A) \[\frac{\sqrt{3}}{4}N\] done clear
B) \[\sqrt{3}\,N\] done clear
C) 0.5 N done clear
D) 1.5N done clear
View Answer play_arrowA) \[\frac{R}{4}\]from the centre done clear
B) \[\frac{R}{3}\]from the centre done clear
C) \[\frac{R}{5}\]from the centre done clear
D) \[\frac{R}{6}\]from the centre done clear
View Answer play_arrowA) \[\sqrt{900\times 980}\,\,cm/s\] done clear
B) \[\sqrt{100\times 980}\,\,cm/s\] done clear
C) \[\sqrt{920\times 980}\,\,cm/s\] done clear
D) \[\sqrt{950\times 980}\,\,cm/s\] done clear
View Answer play_arrowA) \[q=\frac{Q}{4}\] done clear
B) \[q=\frac{Q}{2}\] done clear
C) \[q=Q\] done clear
D) None of these done clear
View Answer play_arrowA) K done clear
B) \[\frac{1}{K}\] done clear
C) \[\frac{A}{{{d}^{2}}K}\] done clear
D) \[\frac{{{d}^{2}}K}{A}\] done clear
View Answer play_arrowA) \[\frac{1}{n}\] done clear
B) \[n\] done clear
C) \[{{n}^{2}}\] done clear
D) \[\frac{1}{{{n}^{2}}}\] done clear
View Answer play_arrowA) 0.5V done clear
B) 1.0V done clear
C) 1.5V done clear
D) 2.0V done clear
View Answer play_arrowA) \[2v\sqrt{\frac{h}{g}}\] done clear
B) \[v\sqrt{\frac{h}{g}}\] done clear
C) \[v\sqrt{\frac{2h}{g}}\] done clear
D) \[v\sqrt{\frac{h}{2g}}\] done clear
View Answer play_arrowA) \[\frac{g\mu }{v}\] done clear
B) \[\frac{g}{v}\] done clear
C) \[\frac{v}{g}\] done clear
D) \[\frac{v}{g\mu }\] done clear
View Answer play_arrowA) \[h\] done clear
B) \[\frac{3}{4}h\] done clear
C) \[\frac{1}{2}h\] done clear
D) \[\frac{1}{4}h\] done clear
View Answer play_arrowA) h done clear
B) \[\frac{3}{4}h\] done clear
C) \[\frac{1}{2}h\] done clear
D) \[\frac{1}{4}h\] done clear
View Answer play_arrowA) 8 m/s (approx) done clear
B) 800 m/s done clear
C) 7 m/s done clear
D) 6 m/s (approx) done clear
View Answer play_arrowA) \[\frac{\sigma }{{{\varepsilon }_{0}}}\] done clear
B) \[\frac{\sigma }{{{\varepsilon }_{0}}}\,(R-r)\] done clear
C) \[\frac{\sigma }{{{\varepsilon }_{0}}}\,(R+r)\] done clear
D) None of these done clear
View Answer play_arrowA) 20 done clear
B) 200 done clear
C) 2000 done clear
D) 20000 done clear
View Answer play_arrowA) \[h=g{{t}_{1}}{{t}_{2}}\] done clear
B) \[h=2g{{t}_{1}}{{t}_{2}}\] done clear
C) \[h=\frac{1}{2}\,g{{t}_{1}}{{t}_{2}}\] done clear
D) \[h=\frac{1}{4}g{{t}_{1}}{{t}_{2}}\] done clear
View Answer play_arrowA) \[2\,m{{v}^{2}}\] done clear
B) \[\frac{3}{2}\,m{{v}^{2}}\] done clear
C) \[\frac{1}{2}\,m{{v}^{2}}\] done clear
D) \[3\,m{{v}^{2}}\] done clear
View Answer play_arrowquestion_answer17) In figure, if the surfaces are frictionless, the ratio \[{{T}_{1}}:{{T}_{2}}\] is
A) \[\sqrt{3}:2\] done clear
B) \[1:\sqrt{3}\] done clear
C) 1 : 5 done clear
D) 5 : 1 done clear
View Answer play_arrowA) \[\frac{Mgd}{4}\] done clear
B) \[\frac{-Mgd}{4}\] done clear
C) \[\frac{3Mgd}{4}\] done clear
D) \[\frac{-3Mgd}{4}\] done clear
View Answer play_arrowA) \[\frac{3v}{4l}\], anti-clockwise done clear
