A) \[\frac{\alpha \beta }{\alpha +\beta }t\] done clear
B) \[\frac{\alpha \beta }{\alpha -\beta }t\] done clear
C) \[\sqrt{\alpha \beta }\,t\] done clear
D) \[\frac{\alpha +\beta }{2}t\] done clear
View Answer play_arrowA) \[\theta ={{\tan }^{-1}}\,\left( \frac{3}{4} \right)\] with the vertical towards South done clear
B) \[\theta ={{\tan }^{-1}}\,\left( \frac{3}{4} \right)\] with the vertical towards North done clear
C) \[\theta ={{\cot }^{-1}}\,\left( \frac{3}{4} \right)\] with the vertical towards South done clear
D) \[\theta ={{\cot }^{-1}}\,\left( \frac{3}{4} \right)\] with the vertical towards North done clear
View Answer play_arrowA) \[(M+m)g\,\tan \,\beta \] done clear
B) \[g\,\tan \,\beta \] done clear
C) \[mg\,\cos \,\beta \] done clear
D) \[(M+m)\,g\,\cos ec\,\beta \] done clear
View Answer play_arrowA) \[\sqrt{\frac{g}{L}}\] done clear
B) \[\frac{1}{2}\sqrt{\frac{g}{L}}\] done clear
C) \[\frac{3}{2}\sqrt{\frac{g}{L}}\] done clear
D) \[2\sqrt{\frac{g}{L}}\] done clear
View Answer play_arrowA) \[\frac{d}{D}h\] done clear
B) \[\left( \frac{d}{D}-1 \right)h\] done clear
C) \[h\] done clear
D) Zero done clear
View Answer play_arrowA) \[{{V}_{1}}={{V}_{2}},\,\,{{V}_{3}}={{V}_{4}}\] and \[{{V}_{2}}>{{V}_{3}}\] done clear
B) \[{{V}_{1}}={{V}_{2}},\,\,{{V}_{3}}={{V}_{4}}\] and \[{{V}_{2}}<{{V}_{3}}\] done clear
C) \[{{V}_{1}}={{V}_{2}}={{V}_{3}}={{V}_{4}}\] done clear
D) \[{{V}_{4}}>{{V}_{3}}>{{V}_{2}}>{{V}_{1}}\] done clear
View Answer play_arrowA) \[\frac{125\times {{10}^{-3}}}{2}\] done clear
B) \[\frac{12.5\times {{10}^{-3}}}{2}\] done clear
C) \[\frac{1.25\times {{10}^{-3}}}{2}\] done clear
D) \[\frac{0.125\times {{10}^{-3}}}{2}\] done clear
View Answer play_arrowA) \[\frac{1}{25}{{\,}_{o}}{{C}^{-1}}\] done clear
B) \[\frac{1}{50}{{\,}_{o}}{{C}^{-1}}\] done clear
C) \[\frac{1}{80}{{\,}_{o}}{{C}^{-1}}\] done clear
D) \[\frac{1}{75}{{\,}_{o}}{{C}^{-1}}\] done clear
View Answer play_arrowA) only A done clear
B) A and B done clear
C) All the three metals done clear
D) None of these done clear
View Answer play_arrowquestion_answer10) After 1 a and 2 \[\beta \]-emissions
A) mass number reduces by 6 done clear
B) mass number reduces by 4 done clear
C) mass number reduces by 2 done clear
D) mass number remains unchanged done clear
View Answer play_arrowA) 9.8 done clear
B) 98 done clear
C) 980 done clear
D) 9800 done clear
View Answer play_arrowA) 1s done clear
B) 7 s done clear
C) 5 s done clear
D) 3 s done clear
View Answer play_arrowA) \[g/5\,\,m{{s}^{-2}}\] done clear
B) \[6g\,\,m{{s}^{-2}}\] done clear
C) \[g/2\,\,m{{s}^{-2}}\] done clear
D) \[g\,\,m{{s}^{-2}}\] done clear
View Answer play_arrowA) \[mgl\,\cos \,\,({{\theta }_{1}}-{{\theta }_{2}})\] done clear
B) \[mgl\,\,(\cos \,{{\theta }_{2}}-\cos {{\theta }_{1}})\] done clear
C) \[mgl\,\,(\cos \,{{\theta }_{1}}-\cos \,{{\theta }_{2}})\] done clear
D) \[mgl\,\,\sin \,({{\theta }_{1}}-{{\theta }_{2}})\] done clear
View Answer play_arrowA) \[\frac{{{\alpha }^{2}}}{2\beta }\] done clear
B) \[\frac{{{\alpha }^{2}}-{{\beta }^{2}}}{2\alpha }\] done clear
C) \[\frac{{{\alpha }^{2}}-{{\beta }^{2}}}{2\beta }\] done clear
D) \[\frac{\alpha (\alpha -\beta )}{2}\] done clear
View Answer play_arrowA) \[4\sqrt{gR}\] done clear
B) \[\sqrt{2gR}\] done clear
C) \[\sqrt{gR}\] done clear
D) \[\sqrt{4gR}\] done clear
