Physics-
General
Easy

Question

Two 1ong wires are placed parallel to each other 10cm apart as shown in fig The magnetic field at piont P is

  1. 5 divided by 6 cross times 10 to the power of negative 3 end exponent T directed perpendicular into the paper    
  2. 1 divided by 3 cross times 10 to the power of negative 3 end exponent T directed perpendicular out of the paper    
  3. 5 divided by 6 cross times 10 to the power of negative 3 end exponent T directed perpendicular out of the paper    
  4. 1 divided by 6 cross times 10 to the power of negative 3 end exponent T directed perpendicular into the paper    

The correct answer is: 1 divided by 6 cross times 10 to the power of negative 3 end exponent T directed perpendicular into the paper

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A proton accelerated by a pd V=500 KV moves through a transverse magnetic field B=0.51 T as shown in figure Then the angle q through which the proton deviates from the initial direction of its motion is (approximately)

   

A proton accelerated by a pd V=500 KV moves through a transverse magnetic field B=0.51 T as shown in figure Then the angle q through which the proton deviates from the initial direction of its motion is (approximately)

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A particle of mass m and charge q, moving with velocity V enters Region II normal to the boundary as shown in fig Region II has a uniform magnetic field B perpendicular to the plane of the paper The length of the Region II is l Then

   

A particle of mass m and charge q, moving with velocity V enters Region II normal to the boundary as shown in fig Region II has a uniform magnetic field B perpendicular to the plane of the paper The length of the Region II is l Then

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A small sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The force acting on the sphere are shown in figure. Which of the following statements is wrong?

Here W=T(cosθ+sinθ)<T so P+Q=T(cosθ+sinθ)<T Whereas [a], [b] and [c] are correct and [d] is wrong.    

A small sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The force acting on the sphere are shown in figure. Which of the following statements is wrong?

physics-General
Here W=T(cosθ+sinθ)<T so P+Q=T(cosθ+sinθ)<T Whereas [a], [b] and [c] are correct and [d] is wrong.    
parallel
General
Maths-

L t subscript x not stretchy rightwards arrow pi over 2 end subscript fraction numerator sec space x minus tan space x over denominator pi over 2 minus x end fraction

L t subscript x not stretchy rightwards arrow pi over 2 end subscript fraction numerator sec space x minus tan space x over denominator pi over 2 minus x end fraction
equals limit as x rightwards arrow straight pi over 2 of fraction numerator begin display style fraction numerator 1 over denominator cos space x end fraction end style minus begin display style fraction numerator sin space x over denominator cos x end fraction end style over denominator begin display style straight pi over 2 end style minus x end fraction
equals limit as x rightwards arrow straight pi over 2 of open parentheses fraction numerator 1 minus sin space x over denominator cos space x end fraction close parentheses open parentheses fraction numerator 1 over denominator begin display style straight pi over 2 end style minus x end fraction close parentheses
straight pi over 2 minus x equals y rightwards double arrow x equals straight pi over 2 minus y
equals limit as y rightwards arrow 0 of fraction numerator 1 minus sin open parentheses begin display style straight pi over 2 end style minus y close parentheses over denominator y cos open parentheses begin display style straight pi over 2 end style minus y close parentheses end fraction
equals limit as y rightwards arrow 0 of fraction numerator 1 minus cos space y over denominator y. sin y end fraction
equals limit as y rightwards arrow 0 of fraction numerator 1 minus cos y over denominator y squared end fraction. fraction numerator y over denominator sin space y end fraction
equals limit as y rightwards arrow 0 of fraction numerator 2 sin squared begin display style y over 2 end style over denominator open parentheses begin display style y over 2 end style close parentheses squared 4 end fraction. fraction numerator y over denominator sin y end fraction
equals 2 over 4 equals 1 half

L t subscript x not stretchy rightwards arrow pi over 2 end subscript fraction numerator sec space x minus tan space x over denominator pi over 2 minus x end fraction