B) \[\frac{4v}{3l},\]anti-clockwise done clear
C) \[\frac{3v}{4l},\]clockwise done clear
D) \[\frac{4v}{3l},\]clockwise done clear
View Answer play_arrowA) \[2\pi \,\sqrt{\frac{M}{g}}\] done clear
B) \[2\pi \,\sqrt{\frac{MA}{dg}}\] done clear
C) \[2\pi \,\sqrt{\frac{M}{Adg}}\] done clear
D) \[2\pi \,\sqrt{\frac{M}{2Adg}}\] done clear
View Answer play_arrowA) \[10,5,\,\frac{5}{2},\,...\] done clear
B) \[20,\,\frac{20}{3},\,\frac{20}{5},\,...\] done clear
C) 30, 20, 10, ? done clear
D) 35, 25, 15, ? done clear
View Answer play_arrowA) \[\cos \,\theta :1\] done clear
B) \[\sin \,\theta :1\] done clear
C) \[1:\,\cos \,\theta \] done clear
D) \[1:\,\sin \,\theta \] done clear
View Answer play_arrowA) \[\frac{\omega BA}{\pi }\] done clear
B) \[\frac{\omega BA}{2\pi }\] done clear
C) \[\frac{\omega BA}{4\pi }\] done clear
D) \[\frac{2\omega BA}{\pi }\] done clear
View Answer play_arrowA) \[2.84\times {{10}^{12}}\] done clear
B) \[2.84\times {{10}^{11}}\] done clear
C) \[9.37\times {{10}^{11}}\] done clear
D) \[6.48\times {{10}^{11}}\] done clear
View Answer play_arrowA) \[{{\lambda }_{1}}+{{\lambda }_{2}}\] done clear
B) \[\frac{2{{\lambda }_{1}}{{\lambda }_{2}}}{\sqrt{\lambda _{1}^{2}+\lambda _{2}^{2}}}\] done clear
C) \[\frac{{{\lambda }_{1}}{{\lambda }_{2}}}{\sqrt{|\lambda _{1}^{2}+\lambda _{2}^{2}|}}\] done clear
D) \[\frac{{{\lambda }_{1}}+{{\lambda }_{2}}}{2}\] done clear
View Answer play_arrowA) 28 done clear
B) 29 done clear
C) 65 done clear
D) 66 done clear
View Answer play_arrowA) 24.6eV done clear
B) 79.0 eV done clear
C) 54.4 eV done clear
D) None of these done clear
View Answer play_arrowA) 16: 1 done clear
B) 1 : 16 done clear
C) 2 : 7 done clear
D) 7 : 2 done clear
View Answer play_arrowA) 5 done clear
B) 6 done clear
C) 10 done clear
D) infinite done clear
View Answer play_arrowA) The force exerted by light on the sphere is the greatest when surface of sphere is perfectly reflecting and is equal to \[\frac{2l\times \pi {{R}^{2}}}{c}\] done clear
B) The force exerted by light on the sphere is independent of the nature of surface, i.e.. it is same for perfect reflector, perfect absorber, and is partially reflecting and for all it is equal to \[\frac{l\times \pi {{R}^{2}}}{c}\]. done clear
C) The force exerted by light on sphere is least when surface of the sphere a is perfect absorber, and is equal to \[\frac{l\times \pi {{R}^{2}}}{c}\]. done clear
D) Both [a] and [c] are correct. done clear
View Answer play_arrowA) 67.5 done clear
B) 32.5 done clear
C) 45.3 done clear
D) 63.1 done clear
View Answer play_arrowA) 9 cm Hg done clear
B) 18 cm Hg done clear
C) 27 cm Hg done clear
D) None of these done clear
View Answer play_arrowA) \[M{{n}_{3}}{{O}_{4}}\] done clear
B) \[Pb{{O}_{2}}\] done clear
C) \[P{{b}_{3}}{{O}_{4}}\] done clear
D) \[F{{e}_{2}}{{O}_{3}}\] done clear
View Answer play_arrowquestion_answer34) Which of the following are optically active?