View Answer play_arrowA) \[{{t}_{1}}={{t}_{2}}={{t}_{3}}\] done clear
B) \[{{t}_{1}}<{{t}_{2}}={{t}_{3}}\] done clear
C) \[{{t}_{1}}<{{t}_{2}}<{{t}_{3}}\] done clear
D) \[{{t}_{1}}>{{t}_{2}}>{{t}_{3}}\] done clear
View Answer play_arrowA) The particle will come to rest instantaneously, at t = 6.8 s. done clear
B) The final velocity of the particle will be 18m/s, done clear
C) Work done by the force on the particle is 375 J. done clear
D) All of the above done clear
View Answer play_arrowA) \[\frac{Mg}{AK}\] done clear
B) \[\frac{Mg}{3AK}\] done clear
C) \[\frac{3Mg}{AK}\] done clear
D) \[\frac{Mg}{2AK}\] done clear
View Answer play_arrowA) \[{{r}^{-1}}\] done clear
B) \[{{r}^{-2}}\] done clear
C) \[{{r}^{-3/2}}\] done clear
D) \[{{r}^{-5/2}}\] done clear
View Answer play_arrowA) large value of current done clear
B) a constant voltage done clear
C) a current that is increasing without any change in applied voltage done clear
D) All of the above done clear
View Answer play_arrowA) KE and PE both increases done clear
B) KE and PE both decreases done clear
C) KE increases while PE decreases done clear
D) KE decreases while PE increases done clear
View Answer play_arrowA) the particle starts with a certain velocity, but the motion is related, finally the particle stops done clear
B) the velocity of the particle is constant throughout done clear
C) the acceleration of the particle is constant throughout done clear
D) the particle starts with certain velocity and then its motion is accelerated done clear
View Answer play_arrowA) \[{{v}_{0}}=R\omega \] done clear
B) \[v={{v}_{0}}\,+R\omega \] done clear
C) \[v={{v}_{0}}-R\omega \] done clear
D) \[v={{v}_{0}}\] done clear
View Answer play_arrowquestion_answer25) In the circuit shown, the current in \[3\,\,\Omega \]resistor is
A) 1 A done clear
B) \[\frac{30}{7}A\] done clear
C) \[\frac{5}{7}A\] done clear
D) Information insufficient done clear
View Answer play_arrowA) electric field near A in the cavity = electric field near B in the cavity done clear
B) charge density at A = charge density at B done clear
C) potential at A = potential at B done clear
D) None of the above done clear
View Answer play_arrowA) 447.6 A done clear
B) 559.5 A done clear
C) 4A done clear
D) 800 A done clear
View Answer play_arrow\[{{F}_{1}}\]: The weight of the hot air balloon |
\[{{F}_{2}}\]: The weight of the student |
\[{{F}_{3}}\]: The force of the student pulling on the earth |
\[{{F}_{4}}\]: The force of the hot air balloon pulling on the student |
A) \[{{F}_{4}}>{{F}_{2}}\] done clear
B) \[{{F}_{3}}=-{{F}_{4}}\] done clear
C) \[{{F}_{2}}>{{F}_{1}}\] done clear
D) \[{{F}_{2}}=-{{F}_{4}}\] done clear
View Answer play_arrowA) both \[{{c}_{1}}\] and \[{{c}_{2}}\] will move w.r.t. ground done clear
B) neither \[{{c}_{1}}\] nor \[{{c}_{2}}\] will move w.r.t. ground done clear
C) \[{{c}_{1}}\] will move but \[{{c}_{2}}\] will remain stationary w.r.t. the ground done clear
D) \[{{c}_{2}}\] will move but \[{{c}_{1}}\] will remain stationary w.r.t. the ground done clear
View Answer play_arrowA) \[\frac{mg{{R}^{2}}}{l}\] done clear
B) \[\frac{mg{{R}^{2}}}{l}\sin \,\left( \frac{l}{R} \right)\] done clear
C) \[\frac{mg{{R}^{2}}}{l}\cos \,\left( \frac{l}{R} \right)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer31) Give the stability of following carbocations.
