question_answer1) Direction of magnetic field at equatorial point is
A) parallel to M done clear
B) perpendicular to M done clear
C) making an angle of \[{{45}^{o}}\]with M done clear
D) anti-parallel to M done clear
View Answer play_arrowA) \[3W\] done clear
B) \[\sqrt{3}\,W\] done clear
C) \[\frac{W}{3}\] done clear
D) \[\frac{W}{\sqrt{3}}\] done clear
View Answer play_arrow| Statement I The lightning conductor at the top of high building has sharp pointed ends. |
| Statement II The surface density of charge at sharp points is very high resulting in setting up of electric wind. |
A) Both Statement I and Statement II are true and the Statement II is the correct explanation of the Statement I. done clear
B) Both Statement I and Statement II are true but the Statement II is not the correct explanation of the Statement II. done clear
C) Statement I is true but Statement II is false. done clear
D) Both Statement I and Statement II are false. done clear
View Answer play_arrowA) 12.50 N-m done clear
B) 18.75 N-m done clear
C) 25.00 N-m done clear
D) 6.25 N-m done clear
View Answer play_arrowA) 5 : 7 done clear
B) 3 : 5 done clear
C) \[\sqrt{3}\,:\,\sqrt{5}\] done clear
D) \[\sqrt{3}\,:\,\sqrt{7}\] done clear
View Answer play_arrow| 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. done clear
B) Both Statement I and Statement II are true but the Statement II is not the correct explanation of the Statement II. done clear
C) Statement I is true but Statement II is false. done clear
D) Both Statement I and Statement II are false. done clear
View Answer play_arrowquestion_answer7) Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to
A) \[\frac{1}{R}\] done clear
B) \[\frac{1}{\sqrt{R}}\] done clear
C) R done clear
D) \[\frac{1}{{{R}^{3/2}}}\] done clear
View Answer play_arrow| 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. done clear
B) Both Statement I and Statement II are true but the Statement II is not the correct explanation of the Statement II. done clear
C) Statement I is true but Statement II is false. done clear
D) Both Statement I and Statement II are false. done clear
View Answer play_arrowA) cannot be compared done clear
B) equal to T done clear
C) less than T done clear
D) more than T done clear
View Answer play_arrowA) 50 done clear
B) 40 done clear
C) 30 done clear
D) 20 done clear
View Answer play_arrowA) 4a done clear
B) 2a done clear
C) \[\frac{a}{4}\] done clear
D) \[\frac{a}{2}\] done clear
View Answer play_arrowA) \[{{a}_{r}}=0\] and \[{{a}_{t}}=0\] done clear
B) \[{{a}_{r}}=0\] but \[{{a}_{t}}\ne 0\] done clear
C) \[{{a}_{r}}\ne 0\] but \[{{a}_{t}}=0\] done clear
D) \[{{a}_{r}}\ne 0\] and \[{{a}_{t}}\ne 0\] done clear
View Answer play_arrowA) 90 done clear
B) 10 done clear
C) 1.25 done clear
D) 100 done clear
View Answer play_arrowA) four times the initial energy done clear
B) equal to the initial energy done clear
C) twice the initial energy done clear
D) thrice the initial energy done clear
View Answer play_arrowA) 10 s done clear
B) 1000 s done clear
C) 1 day done clear
D) None of these done clear
View Answer play_arrowA) remains unchanged done clear
B) is doubled done clear
C) is halved done clear
D) becomes four times done clear
View Answer play_arrowA) \[2.5\,\,\Omega \] done clear
B) \[7.5\,\,\Omega \] done clear
C) \[10\,\,\Omega \] done clear
D) \[12.5\,\,\Omega \] done clear
View Answer play_arrowA) 3.9 V done clear
B) 2 V done clear
C) 0.1 V done clear
D) 3.8 V done clear
View Answer play_arrowA) 240 done clear
B) 120 done clear
C) 60 done clear
D) 480 done clear
View Answer play_arrow 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: |
A) ball will perform pure rolling motion done clear
B) ball will perform impure rolling motion on incline done clear
C) ball will slide down on incline done clear
D) ball will perform pure rolling motion on incline if it was initially in pure rolling motion on the horizontal surface done clear
View Answer play_arrow 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: |
A) ball can perform pure rolling motion for some time done clear
B) ball can perform impure rolling motion for some time done clear
C) friction will aid the rotational motion done clear
D) All of the above done clear