(I) |
(II) |
(III) |
(IV) |
A) I and II done clear
B) II and III done clear
C) III and IV done clear
D) II, III and IV done clear
View Answer play_arrowA) \[S{{F}_{4}},\,\,Xe{{F}_{4}}\] done clear
B) \[l_{3}^{-},\,Xe{{F}_{2}}\] done clear
C) \[lCl_{4}^{+},\,\,SiC{{l}_{4}}\] done clear
D) \[ClO_{3}^{-},\,\,PO_{4}^{3-}\] done clear
View Answer play_arrowA) 780 K done clear
B) \[1.32\times {{10}^{5}}\,K\] done clear
C) \[7.84\times {{10}^{4}}K\] done clear
D) \[1900\,K\] done clear
View Answer play_arrowA) \[N{{H}_{3}}>N{{F}_{3}}>NC{{l}_{3}}\] done clear
B) \[N{{H}_{3}}>NC{{l}_{3}}>N{{F}_{3}}\] done clear
C) \[NC{{l}_{3}}>N{{H}_{3}}>N{{F}_{3}}\] done clear
D) \[N{{F}_{3}}>NC{{l}_{3}}>N{{H}_{3}}\] done clear
View Answer play_arrowA) 60.3 torr done clear
B) 65.7 torr done clear
C) 71.42 ton- done clear
D) None of these done clear
View Answer play_arrowquestion_answer39) The tautomerism involving (1, 5) migration of hydrogen atom can be observed in
A) I and II done clear
B) II and III done clear
C) II, III and IV done clear
D) I, II and III done clear
View Answer play_arrowquestion_answer40) In which of the following Aufbau principle and Hund's rule is violated?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer41) Which of the following order are correct?
(i) Solubility in water\[LiOH<NaOH<KOH<RbOH<CsOH\] |
(ii) Thermal stability\[BeS{{O}_{4}}<MgS{{O}_{4}}<CaS{{O}_{4}}<SrS{{O}_{4}}<BaS{{O}_{4}}\] |
(iii) Melting point \[NaCl>KCl>RbCl>CsCl>LiCl\] |
(iv) Solubility in water \[L{{i}_{2}}C{{O}_{3}}<N{{a}_{2}}C{{O}_{3}}<{{K}_{2}}C{{O}_{3}}<R{{b}_{2}}C{{O}_{3}}\] |
A) I, II and III done clear
B) I, II and IV done clear
C) II, III and IV done clear
D) All of these done clear
View Answer play_arrowquestion_answer42) The product obtained from the following reaction is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowA) 3 done clear
B) 5 done clear
C) 7 done clear
D) 9 done clear
View Answer play_arrowquestion_answer44) Which of the following is incorrect about the following?
A) I and II are geometrical isomers done clear
B) I and III are geometrical isomers done clear
C) II and III are optically active done clear
D) II and III are same done clear
View Answer play_arrowquestion_answer45) The number of geometrical isomers shown by the following compound is
A) 4 done clear
B) 6 done clear
C) 8 done clear
D) None of these done clear
View Answer play_arrowquestion_answer46) A reaction \[A\to B\] involves the following mechanism
Step 1 \[2A\xrightarrow{{{k}_{1}}}C\] (fast) |
Stem 2 \[C\xrightarrow{{{k}_{2}}}D\] (slow) |
Step3 \[3D\,\xrightarrow{{{k}_{3}}}B\] (fast) |
A) rate\[={{k}_{1}}{{[A]}^{2}}\] done clear
B) rate done clear
C) rate\[={{k}_{2}}[C]\,\,[D]\] done clear
D) rate\[={{k}_{1}}{{k}_{2}}{{k}_{3}}\,[C]\,\,[D]\] done clear
View Answer play_arrowquestion_answer47) Identify the correct statement.