(I) \[C{{H}_{3}}-{{\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{{{C}^{\oplus }}}}}\,}^{{}}}\] | (II) |
(III)\[C{{H}_{3}}-{{\underset{\begin{smallmatrix} | \\ {{C}_{2}}{{H}_{5}} \end{smallmatrix}}{\overset{\begin{smallmatrix} {{C}_{2}}{{H}_{5}} \\ | \end{smallmatrix}}{\mathop{{{C}^{\oplus }}}}}\,}^{{}}}\] | (IV)\[{{C}_{2}}{{H}_{5}}\,-{{\underset{\begin{smallmatrix} | \\ {{C}_{2}}{{H}_{5}} \end{smallmatrix}}{\overset{\begin{smallmatrix} {{C}_{2}}{{H}_{5}} \\ | \end{smallmatrix}}{\mathop{{{C}^{\oplus }}}}}\,}^{{}}}\] |
A) IV > III > II > I done clear
B) IV > III > I > II done clear
C) I > II > III > IV done clear
D) I > III > II > IV done clear
View Answer play_arrowquestion_answer32) Which of the following will allow free rotation about double bond?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer33) The ratio of ionization energy of H and \[B{{e}^{3+}}\]is
A) 1 : 1 done clear
B) 1 : 3 done clear
C) 1 : 9 done clear
D) 1 : 16 done clear
View Answer play_arrowquestion_answer34) The shape of the molecule \[XeO{{F}_{2}}\] is
A) Tetrahedral done clear
B) square pyramidal done clear
C) T-shape done clear
D) square planar done clear
View Answer play_arrowA) 1 : 2 done clear
B) 1 : 1 done clear
C) 1 : 16 done clear
D) 15 : 16 done clear
View Answer play_arrow\[S+\frac{3}{2}{{O}_{2}}\xrightarrow{\,}\,S{{O}_{3}}^{+}y\,S{{O}_{2}}\,\,2x\,\,kcal\] |
\[S{{O}_{2}}+\frac{1}{2}\,{{O}_{2}}\to \,\,S{{O}_{3}}+y\,kcal\] |
A) \[y-2x\] done clear
B) \[2x-y\] done clear
C) \[x+y\] done clear
D) \[\frac{2x}{y}\] done clear
View Answer play_arrowA) 103.8% done clear
B) 105.9% done clear
C) 108.8% done clear
D) 110.5% done clear
View Answer play_arrowA) 11% done clear
B) 10% done clear
C) 100% done clear
D) 110% done clear
View Answer play_arrowquestion_answer39) The number of peroxide linkages in \[{{P}_{4}}{{O}_{10}}\]is
A) 0 done clear
B) 2 done clear
C) 4 done clear
D) 8 done clear
View Answer play_arrowA) 560 mm Hg done clear
B) 680 mm Hg done clear
C) 920 mm Hg done clear
D) 600 mm Hg done clear
View Answer play_arrowquestion_answer41) The compound which may exhibit tautomerism is
(I) | (II) |
(III) | (IV) \[C{{H}_{3}}-CH=CH-CHO\] |
A) I, II and III done clear
B) II, III and IV done clear
C) I and III done clear
D) I, II, III and IV done clear
View Answer play_arrowquestion_answer42) The cation which gives a yellow precipitate with potassium chromate is
A) \[NH_{4}^{+}\] done clear
B) \[B{{a}^{2+}}\] done clear
C) \[C{{a}^{2+}}\] done clear
D) \[N{{a}^{+}}\] done clear
View Answer play_arrowquestion_answer43) Which of the following compounds is achiral?