View Answer play_arrow| 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: |
A) If incline is smooth, then the maximum height attained by the ball is \[\frac{v_{0}^{2}}{2g}\]. done clear
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 \[\frac{7v_{0}^{2}}{10g}\]. done clear
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 \[\frac{v_{0}^{2}}{2g}\]. done clear
D) All of the above done clear
View Answer play_arrow 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: |
A) The electric field in region with dielectric is greater than that of electric field in the air-filled region. done clear
B) The electric field in the region with dielectric is less than that of electric field in the air-filled region. done clear
C) The electric field in the region with dielectric is equal to that of electric field in the air-filled region. done clear
D) Nothing can be predicted about electric field from the given information. done clear
View Answer play_arrow| 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: |
A) \[\frac{Q}{2}\] done clear
B) \[\frac{Q}{1+K}\] done clear
C) \[\frac{KQ}{1+K}\] done clear
D) \[\frac{Q}{K-1}\] done clear
View Answer play_arrow 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: |
A) \[\frac{KQ}{1+K}\] done clear
B) \[\frac{{{K}^{2}}Q}{1+K}\] done clear
C) \[\frac{-{{K}^{2}}Q}{1+K}\] done clear
D) \[\frac{-K(K-1)Q}{1+K}\] done clear
View Answer play_arrow| Directions (Q. Nos. 26): For the following questions. Choose the correct answers from the codes [a], [b], [c] and [d] defined as follows. |
| Statement I Charge is invariant in nature i.e., in different inertial frames charge on an object is same. |
| Statement II A gas consisting of hydrogen molecules is neutral in nature. |
A) Statement I is true. Statement II is also true and Statement II is the correct explanation of Statement I. done clear
B) Statement I is true. Statement II is also true and Statement II is not the correct explanation of Statement I. done clear
C) Statement I is true. Statement II is false. done clear
D) Statement I is false. Statement II is true. done clear
View Answer play_arrow| 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. done clear
B) Statement I is true. Statement II is also true and Statement II is not the correct explanation of Statement I. done clear
C) Statement I is true. Statement II is false. done clear
D) Statement I is false. Statement II is true. done clear
View Answer play_arrow| 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. done clear
B) Statement I is true. Statement II is also true and Statement II is not the correct explanation of Statement I. done clear
C) Statement I is true. Statement II is false. done clear
D) Statement I is false. Statement II is true. done clear
View Answer play_arrowA) Magnet experiences a net torque in clockwise direction and zero net force. done clear
B) Magnet experiences a net force towards left and a net torque in anti-clockwise direction. done clear
C) Magnet experiences a net force towards right and a net torque in anti-clockwise direction. done clear
D) Magnet experiences zero net force and a net torque in anti-clockwise direction. done clear
View Answer play_arrowA) The charge on outer surface of shell is uniformly distributed. done clear
B) The charge on outer surface of shell is non-uniformly distributed. done clear
C) The nature of distribution of charge on outer surface of shell cannot be predicted from the given information. done clear
D) None of the above done clear
View Answer play_arrowA) \[\text{ }7.06{}^\circ C\] done clear
B) \[3.51{}^\circ C~\] done clear
C) \[\text{ }3.51{}^\circ C\] done clear
D) \[10{}^\circ C\] done clear
View Answer play_arrowA) \[\frac{{{v}_{2}}-{{v}_{1}}}{k-1}\] done clear
B) \[\frac{k{{v}_{1}}-{{v}_{2}}}{k-1}\] done clear
C) \[\frac{k{{v}_{2}}-{{v}_{1}}}{k-1}\] done clear
D) \[\frac{{{v}_{2}}-{{v}_{1}}}{k}\] done clear
View Answer play_arrowquestion_answer33) Identify the compound which is not aromatic.
A) 
done
clear
B) 
done
clear
C) 
done
clear
D) 
done
clear
A) \[{{l}_{2}}+C{{u}^{2+}}\] done clear
B) \[Cu{{l}_{2}}\] done clear
C) \[{{l}_{2}}+Cu\] done clear
D) \[C{{u}_{2}}{{l}_{2}}\] done clear
View Answer play_arrowquestion_answer35) Which of the following bromide will undergo faster dehydrobromination?