A) \[{{P}_{4}}{{O}_{11}}\]contains peroxide linkages done clear
B) \[{{P}_{4}}{{O}_{10}}\]contains\[p\pi -d\pi \] back bonding done clear
C) In \[{{P}_{4}}{{O}_{10}}\] each P atom is bonded to three oxygen atoms done clear
D) \[{{P}_{4}}{{O}_{10}}\]hydrolyze in water forming phosphorous acid done clear
View Answer play_arrowA) done clear
B) done clear
C) done clear
D) None of these done clear
View Answer play_arrow(I) Oxygen gas at T temperature |
(II) Hydrogen gas at 2T temperature |
(III) Helium gas at 2T temperature |
(IV) Sulphur dioxide gas at 2T temperature |
A) I and II done clear
B) II and III done clear
C) I and IV done clear
D) III and IV done clear
View Answer play_arrowquestion_answer50) A reactant forms two products
\[A\xrightarrow{{{k}_{1}}}B\] Activation energy \[{{E}_{{{a}_{1}}}}\] |
\[A\xrightarrow{{{k}_{2}}}C\] Activation energy \[E{{\,}_{{{a}_{2}}}}\] |
A) \[{{k}_{2}}={{k}_{1}}{{e}^{-{{E}_{{{a}_{1}}}}/RT}}\] done clear
B) \[{{k}_{2}}={{k}_{1}}{{e}^{-{{E}_{{{a}_{2}}}}/RT}}\] done clear
C) \[{{k}_{1}}={{k}_{2}}{{e}^{-{{E}_{{{a}_{1}}}}/RT}}\] done clear
D) \[{{k}_{1}}=2{{k}_{2}}{{e}^{{{E}_{{{a}_{2}}}}/RT}}\] done clear
View Answer play_arrowA) \[C{{l}_{2}}{{O}_{7}}\] done clear
B) \[{{l}_{2}}{{O}_{5}}\] done clear
C) \[Cl{{O}_{2}}\] done clear
D) \[Br{{O}_{3}}\] done clear
View Answer play_arrowA) increases done clear
B) decreases done clear
C) remains same done clear
D) Non-e of these done clear
View Answer play_arrowquestion_answer53) Which of the following can give iodo form test?
(I) \[C{{H}_{3}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\] | (II) \[{{C}_{6}}{{H}_{5}}-C{{H}_{2}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\] |
(III) \[C{{H}_{3}}-CHO\] | (IV) \[{{C}_{6}}{{H}_{5}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\] |
A) Only IV done clear
B) III and IV done clear
C) III and IV done clear
D) All of these done clear
View Answer play_arrowquestion_answer54) The mono chlorinated products obtained from the reaction is
A) 4 done clear
B) 5 done clear
C) 6 done clear
D) 7 done clear
View Answer play_arrowA) \[{{A}_{4}}{{B}_{4}}{{O}_{7}}\] done clear
B) \[{{A}_{8}}{{B}_{6}}{{O}_{7}}\] done clear
C) \[{{A}_{8}}{{B}_{8}}{{O}_{7}}\] done clear
D) \[{{A}_{6}}{{B}_{8}}{{O}_{6}}\] done clear
View Answer play_arrowquestion_answer56) Which of the following compounds will not undergo tautomerism?