A) done clear
B) \[C{{H}_{3}}-CHOHCN\] done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer44) Which of the following complexes are inner-orbital complex and diamagnetic?
A) \[{{[Fe{{(CN)}_{6}}]}^{4-}}\] done clear
B) \[{{[Fe{{({{H}_{2}}O)}_{6}}]}^{2+}}\] done clear
C) \[{{[Cu{{(N{{H}_{3}})}_{6}}]}^{2+}}\] done clear
D) \[{{[Ni{{(CN)}_{6}}]}^{4-}}\] done clear
View Answer play_arrowA) 150 torr done clear
B) 180 torr done clear
C) 188.88 torr done clear
D) 198.88 torr done clear
View Answer play_arrowquestion_answer46) The product formed in the reaction,
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowA) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowA) K and \[K{{O}_{2}}\] done clear
B) Na and \[N{{a}_{2}}{{O}_{2}}\] done clear
C) \[Ca\] and \[Ca{{H}_{2}}\] done clear
D) \[Ba\] and \[Ba{{O}_{2}}\] done clear
View Answer play_arrowA) \[4\times {{10}^{-4}}\] done clear
B) \[2\times {{10}^{-4}}\] done clear
C) \[{{10}^{-4}}\] done clear
D) \[8\times {{10}^{-4}}\] done clear
View Answer play_arrowA) 1.1 hr done clear
B) 46 hr done clear
C) 53.6 hr done clear
D) 24.00 hr done clear
View Answer play_arrowA) 3, 3 done clear
B) \[\frac{7}{2},\,4\] done clear
C) \[\frac{7}{2},\,\,\frac{7}{2}\] done clear
D) \[4,\,\,\frac{7}{2}\] done clear
View Answer play_arrowquestion_answer52) During the electro-osmosis of \[Fe{{(OH)}_{3}}\] sol
A) sol particles move towards anode done clear
B) sol particles move towards cathode done clear
C) the dispersion medium moves towards anode done clear
D) the dispersion medium moves towards cathode done clear
View Answer play_arrowDirection: Solution of an acid and its anion (that is its conjugate base) or of a base and its common cation is buffer. On adding small amount of acid or base, the pH of solution changes very little (negligible change). The pH of buffer solution is determined as follows: |
ph of acidic in buffer \[=\,p{{K}_{a}}+\,\log \,\,\frac{[conjugate\,base]}{[acid]}\] |
\[pOH\] of basic buffer \[=p{{K}_{b}}+\log \,\frac{[conjugate\,\,acid]}{[base]}\] |
A buffer solution can work effectively provided the value of \[\frac{[conjugate\,\,base]}{[acid]}\] for acidic buffer or \[\frac{[conjugate\,\,acid]}{[acid]}\] for basic buffer lies within the range of 1 : 10 or 10 : 1. |
A) 5.34 done clear
B) 8.66 done clear
C) 7.46 done clear
D) None of these done clear
View Answer play_arrowDirection: Solution of an acid and its anion (that is its conjugate base) or of a base and its common cation is buffer. On adding small amount of acid or base, the pH of solution changes very little (negligible change). The pH of buffer solution is determined as follows: |
ph of acidic in buffer \[=\,p{{K}_{a}}+\,\log \,\,\frac{[conjugate\,base]}{[acid]}\] |
\[pOH\] of basic buffer \[=p{{K}_{b}}+\log \,\frac{[conjugate\,\,acid]}{[base]}\] |
A buffer solution can work effectively provided the value of \[\frac{[conjugate\,\,base]}{[acid]}\] for acidic buffer or \[\frac{[conjugate\,\,acid]}{[acid]}\] for basic buffer lies within the range of 1 : 10 or 10 : 1. |
A) 4.5 done clear
B) 4.8 done clear
C) 5.1 done clear
D) 5.4 done clear