A) 
done
clear
B) 
done
clear
C) 
done
clear
D) 
done
clear
A) \[C{{u}_{4}}A{{g}_{4}}Au\] done clear
B) \[C{{u}_{4}}A{{g}_{2}}Au\] done clear
C) \[Au\,Ag\,Cu\] done clear
D) \[C{{u}_{4}}A{{g}_{3}}Au\] done clear
View Answer play_arrowquestion_answer37) Which of the following cannot be used as an acylating agent?
A) \[C{{H}_{3}}COCl\] done clear
B) \[{{(C{{H}_{3}}CO)}_{2}}O\] done clear
C) \[C{{H}_{3}}COOH\] done clear
D) \[C{{H}_{3}}C{{H}_{2}}COCl\] done clear
View Answer play_arrowquestion_answer38) The species having tetrahedral shape is
A) \[{{[PbC{{l}_{4}}]}^{2-}}\] done clear
B) \[{{[Ni\,{{(CN)}_{4}}]}^{2-}}\] done clear
C) \[{{[Pb\,{{(CN)}_{4}}]}^{2-}}\] done clear
D) \[{{[NiC{{l}_{4}}]}^{2-}}\] done clear
View Answer play_arrowA) 272.84 kcal done clear
B) 260 kcal done clear
C) 180 kcal done clear
D) 130 kcal done clear
View Answer play_arrowA) 
done
clear
B) 
done
clear
C) 
done
clear
D) 
done
clear
A) I > II > III done clear
B) II > I > III done clear
C) III > II > I done clear
D) I > III > II done clear
View Answer play_arrowquestion_answer42) A gas can be liquefied most suitably at
A) \[T={{T}_{c}}\] and \[p<{{p}_{c}}\] done clear
B) \[T<{{T}_{c}}\] and \[p={{p}_{0}}\] done clear
C) \[T<{{T}_{c}}\] and \[p>{{p}_{c}}\] done clear
D) \[T>{{T}_{c}}\] and \[p>{{p}_{c}}\] done clear
View Answer play_arrowA) 4.606 cal done clear
B) \[\frac{0.2}{2.303}cal\] done clear
C) 2 cal done clear
D) None of these done clear
View Answer play_arrowA) \[9\times {{10}^{-4}}\] done clear
B) \[81\times {{10}^{-4}}\] done clear
C) \[9\times {{10}^{-5}}\] done clear
D) \[2.8\times {{10}^{-3}}\] done clear
View Answer play_arrowA) 
done
clear
B) 
done
clear
C) 
done
clear
D) 
done
clear
question_answer46) Which of the following trihalides of nitrogen behaves as the weakest base?
A) \[N{{F}_{3}}\] done clear
B) \[NC{{l}_{3}}\] done clear
C) \[NB{{r}_{3}}\] done clear
D) \[N{{l}_{3}}\] done clear
View Answer play_arrowA) Increase by 0.059 V done clear
B) Decrease by 0.059 V done clear
C) Increase by 0.41 V done clear
D) Decrease by 0.41 V done clear
View Answer play_arrowquestion_answer48) Which of the following will not show stereoisomerism?
A) 
done
clear
B) 
done
clear
C) 
done
clear
D) 
done
clear
question_answer49) The compound insoluble in acetic acid is
A) calcium oxide done clear
B) calcium carbonate done clear
C) calcium oxalate done clear
D) calcium hydroxide done clear
View Answer play_arrowA) 0.1 N \[Zn{{(N{{O}_{3}})}_{2}}\] done clear
B) 0.1 N \[N{{a}_{3}}P{{O}_{4}}\] done clear
C) 0.1 N \[ZnS{{O}_{4}}\] done clear
D) 0.1 N \[AlC{{l}_{3}}\] done clear
View Answer play_arrowA) 
done
clear
B) 
done
clear
C) 
done
clear
D) None of these done clear
View Answer play_arrowquestion_answer52) Which of the following cannot be oxidized by \[{{H}_{2}}{{O}_{2}}\] ?
