Solved papers for JEE Main & Advanced AIEEE Solved Paper-2004

done AIEEE Solved Paper-2004 Total Questions - 7

• question_answer1) If \[\int{\frac{\sin x}{\sin (x-\alpha )}}dx\] \[=Ax+B\text{ }\log \text{ }\sin (x-\alpha )+C,\]then value of \[(A,\text{ }B)\]is
  A)
  \[(sin\text{ }\alpha ,\text{ }cos\text{ }\alpha )\]     
  done clear
  B)
         (b)\[(cos\text{ }\alpha ,\text{ }sin\text{ }\alpha \text{)}\]
  done clear
  C)
         \[(-\sin \text{ }\alpha ,\text{ }\cos \text{ }\alpha )\]
  done clear
  D)
         \[(-\cos \text{ }\alpha ,\text{ }\sin \text{ }\alpha )\]
  done clear
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• question_answer2) With two forces acting at a point, the maximum effect is obtained when their resultant is 4N. If they act at right angles, then their resultant is 3N. Then, the forces are
  A)
  \[(2+\sqrt{2})N\]and\[(2-\sqrt{2})N\]
  done clear
  B)
  \[(2+\sqrt{3})N\]and\[(2-\sqrt{3})N\]
  done clear
  C)
  \[\left( 2+\frac{1}{2}\sqrt{2} \right)N\]and \[\left( 2-\frac{1}{2}\sqrt{2} \right)N\]
  done clear
  D)
  \[\left( 2+\frac{1}{2}\sqrt{3} \right)N\]and\[\left( 2-\frac{1}{2}\sqrt{3} \right)N\]            
  done clear
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• question_answer3) In a right angled \[\Delta ABC,\,\,\angle A={{90}^{\text{o}}}\] and sides a,b,c are respectively, 5 cm, 4 cm and 3 cm. If a force F has moments 0, 9 and 16 (in N cm) units respectively about vertices A, B and C, the magnitude of F is
  A)
  3                             
  done clear
  B)
         4                             
  done clear
  C)
  5                             
  done clear
  D)
         9
  done clear
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• question_answer4) Three forces P, Q and R acting along\[IA,IB\]and \[IC,\]where\[I\]is the incentre of a\[\Delta ABC,\]are in equilibrium. Then, P : Q : R is
  A)
  \[\cos \frac{A}{2}:\cos \frac{B}{2}:\cos \frac{C}{2}\]
  done clear
  B)
  \[\sin \frac{A}{2}:\sin \frac{B}{2}:\sin \frac{C}{2}\]
  done clear
  C)
  \[\sec \frac{A}{2}:\sec \frac{B}{2}:\sec \frac{C}{2}\]
  done clear
  D)
  \[\cos ec\,\frac{A}{2}:\,\,\cos ec\,\frac{B}{2}\,:\,\cos ec\,\frac{C}{2}\]
  done clear
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• question_answer5) A particle moves towards East from a point A to a point B at the rate of 4 km/h and then towards North from B to C at rate of 5 km/h. If AB = 12 km and BC = 5 km, then its average speed for its journey from A to C and resultant average velocity direct from A to C are respectively
  A)
  \[\frac{17}{14}km/h\text{ }and\frac{13}{4}km/h\]
  done clear
  B)
  \[\frac{13}{4}km/h\text{ }and\frac{17}{4}km/h\]
  done clear
  C)
  \[\frac{17}{9}km/h\text{ }and\frac{13}{9}km/h\]
  done clear
  D)
  \[\frac{13}{9}km/h\text{ }and\frac{17}{9}km/h\]
  done clear
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• question_answer6) A velocity 1/4 m/s is resolved into two components along OA and OB making angles \[30{}^\circ \]and\[45{}^\circ \]respectively with the given velocity, Then, the component along OB is
  A)
  \[\frac{1}{8}m/s\]           
  done clear
  B)
         \[\frac{1}{4}(\sqrt{3}-1)m/s\]    
  done clear
  C)
  \[\frac{1}{4}m/s\]           
  done clear
  D)
         \[\frac{1}{8}(\sqrt{6}-\sqrt{2})m/s\]
  done clear
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• question_answer7) If\[{{t}_{1}}\]and\[{{t}_{2}}\]are the times of flight of two particles having the same initial velocity u and range R on the horizontal, then\[t_{1}^{2}+t_{2}^{2}\]is equal to
  A)
  \[{{u}^{2}}/g\]                                  
  done clear
  B)
  \[4{{u}^{2}}/{{g}^{2}}\]                
  done clear
  C)
  \[{{u}^{2}}/2g\]         
  done clear
  D)
         1
  done clear
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