View Answer play_arrowDirection: Solution of an acid and its anion (that is its conjugate base) or of a base and its common cation is buffer. On adding small amount of acid or base, the pH of solution changes very little (negligible change). The pH of buffer solution is determined as follows: |
ph of acidic in buffer \[=\,p{{K}_{a}}+\,\log \,\,\frac{[conjugate\,base]}{[acid]}\] |
\[pOH\] of basic buffer \[=p{{K}_{b}}+\log \,\frac{[conjugate\,\,acid]}{[base]}\] |
A buffer solution can work effectively provided the value of \[\frac{[conjugate\,\,base]}{[acid]}\] for acidic buffer or \[\frac{[conjugate\,\,acid]}{[acid]}\] for basic buffer lies within the range of 1 : 10 or 10 : 1. |
A) 5.40 done clear
B) 5.88 done clear
C) 4.92 done clear
D) None of these done clear
View Answer play_arrowDirection: Two liquids A and B have the same molecular weights and for man ideal solution. The solution a/composition \[{{X}_{A}}\] has the vapour pressure 700 mm Hg at \[80{}^\circ C\]. The above solution is distilled without reflux till 3/4 of the solution is collected as condensate. The composition of the condensate is\[X{{'}_{A}}=0.75\] and that of residue is \[{{X}_{A}}=0.3\]. The vapour pressure of the residue at \[80{}^\circ C\] is 600 mm. |
A) 0.6375 done clear
B) 0.2375 done clear
C) 0.8375 done clear
D) 0.9375 done clear
View Answer play_arrowDirection: Two liquids A and B have the same molecular weights and for man ideal solution. The solution a/composition \[{{X}_{A}}\] has the vapour pressure 700 mm Hg at \[80{}^\circ C\]. The above solution is distilled without reflux till 3/4 of the solution is collected as condensate. The composition of the condensate is\[X{{'}_{A}}=0.75\] and that of residue is \[{{X}_{A}}=0.3\]. The vapour pressure of the residue at \[80{}^\circ C\] is 600 mm. |
A) 807.41 mm of Hg done clear
B) 511.11 mm of Hg done clear
C) 707.41 41 mm of Hg done clear
D) 207.41 mm of Hg done clear
View Answer play_arrowDirection: Two liquids A and B have the same molecular weights and for man ideal solution. The solution a/composition \[{{X}_{A}}\] has the vapour pressure 700 mm Hg at \[80{}^\circ C\]. The above solution is distilled without reflux till 3/4 of the solution is collected as condensate. The composition of the condensate is\[X{{'}_{A}}=0.75\] and that of residue is \[{{X}_{A}}=0.3\]. The vapour pressure of the residue at \[80{}^\circ C\] is 600 mm. |
A) 807.41 mm of Hg done clear
B) 511.11 mm of Hg done clear
C) 707.41 mm of Hg done clear
D) 207.41 mm of Hg done clear
View Answer play_arrowDirection: For the following questions choose the correct answers from the codes [a], [b], [c] and [d] defined as follows. |
Statement I In the electrolytic cell, flow of electron is from anode to cathode through internal supply. |
Statement II In an electrolytic cell, cathode is the electron rich electrode. |
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 answers from the codes [a], [b], [c] and [d] defined as follows. |
Statement I Internal energy of a system is an extensive property. |
Statement II The internal energy of a system depends upon the amount and physical state of the substance. |