(I) | (II) | (III) | (IV) |
A) (II) and (III) done clear
B) (I), (II) and done clear
C) (III) Only (I) done clear
D) All of these done clear
View Answer play_arrowA) 6 done clear
B) 4 done clear
C) 8.5 done clear
D) None of these done clear
View Answer play_arrowquestion_answer58) The optically active compound among the following is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer59) Flocculating value of ion depends on
A) the shape of flocculating ion done clear
B) the amount of flocculating ion done clear
C) nature of the charge on the flocculating ion done clear
D) both; the nature and magnitude of the charge of the flocculating ion done clear
View Answer play_arrowquestion_answer60) The product 'B' on reaction with base \[O{{H}^{\odot -}}\] can undergo
A) cross aldol condensation done clear
B) intra mole cular aldol condensation done clear
C) cross Cannizzaro's reaction done clear
D) intra molecular Cannizzaro's reaction done clear
View Answer play_arrowA) \[\frac{1}{{{k}^{2}}+{{a}^{2}}}\,\left( kb+\frac{a\cdot b}{k}a+a\times b \right)\] done clear
B) \[\frac{1}{{{k}^{2}}+{{a}^{2}}}\,\left( kb-\frac{a\cdot b}{k}a+a\times b \right)\] done clear
C) \[\frac{1}{{{k}^{2}}+{{a}^{2}}}\,\left( kb-\frac{a\cdot b}{k}a-a\times b \right)\] done clear
D) \[\frac{1}{{{k}^{2}}-{{a}^{2}}}\,\left( kb-\frac{a\cdot b}{k}-a\times b \right)\] done clear
View Answer play_arrowquestion_answer62) The value of \[{{\tan }^{-1}}({{e}^{i\theta }})\] is equal to
A) \[\frac{n\pi }{2}+\frac{\pi }{4}+\frac{i}{2}\log \,\tan \,\left( \frac{\pi }{4}+\frac{\theta }{2} \right)\] done clear
B) \[\frac{n\pi }{2}-\frac{\pi }{4}-\frac{i}{2}\log \,\tan \,\left( \frac{\pi }{4}+\frac{\theta }{2} \right)\] done clear
C) \[\frac{n\pi }{2}+\frac{\pi }{4}+\frac{i}{2}\log \,\tan \,\left( \frac{\pi }{4}-\frac{\theta }{2} \right)\] done clear
D) \[\frac{n\pi }{2}+\frac{\pi }{4}+\frac{i}{2}\log \,\tan \,\left( \frac{\pi }{4}+\frac{\theta }{2} \right)\] done clear
View Answer play_arrowA) \[-\frac{n}{2}\] done clear
B) \[-n\] done clear
C) \[\frac{n}{2}\] done clear
D) \[n\] done clear
View Answer play_arrowA) \[\left( \left( n+\frac{1}{2} \right)\,\pi ,\,m\pi ,\,r\pi \right)\] done clear
B) \[\left( (n-1)\,\frac{\pi }{2},\,\,m\pi ,\,\,r\pi \right)\] done clear
C) \[\left( (2n-1)\,\frac{\pi }{3},\,\,m\pi ,\,\,\frac{r\pi }{2} \right)\] done clear
D) \[\left( (n+1)\,\frac{\pi }{2},\,\,m\pi ,\,r\pi \right)\] done clear
View Answer play_arrowA) \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] done clear
B) \[\frac{1}{2}\,({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\] done clear
C) \[{{a}^{2}}-{{b}^{2}}+{{c}^{2}}\] done clear
D) \[\frac{3}{\Delta }\] done clear
View Answer play_arrowA) 2 done clear
B) 1 done clear
C) 3 done clear
D) 4 done clear
View Answer play_arrowA) p, q and r are all false done clear
B) p, q and r are all true done clear
C) p and q are true and r is false done clear
D) p is true and q and r are false done clear
View Answer play_arrowquestion_answer68) Probability of product of a perfect square when two dice are thrown together
A) \[\frac{1}{9}\] done clear
B) \[\frac{2}{13}\] done clear
C) \[\frac{2}{9}\] done clear
D) \[\frac{4}{9}\] done clear
View Answer play_arrowA) \[\frac{7\sqrt{7}}{2\sqrt{3}}\] done clear
B) \[\frac{5\sqrt{7}}{\sqrt{3}}\] done clear
