],\] where symbols have their usual meanings, \[{{v}_{s}}\] represents the component of velocity of source along the line joining source and detector, at the instant when source emits the wave which is received by detector at some later instant \[{{t}_{0}}\], and at this instant the detector receives the frequency \[{{f}_{AP}}\].
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.
Directions (Q. Nos. 53): An organic compound [A] \[{{C}_{7}}{{H}_{6}}O\] gives positive test with Tollen's reagent. On treatment with alcoholic \[C{{N}^{\odot -}}\] [A] gives the compound [B]\[{{C}_{14}}{{H}_{12}}{{O}_{2}}\]. Compound [B] on reduction with \[Zn-Hg,\,\,HCl\] and dehydration gives an unsaturated compound [C], which adds one mole of\[B{{r}_{2}}/CC{{l}_{4}}\]. The compound [B] can be oxidized with \[HN{{O}_{3}}\] to a compound [D] \[{{C}_{14}}{{H}_{10}}{{O}_{2}}\]. Compound [D] on heating with KOH undergoes rearrangement and subsequent acidification of rearranged products yields an acidic compound (E) \[{{C}_{14}}{{H}_{12}}{{O}_{3}}\].
Direction (Q. Nos. 54): An organic compound [A] \[{{C}_{7}}{{H}_{6}}O\] gives positive test with Tollen's reagent. On treatment with alcoholic \[C{{N}^{\odot -}}\] [A] gives the compound [B]\[{{C}_{14}}{{H}_{12}}{{O}_{2}}\]. Compound [B] on reduction with \[Zn-Hg,\,\,HCl\] and dehydration gives an unsaturated compound [C], which adds one mole of\[B{{r}_{2}}/CC{{l}_{4}}\]. The compound [B] can be oxidized with \[HN{{O}_{3}}\] to a compound [D] \[{{C}_{14}}{{H}_{10}}{{O}_{2}}\]. Compound [D] on heating with KOH undergoes rearrangement and subsequent acidification of rearranged products yields an acidic compound (E) \[{{C}_{14}}{{H}_{12}}{{O}_{3}}\].
Direction (Q. Nos. 55): An organic compound [A] \[{{C}_{7}}{{H}_{6}}O\] gives positive test with Tollen's reagent. On treatment with alcoholic \[C{{N}^{\odot -}}\] [A] gives the compound [B]\[{{C}_{14}}{{H}_{12}}{{O}_{2}}\]. Compound [B] on reduction with \[Zn-Hg,\,\,HCl\] and dehydration gives an unsaturated compound [C], which adds one mole of\[B{{r}_{2}}/CC{{l}_{4}}\]. The compound [B] can be oxidized with \[HN{{O}_{3}}\] to a compound [D] \[{{C}_{14}}{{H}_{10}}{{O}_{2}}\]. Compound [D] on heating with KOH undergoes rearrangement and subsequent acidification of rearranged products yields an acidic compound (E) \[{{C}_{14}}{{H}_{12}}{{O}_{3}}\].
Direction (Q. Nos. 56): A given sample of \[{{N}_{2}}{{O}_{4}}\] in a closed shows 20% dissociation in \[N{{O}_{2}}\] at \[{{27}^{o}}C\] and 1 atm. The sample is now heated up to \[{{127}^{o}}C\] and the analysis of the mixture shows 60% dissociation at\[{{127}^{o}}C\].
The total pressure of equilibrium mixture in atm at \[{{127}^{o}}C\] is
Direction (Q. Nos. 57): A given sample of \[{{N}_{2}}{{O}_{4}}\] in a closed shows 20% dissociation in \[N{{O}_{2}}\] at\[{{27}^{o}}C\]and 1 atm. The sample is now heated up to\[{{127}^{o}}C\]and the analysis of the mixture shows 60% dissociation at\[{{127}^{o}}C\].
The molecular weight of mixture at \[{{27}^{o}}C\] is
Direction (Q. Nos. 58): A given sample of \[{{N}_{2}}{{O}_{4}}\] in a closed shows 20% dissociation in \[N{{O}_{2}}\] at\[{{27}^{o}}C\]and 1 atm. The sample is now heated up to \[{{127}^{o}}C\] and the analysis of the mixture shows 60% dissociation at\[{{127}^{o}}C\].
The equilibrium constant \[({{K}_{p}})\] for the decomposition of \[{{N}_{2}}{{O}_{4}}\] at \[{{27}^{o}}C\] is
Direction (Q. Nos. 85) The geometrical meaning of \[|{{z}_{1}}-{{z}_{2}}|,\] where \[{{z}_{1}}\] and \[{{z}_{2}}\] are points in Argand plane is the distance between the points \[{{z}_{1}}\] and \[{{z}_{2}}\] based on this information, a class of problems about least value can be solved. The property that the sum of two sides of a triangle is greater than the third side is also very useful in solving these problems.
The least value of \[|z-2+2i\,|\,+\,|\,z-3|,\,z\] being a complex number, is
Directions (Q. Nos. 86) The geometrical meaning of \[|{{z}_{1}}-{{z}_{2}}|,\] where \[{{z}_{1}}\] and \[{{z}_{2}}\] are points in Argand plane is the distance between the points \[{{z}_{1}}\] and \[{{z}_{2}}\] based on this information, a class of problems about least value can be solved. The property that the sum of two sides of a triangle is greater than the third side is also very useful in solving these problems.
The least value of \[|\,z+i\,|+|\,z+3i\,|\,+|\,2-z|+|\,-z-7i|,\,\,z\] being a complex number, is
Direction (Q. Nos. 87) For the existence of limit at \[x=a\] of \[y=f(x)\] it must be true that\[\underset{x\to \infty }{\mathop{\lim }}\,\,f(a+h)=\underset{h\to 0}{\mathop{\lim }}\,f(a+h)\]. Here, \[x=a\] is not the end point of the interval, \[\underset{x\to 0}{\mathop{\lim }}\,f(a-h)\] is called LHL and \[\underset{x\to 0}{\mathop{\lim }}\,f(a+h)\] is called RHL.
The value of limit \[\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\,\,[(\sin \,x)],\] where \[[\cdot ]\] denotes the greater integer function is
Direction (Q. Nos. 88) For the existence of limit at \[x=a\] of \[y=f(x)\] it must be true that \[\underset{x\to \infty }{\mathop{\lim }}\,\,f(a+h)=\underset{h\to 0}{\mathop{\lim }}\,f(a+h)\]. Here, \[x=a\] is not the end point of the interval, \[\underset{x\to 0}{\mathop{\lim }}\,f(a-h)\] is called LHL and \[\underset{x\to 0}{\mathop{\lim }}\,f(a+h)\] is called RHL.
\[\underset{x\to 0}{\mathop{\lim }}\,\,\left[ \frac{\sin \,x}{\tan \,x} \right],\] where \[[\cdot ]\] denotes greatest integer function, is