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) 40 done clear
B) 45 done clear
C) 50 done clear
D) 55 done clear
View Answer play_arrowquestion_answer62) Let \[h(x)=\max \,\{-x,\,1,\,{{x}^{2}}\}\] for every real number \[x\]. Then,
A) \[h\] is continuous for all \[x\] done clear
B) \[h\] is differentiable for all \[x\] done clear
C) \[h'(a)=1,\,\,\forall x>1\]c done clear
D) h is not differentiable at two values of \[x\] done clear
View Answer play_arrowA) 1 done clear
B) -1 done clear
C) 0 done clear
D) 2 done clear
View Answer play_arrowA) \[\frac{52}{77}\] done clear
B) \[\frac{50}{77}\] done clear
C) \[\frac{25}{88}\] done clear
D) None of these done clear
View Answer play_arrowA) 0 done clear
B) 1 done clear
C) 3 done clear
D) 4 done clear
View Answer play_arrowA) 4 done clear
B) 3 done clear
C) 2 done clear
D) 1 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) 9 done clear
B) 12 done clear
C) 15 done clear
D) 18 done clear
View Answer play_arrowA) 2 done clear
B) 1 done clear
C) -1 done clear
D) 0 done clear
View Answer play_arrowA) \[9,\,\,x\in \,\,\left[ 0,\,\frac{\pi }{2} \right]\] done clear
B) \[10,\,x\,\,\in \,\,[0,\,\,\pi ]\] done clear
C) \[8,\,\,x\,\in \,\,\left[ -\frac{\pi }{2},\,\frac{\pi }{2} \right]\] done clear
D) \[12,\,\,x\,\,\in \,\,[-\pi ,\,\,\pi ]\] done clear
View Answer play_arrowA) \[f(x)=\left( 3{{x}^{2}}-\frac{1}{2x} \right)\] done clear
B) \[f(x)=\frac{1}{5}\,\left( 3{{x}^{2}}-\frac{1}{2x} \right)\] done clear
C) \[a=1\] done clear
D) \[a=2\] done clear
View Answer play_arrowquestion_answer72) The contrapositive of \[(p\,\vee q)\to r\] is
A) \[\tilde{\ }r\to (p\,\vee q)\] done clear
B) \[r\to (p\,\vee q)\] done clear
C) \[\tilde{\ }r\to (\tilde{\ }p\,\wedge \tilde{\ }q)\] done clear
D) \[p\to (q\vee r)\] done clear
View Answer play_arrowA) \[x+ey+{{e}^{3}}a=0\] done clear
B) \[x-ey-{{e}^{3}}a=0\] done clear
C) \[x+ey-{{e}^{2}}a=0\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer74) Range of the function \[f(x)=\sin x+|\cos \,x|\] is
A) \[[-\sqrt{2},\,\,\sqrt{2}]\] done clear
B) \[[0,\,\,\sqrt{2}]\] done clear
C) \[[1,\,\,\sqrt{2}]\] done clear
D) \[[-1,\,\,\sqrt{2}]\] done clear
View Answer play_arrowA) positive integers done clear
B) whole numbers done clear
C) prime numbers done clear
D) all integers done clear
View Answer play_arrowA) is independent of a done clear
B) is independent of b done clear
C) is independent of a and b done clear
D) depends on both a and b done clear
View Answer play_arrowA) \[\frac{2}{\sqrt{3}}\] done clear
B) \[\sqrt{3}\] done clear
C) \[\frac{1}{\sqrt{3}}\] done clear
D) \[\frac{\sqrt{3}}{2}\] done clear
View Answer play_arrowA) \[\frac{16}{5}\] done clear
B) \[\frac{\sqrt{10025}}{25}-1\] done clear
C) \[\frac{\sqrt{10125}}{25}-1\] done clear
D) 24 done clear
View Answer play_arrowA) 17 done clear
B) 23 done clear
C) 22 done clear
D) 19 done clear
View Answer play_arrowA) 600 done clear
B) 820 done clear
C) 840 done clear
D) 620 done clear
View Answer play_arrowA) is independent of a done clear
B) is independent of b done clear
C) is independent of a and b done clear
D) depends on both a and b done clear