C) \[\frac{14\sqrt{7}}{\sqrt{3}}\] done clear
D) \[\frac{7\sqrt{7}}{5\sqrt{3}}\] done clear
View Answer play_arrowA) 202 done clear
B) 308 done clear
C) 567 done clear
D) 952 done clear
View Answer play_arrowA) \[\frac{\sqrt{2}}{3}{{\tan }^{-1}}\sqrt{2}+\frac{5}{12}\,\log \,2-\frac{1}{4}\,\log \,3\] done clear
B) \[\frac{\sqrt{2}}{3}{{\tan }^{-1}}\sqrt{2}-\frac{5}{12}\,\log \,2-\frac{1}{12}\,\log \,3\] done clear
C) \[\frac{\sqrt{2}}{3}{{\tan }^{-1}}\sqrt{2}+\frac{5}{12}\,\log \,2+\frac{1}{4}\,\log \,3\] done clear
D) \[\frac{\sqrt{2}}{3}{{\tan }^{-1}}\sqrt{2}-\frac{5}{12}\,\log \,2+\frac{1}{\sqrt{12}}\,\log \,3\] done clear
View Answer play_arrowA) one-one and onto done clear
B) one-one but not onto done clear
C) onto but not one-one done clear
D) neither one-one nor onto done clear
View Answer play_arrowA) 1 done clear
B) \[\alpha \] done clear
C) \[{{\alpha }^{2}}\] done clear
D) \[{{\alpha }^{3}}\] done clear
View Answer play_arrowquestion_answer74) If \[{{y}^{x}}-{{x}^{y}}=1,\] then the value of \[\frac{dy}{dx}\] at \[x=1\] is
A) \[2(1-\log \,2)\] done clear
B) \[2(1+\,\log \,2)\] done clear
C) \[2-\log \,2\] done clear
D) \[2+\log \,2\] done clear
View Answer play_arrowA) no solution done clear
B) exactly one solution done clear
C) exactly two solutions done clear
D) more than two solutions done clear
View Answer play_arrow\[\underset{t\to x}{\mathop{\lim }}\,\,\frac{\int\limits_{0}^{t}{\sqrt{1-{{\{f(S)\}}^{2}}}\,dS-\int\limits_{0}^{x}{\sqrt{1-{{\{f(S)\}}^{2}}}dx}}}{f(t)-f(x)}\] |
A) \[\left\{ \sqrt{7},\,\,\sqrt{15} \right\}\] done clear
B) \[\left\{ \frac{\sqrt{7}}{2},\,\,\frac{\sqrt{15}}{2} \right\}\] done clear
C) \[\left\{ \frac{\sqrt{7}}{3},\,\,\frac{\sqrt{15}}{3} \right\}\] done clear
D) \[\left\{ \frac{\sqrt{7}}{4},\,\,\frac{\sqrt{15}}{4} \right\}\] done clear
View Answer play_arrowA) \[\left\{ \left[ \begin{matrix} a & b \\ c & a-b \\ \end{matrix} \right];\,\,a,\,\,b,\,\,c\,\,\in \,R \right\}\] done clear
B) \[\left\{ \left[ \begin{matrix} a & b \\ b & c \\ \end{matrix} \right];\,\,a,\,\,b,\,\,c\,\,\in \,R \right\}\] done clear
C) \[\left\{ \left[ \begin{matrix} a-b & b \\ b & c \\ \end{matrix} \right];\,\,a,\,\,b,\,\,c\,\,\in \,R \right\}\] done clear
D) \[\left\{ \left[ \begin{matrix} a & b \\ b & a-b \\ \end{matrix} \right];\,\,a,\,\,b\,\,\in \,R \right\}\] done clear
View Answer play_arrowA) \[|{{\alpha }^{2}}-{{\beta }^{2}}|\] done clear
B) \[|\alpha \beta \,({{\alpha }^{2}}-{{\beta }^{2}})|\] done clear
C) \[\left| \frac{{{\alpha }^{2}}-{{\beta }^{2}}}{\alpha \beta } \right|\] done clear
D) \[\left| \frac{{{\alpha }^{2}}-{{\beta }^{2}}}{{{\alpha }^{2}}{{\beta }^{2}}} \right|\] done clear
View Answer play_arrowA) \[\sqrt{\frac{7}{4}}\] done clear
B) \[\sqrt{\frac{7}{3}}\] done clear
C) \[\sqrt{\frac{5}{4}}\] done clear
D) \[\sqrt{\frac{5}{3}}\] done clear
View Answer play_arrowA) \[{{x}^{2}}+{{y}^{2}}+x+2y+4=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+x-2y+4=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-x-2y+4=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-x+2y+4=0\] 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 local maximum done clear
B) no local minimum done clear
C) a local minimum done clear
D) no extremism done clear
View Answer play_arrowA) 0 done clear
B) \[{{3}^{n}}\] done clear