A) \[Kl+HCl\] done clear
B) \[{{O}_{3}}\] done clear
C) \[PbS\] done clear
D) \[N{{a}_{2}}S{{O}_{3}}\] done clear
View Answer play_arrow| 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) \[{{C}_{14}}{{H}_{12}}{{O}_{3}}\]. |
A) benzoin condensation done clear
B) aldol condensation done clear
C) Cannizzaro reaction done clear
D) Perkin condensation done clear
View Answer play_arrow| 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) \[{{C}_{14}}{{H}_{12}}{{O}_{3}}\]. |
A) 
done
clear
B) 
done
clear
C) 
done
clear
D) 
done
clear
| 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) \[{{C}_{14}}{{H}_{12}}{{O}_{3}}\]. |
A) 
done
clear
B) 
done
clear
C) 
done
clear
D) 
done
clear
| 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\[{{127}^{o}}C\]. |
A) 1.78 atm done clear
B) 2.01 atm done clear
C) 3.18 atm done clear
D) 4.33 atm done clear
View Answer play_arrow| 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\[{{127}^{o}}C\]. |
A) 76.66 done clear
B) 78.69 done clear
C) 66.52 done clear
D) 80.24 done clear
View Answer play_arrow| 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\[{{127}^{o}}C\]. |
A) 0.165 done clear
B) 0.29 done clear
C) 0.523 done clear
D) 0.625 done clear
View Answer play_arrow| Direction (Q. Nos. 59): For the following questions choose the correct answers from the codes a, b, c and d defined as follows. |
| Statement I The dissociation constants of a polyprotic acid are in the order \[{{K}_{1}}>{{K}_{2}}>{{K}_{3}}\]. |
| Statement II The \[[{{H}^{+}}]\] furnished in first step of dissociation exerts common ion effect to reduce the second dissociation and so on. |
A) Statement I is true. Statement II is also true and Statement II is the correct explanation of Statement I. done clear
B) Statement I is true. Statement II is also true and Statement II is not the correct explanation of Statement I. done clear
C) Statement I is true. Statement II is false. done clear
D) Statement I is false. Statement II is true. done clear
View Answer play_arrow| Direction (Q. Nos. 60): For the following questions choose the correct answers from the codes a, b, c and d defined as follows. |
| Statement I The vapour pressure of 0.1 M sugar solution is more that of 0.1 M KCI solution. |
| Statement II Lowering of vapour pressure is directly proportional to the number of species present in the solution. |
A) Statement I is true. Statement II is also true and Statement II is the correct explanation of Statement I. done clear
B) Statement I is true. Statement II is also true and Statement II is not the correct explanation of Statement I. done clear
C) Statement I is true. Statement II is false. done clear
D) Statement I is false. Statement II is true. done clear
View Answer play_arrowA) \[npq\] done clear
B) \[pq\] done clear
C) \[{{2}^{n}}pq\] done clear
D) 0 done clear
View Answer play_arrowA) when only \[p=q\] done clear
B) when only \[p\ne q\] done clear
C) when only \[p+q=0\] done clear
D) for all \[p,\,\,q\,\,\in R\] done clear
View Answer play_arrowA) 2 sq units done clear
B) 2/3 sq unit done clear
C) 1 sq unit done clear
D) 4/3 sq units done clear
View Answer play_arrowA) a circle done clear
B) a parabola done clear
C) an ellipse done clear
D) a hyperbola done clear
View Answer play_arrowA) \[PG=P{{G}^{2}}\] done clear
B) \[PG=PC\] done clear
C) \[PG=Gg\] done clear
D) \[PC=Cg\] done clear
View Answer play_arrowA) If n is odd, then A is an invertible matrix, done clear
B) If n is even, then A is not an invertible matrix, done clear
C) For all values of n, A is not invertible matrix, done clear
D) A is a skew-symmetric matrix. done clear
View Answer play_arrowA) reflexive on \[{{R}^{+}}\] done clear
B) symmetric on \[{{R}^{+}}\] done clear
C) antisymmetric on \[{{R}^{+}}\] done clear
D) equivalence relation on \[{{R}^{+}}\] done clear
View Answer play_arrowA) \[fof\,\,(2)=2\] done clear
B) \[fof\,\,(2)=1\] done clear
C) \[f({{S}_{n}})\] is divisible by 9 done clear
D) \[fof\,(5)=1\] done clear
View Answer play_arrowA) 2600 done clear
B) 52000 done clear
C) 2510 done clear
D) None of these done clear
View Answer play_arrowA) 1 done clear
B) 2 done clear
C) 3 done clear
D) 4 done clear