Maths-General
L t subscript x not stretchy rightwards arrow pi over 2 end subscript fraction numerator sec space x minus tan space x over denominator pi over 2 minus x end fraction
equals limit as x rightwards arrow straight pi over 2 of fraction numerator begin display style fraction numerator 1 over denominator cos space x end fraction end style minus begin display style fraction numerator sin space x over denominator cos x end fraction end style over denominator begin display style straight pi over 2 end style minus x end fraction
equals limit as x rightwards arrow straight pi over 2 of open parentheses fraction numerator 1 minus sin space x over denominator cos space x end fraction close parentheses open parentheses fraction numerator 1 over denominator begin display style straight pi over 2 end style minus x end fraction close parentheses
straight pi over 2 minus x equals y rightwards double arrow x equals straight pi over 2 minus y
equals limit as y rightwards arrow 0 of fraction numerator 1 minus sin open parentheses begin display style straight pi over 2 end style minus y close parentheses over denominator y cos open parentheses begin display style straight pi over 2 end style minus y close parentheses end fraction
equals limit as y rightwards arrow 0 of fraction numerator 1 minus cos space y over denominator y. sin y end fraction
equals limit as y rightwards arrow 0 of fraction numerator 1 minus cos y over denominator y squared end fraction. fraction numerator y over denominator sin space y end fraction
equals limit as y rightwards arrow 0 of fraction numerator 2 sin squared begin display style y over 2 end style over denominator open parentheses begin display style y over 2 end style close parentheses squared 4 end fraction. fraction numerator y over denominator sin y end fraction
equals 2 over 4 equals 1 half
General
maths-

Let f : (0, ¥) → R and F(x) = 0xt f (t) dt. If F (x2) = x4 + x5, then r=112f(r2), is equal to

   

Let f : (0, ¥) → R and F(x) = 0xt f (t) dt. If F (x2) = x4 + x5, then r=112f(r2), is equal to

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L t subscript x not stretchy rightwards arrow pi over 2 end subscript left square bracket sec space 3 x cos space 5 x right square bracket

equals limit as x rightwards arrow bevelled straight pi over 2 of space open parentheses fraction numerator cos space 5 x over denominator cos space 3 x end fraction close parentheses
U sin g space L apostrophe H o s p i t a l space t h e o r e m comma
equals limit as x rightwards arrow bevelled straight pi over 2 of space space fraction numerator begin display style fraction numerator d blank over denominator d x end fraction open parentheses cos space 5 x close parentheses end style over denominator begin display style fraction numerator d blank over denominator d x end fraction open parentheses cos space 3 x close parentheses end style end fraction
equals limit as x rightwards arrow bevelled straight pi over 2 of space space fraction numerator negative left parenthesis sin space 5 x right parenthesis.5 over denominator negative left parenthesis sin space 3 x right parenthesis.3 end fraction
equals 5 over 3 space. limit as x rightwards arrow bevelled straight pi over 2 of space fraction numerator sin space 5 x over denominator sin space 3 x end fraction
equals 5 over 3 cross times fraction numerator sin space 5 cross times begin display style straight pi over 2 end style over denominator sin space 3 cross times begin display style pi over 2 end style end fraction
equals 5 over 3 cross times fraction numerator sin space 450 degree over denominator sin space 270 degree end fraction
equals 5 over 3 cross times fraction numerator 1 over denominator negative 1 end fraction
equals fraction numerator negative 5 over denominator 3 end fraction.

L t subscript x not stretchy rightwards arrow pi over 2 end subscript left square bracket sec space 3 x cos space 5 x right square bracket

Maths-General
equals limit as x rightwards arrow bevelled straight pi over 2 of space open parentheses fraction numerator cos space 5 x over denominator cos space 3 x end fraction close parentheses
U sin g space L apostrophe H o s p i t a l space t h e o r e m comma
equals limit as x rightwards arrow bevelled straight pi over 2 of space space fraction numerator begin display style fraction numerator d blank over denominator d x end fraction open parentheses cos space 5 x close parentheses end style over denominator begin display style fraction numerator d blank over denominator d x end fraction open parentheses cos space 3 x close parentheses end style end fraction
equals limit as x rightwards arrow bevelled straight pi over 2 of space space fraction numerator negative left parenthesis sin space 5 x right parenthesis.5 over denominator negative left parenthesis sin space 3 x right parenthesis.3 end fraction
equals 5 over 3 space. limit as x rightwards arrow bevelled straight pi over 2 of space fraction numerator sin space 5 x over denominator sin space 3 x end fraction
equals 5 over 3 cross times fraction numerator sin space 5 cross times begin display style straight pi over 2 end style over denominator sin space 3 cross times begin display style pi over 2 end style end fraction
equals 5 over 3 cross times fraction numerator sin space 450 degree over denominator sin space 270 degree end fraction
equals 5 over 3 cross times fraction numerator 1 over denominator negative 1 end fraction
equals fraction numerator negative 5 over denominator 3 end fraction.
parallel
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The enzyme pepsin hydrolyses:

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chemistry-General
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