C) \[{{5}^{n}}\] done clear
D) None of these done clear
View Answer play_arrowA) 1900 done clear
B) 2000 done clear
C) 2100 done clear
D) 2200 done clear
View Answer play_arrowDirection: Let ABC be a triangle, R be the circumradius of the triangle. Also, given \[{{R}^{2}}=\frac{1}{8}\,({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\], then |
A) \[\sum{\cos \,2A=-1}\] done clear
B) \[\sum{\cos \,2A=1}\] done clear
C) \[\sum{\sin \,2A=1}\] done clear
D) \[\sum{\sin \,2A=-1}\] done clear
View Answer play_arrowDirection: Let ABC be a triangle, R be the circumradius of the triangle. Also, given \[{{R}^{2}}=\frac{1}{8}\,({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\], then |
A) equilateral done clear
B) isosceles and scalene done clear
C) cannot say done clear
D) right angled done clear
View Answer play_arrowDirection: Let a, b and c are three non-coplanar vectors, i.e., \[[a\,b\,c]\,\ne 0\]. The three new vectors \[a',\,\,b'\] and c' defined by the equation \[a'=\frac{b\times c}{[a\,\,b\,\,c]},\,\,b'=\frac{c\times a}{[a\,\,b\,\,c]}\]and\[c'=\frac{a\times b}{[a\,\,b\,\,c]}\] are called reciprocal system to the vectors a, b and c. |
A) \[a\times a'+b\times b'+c\times c'\] done clear
B) \[2\,(a'\times b'\times c')\] done clear
C) \[\frac{[a\,\,b\,\,c]}{2}\] done clear
D) 0 done clear
View Answer play_arrowDirection: Let a, b and c are three non-coplanar vectors, i.e., \[[a\,b\,c]\,\ne 0\]. The three new vectors \[a',\,\,b'\] and c' defined by the equation \[a'=\frac{b\times c}{[a\,\,b\,\,c]},\,\,b'=\frac{c\times a}{[a\,\,b\,\,c]}\]and\[c'=\frac{a\times b}{[a\,\,b\,\,c]}\] are called reciprocal system to the vectors a, b and c. |
A) \[\frac{2i+k}{3},\,\,\frac{-8i+3j-7k}{3},\,\,\frac{7i+3j+5k}{3}\] done clear
B) \[\frac{2i+k}{3},\,\,\frac{-8i+3j+7k}{3},\,\,\frac{7i+3j+5k}{3}\] done clear
C) \[\frac{2i+k}{3},\,\,\frac{-8i+3j+7k}{3},\,\,\frac{7i-3j+5k}{3}\] done clear
D) \[\frac{2i+k}{3},\,\,\frac{-8i+3j-7k}{3},\,\,\frac{-7i+3j-5k}{3}\] done clear
View Answer play_arrowDirection: For the following questions, choose the correct answer from the codes [a], [b], [c] and [d] defined as follows. |
Let us define the function as \[{{\cos }^{-1}}\,(\cos \theta )=\theta \]and\[2{{\tan }^{-1}}x=\frac{2x}{1-{{x}^{2}}}\]. |
Statement I If \[\sin \,[2\,{{\cos }^{-1}}\{\cot \,(2\,{{\tan }^{-1}}x)\}]=0,\] then \[x=\pm 1,\,\,\pm \,(1\pm \sqrt{2})\] |
Statement II \[\cot \,\,(2\,{{\tan }^{-1}}x)=\frac{1-{{x}^{2}}}{2x}\] |
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_arrowDirection: For the following questions, choose the correct answer from the codes [a], [b], [c] and [d] defined as follows. |
Consider the identify \[\frac{\sin \,\frac{\theta }{2}-\sin \,\frac{\phi }{2}}{\cos \,\frac{\theta }{2}+\cos \,\frac{\theta }{2}}=\tan \,\frac{\theta -\phi }{4}\]. |
Statement I \[{{\left( \frac{\cos A+\cos B}{\sin A-\sin B} \right)}^{n}}+{{\left( \frac{sinA+sinB}{\cos A-\cos B} \right)}^{n}}\] \[=\left\{ \begin{matrix} 2{{\cot }^{n}}\frac{A-B}{2}, & \text{if}\,\text{n}\,\text{is}\,\text{odd} \\ 0, & \text{if}\,\text{n}\,\text{is}\,\text{seven} \\ \end{matrix} \right.\] |
Statement II \[\frac{\cos \,A+\cos \,B}{\sin \,A-\sin \,B}=\cot \,\frac{A-B}{2}\]. |
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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