View Answer play_arrowquestion_answer82) If Z is an idempotent matrix, then \[{{(l+Z)}^{n}}\]
A) \[l{{+}^{n}}Z\] done clear
B) \[l+({{2}^{n}}-1)Z\] done clear
C) \[l-({{2}^{n}}-1)Z\] done clear
D) None of these done clear
View Answer play_arrow\[\sin \,a+7\,\sin \,b=4\,(\sin \,c+2\,\sin \,d)\] |
\[\cos \,a+7\,\cos \,b=4\,(\cos \,c+2\,\cos \,d)\] |
and the numerical value of \[\frac{7\,\cos \,(b-c)}{\cos \,(a-d)}\] is m. the correct statement is/are |
A) m is a prime number done clear
B) n is a composite number done clear
C) m, n both are perfect square done clear
D) m is divisible by n. done clear
View Answer play_arrowA) 17 done clear
B) 33 done clear
C) 50 done clear
D) 47 done clear
View Answer play_arrowDirection: Sometimes use of graph is very important to find the number of solutions of an equation. To find the number of solutions of the equation \[{{f}_{1}}(x)={{f}_{2}}(x)\]. We drain the graph of\[y={{f}_{1}}(x),\]\[y={{f}_{2}}(x)\] and the number of point of intersection of these graphs is equal to the number of solution. Let us consider the function \[f(x)=\,|x-1|+\,|x-3|+\,|x-7|+|x-13|\] |
A) 10 done clear
B) 16 done clear
C) 20 done clear
D) 28 done clear
View Answer play_arrowDirection: Sometimes use of graph is very important to find the number of solutions of an equation. To find the number of solutions of the equation \[{{f}_{1}}(x)={{f}_{2}}(x)\]. We drain the graph of\[y={{f}_{1}}(x),\]\[y={{f}_{2}}(x)\] and the number of point of intersection of these graphs is equal to the number of solution. Let us consider the function \[f(x)=\,|x-1|+\,|x-3|+\,|x-7|+|x-13|\] |
A) zero done clear
B) two done clear
C) three done clear
D) infinitely many done clear
View Answer play_arrowDirection: The mean value of the continuous functions f(x) in the interval [a, b} is given by the formula |
Mean value \[=\frac{\int\limits_{a}^{b}{f(x)\,dx}}{b-a}\] |
A) \[\frac{1}{3}\] done clear
B) \[\frac{1}{2}\] done clear
C) 0 done clear
D) 1 done clear
View Answer play_arrowDirection: The mean value of the continuous functions f(x) in the interval [a, b} is given by the formula |
Mean value \[=\frac{\int\limits_{a}^{b}{f(x)\,dx}}{b-a}\] |
A) \[\frac{2}{\pi }\] done clear
B) \[\frac{1}{\pi }\] done clear
C) \[\frac{4}{\pi }\] done clear
D) \[\frac{8}{\pi }\] done clear
View Answer play_arrowDirection: For the following questions. Choose the correct answer to the codes [a], [b], [c] and [d] defined as follows. |
Statement I If \[\sin \,x+{{\sin }^{2}}x=1,\] then value of the expression \[{{\cos }^{12}}\,x+3\,{{\cos }^{10}}x+3\,{{\cos }^{8}}x+{{\cos }^{6}}x-1\] |
Statement II \[{{\cos }^{2}}\,x=\frac{\sqrt{5}-1}{2}\]. |
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
View Answer play_arrowDirection: For the following questions. Choose the correct answer to the codes [a], [b], [c] and [d] defined as follows. |
Let us consider the any \[\Delta \,ABC,\] whose sum of all angles is \[180{}^\circ \]. |
Statement I If \[\angle A\] is obtuse, then \[\tan \,B\,\tan C<1\]. |
Statement II \[\tan \,A+\tan \,B+\tan \,C=\tan \,A\,\tan \,B\,\tan \,C\]. |
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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