View Answer play_arrowA) 10 done clear
B) 9 done clear
C) 7 done clear
D) 6 done clear
View Answer play_arrowA) 4 units done clear
B) 5 units done clear
C) 6 units done clear
D) 7 units done clear
View Answer play_arrowA) 4 done clear
B) 5 done clear
C) 7 done clear
D) 8 done clear
View Answer play_arrowA) F done clear
B) T done clear
C) T, if r is F done clear
D) None of these done clear
View Answer play_arrowA) 0 done clear
B) 1 done clear
C) 2 done clear
D) 3 done clear
View Answer play_arrowA) a > b > d > c done clear
B) d > c > a > b done clear
C) b > a > d > c done clear
D) a < b < d < c done clear
View Answer play_arrowA) unique solution done clear
B) infinitely many solutions done clear
C) no solution done clear
D) trivial solution done clear
View Answer play_arrowA) \[\frac{1}{2}\] done clear
B) \[-\frac{1}{2}\] done clear
C) \[-\frac{3}{2}\] done clear
D) \[\sqrt{3}\] done clear
View Answer play_arrowA) 16 sq units done clear
B) 8 sq units done clear
C) 32 sq units done clear
D) \[18\sqrt{3}\] sq units done clear
View Answer play_arrowA) \[\frac{25\sqrt{3}}{2}\] done clear
B) \[\frac{25\sqrt{3}}{4}\] done clear
C) \[\frac{75\sqrt{3}}{2}\] done clear
D) \[\frac{75\sqrt{3}}{4}\] done clear
View Answer play_arrowA) (0, 1) done clear
B) (1, 2) done clear
C) (2, 3) done clear
D) (- 1, 0) done clear
View Answer play_arrowA) 1 done clear
B) 2 done clear
C) infinitely many done clear
D) 0 done clear
View Answer play_arrowA) 3 done clear
B) 6 done clear
C) 9 done clear
D) 12 done clear
View Answer play_arrowA) \[\frac{{{(1+\alpha )}^{50}}(50-\alpha )+{{\alpha }^{51}}}{{{\alpha }^{49}}}\] done clear
B) \[\frac{{{(1+\alpha )}^{51}}(50-\alpha )+{{\alpha }^{2}}}{{{\alpha }^{50}}}\] done clear
C) \[{{\left( \frac{1+\alpha }{\alpha } \right)}^{50}}+{{\alpha }^{2}}\] done clear
D) \[\left( \frac{50-\alpha }{\alpha } \right)+{{\alpha }^{2}}\] done clear
View Answer play_arrow| 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. |
A) \[\sqrt{2}\] done clear
B) \[\sqrt{5}\] done clear
C) \[2+\sqrt{13}\] done clear
D) \[1+\sqrt{5}\] done clear
View Answer play_arrow| 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. |
A) \[1+\sqrt{7}\] done clear
B) \[\sqrt{13}\] done clear
C) \[2+\sqrt{13}\] done clear
D) \[\sqrt{7}+\sqrt{13}\] done clear
View Answer play_arrow| 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. |
A) 0 done clear
B) Does not exist done clear
C) - 1 done clear
D) 1 done clear
View Answer play_arrow| 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. |
A) 0 done clear
B) 1 done clear
C) - 1 done clear
D) not in existence done clear
View Answer play_arrow| Direction (Q. Nos. 89) For the following questions. Choose the correct answers from the codes [a], [b], [c] and [d] defined as follows. |
| Let us define a function \[f(x)=\sin \,\sqrt{2}x+\sin \,ax\] |
| Statement I The maximum value of \[f(x)\] cannot be 2, (where a is positive rational number) |
| Statement II \[\frac{\sqrt{2}}{a}\] is irrational. |
A) Statement I is true/ Statement II is also true and Statement II is the correct explanation of Statement I. done clear
B) Statement I is true. Statement II is also true and Statement II is not the correct explanation of Statement I. done clear
C) Statement I is true. Statement II is false. done clear
D) Statement I is false. Statement II is true. done clear
View Answer play_arrow| Direction (Q. Nos. 90) For the following questions. Choose the correct answers from the codes [a], [b], [c] and [d] defined as follows. |
| Consider the equation of circle is \[S={{x}^{2}}+{{y}^{2}}={{a}^{2}}\] |
| Statement I The chord of contact of tangent from these points A, B, C to the circle S are concurrent, then A, B,C will be collinear. |
| Statement II A, B, C always lies on the normal to the circle S. |
A) Statement I is true/ Statement II is also true and Statement II is the correct explanation of Statement I. done clear
B) Statement I is true. Statement II is also true and Statement II is not the correct explanation of Statement I. done clear
C) Statement I is true. Statement II is false. done clear
D) Statement I is false. Statement II is true. done clear
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