JEE MAIN

<div><div><li> <p>The position vector of a moving body at any instant of time is given as 
  <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
    <mrow> 
     <mover> 
      <mi>
        r 
      </mi> 
      <mo accent="true">
        ⃗ 
      </mo> 
     </mover> 
     <mo>
       = 
     </mo> 
     <mrow> 
      <mo stretchy="true" form="prefix">
        ( 
      </mo> 
      <mn>
        5 
      </mn> 
      <msup> 
       <mi>
         t 
       </mi> 
       <mn>
         2 
       </mn> 
      </msup> 
      <mspace width="0.222em"></mspace> 
      <mover> 
       <mi>
         i 
       </mi> 
       <mo accent="true">
         ̂ 
       </mo> 
      </mover> 
      <mo>
        − 
      </mo> 
      <mn>
        5 
      </mn> 
      <mi>
        t 
      </mi> 
      <mspace width="0.222em"></mspace> 
      <mover> 
       <mi>
         j 
       </mi> 
       <mo accent="true">
         ̂ 
       </mo> 
      </mover> 
      <mo stretchy="true" form="postfix">
        ) 
      </mo> 
     </mrow> 
     <mi>
       m 
     </mi> 
    </mrow> 
    <annotation encoding="application/x-tex">
      \overrightarrow{r} = \left( 5t^{2}\ \widehat{i} - 5t\ \widehat{j} \right)m 
    </annotation> 
   </semantics> 
  </math>. The magnitude and direction of vector at t=2s is -</p> </li></div></div>

<div><p style="text-align:left;">Given 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mover> 
     <mi>
       r 
     </mi> 
     <mo accent="true">
       ⃗ 
     </mo> 
    </mover> 
    <mo>
      = 
    </mo> 
    <mn>
      5 
    </mn> 
    <msup> 
     <mi>
       t 
     </mi> 
     <mn>
       2 
     </mn> 
    </msup> 
    <mover> 
     <mi>
       i 
     </mi> 
     <mo accent="true">
       ̂ 
     </mo> 
    </mover> 
    <mo>
      − 
    </mo> 
    <mn>
      5 
    </mn> 
    <mi>
      t 
    </mi> 
    <mover> 
     <mi>
       j 
     </mi> 
     <mo accent="true">
       ̂ 
     </mo> 
    </mover> 
   </mrow> 
   <annotation encoding="application/x-tex">
     \overrightarrow{r} = 5t^{2}\widehat{i} - 5t\widehat{j} 
   </annotation> 
  </semantics> 
 </math></p><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/da4a8b2d-1ed6-4fde-91e0-7e99c94b2999.jpg" style="width:1.02764in;height:0.97118in" alt=""> </p><p>Angle with x-axis</p><p style="text-align:left;"> 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      t 
    </mi> 
    <mi>
      a 
    </mi> 
    <mi>
      n 
    </mi> 
    <mi>
      β 
    </mi> 
    <mo>
      = 
    </mo> 
    <mfrac> 
     <mn>
       5 
     </mn> 
     <mn>
       20 
     </mn> 
    </mfrac> 
    <mo>
      = 
    </mo> 
    <mfrac> 
     <mn>
       1 
     </mn> 
     <mn>
       4 
     </mn> 
    </mfrac> 
    <mspace width="0.222em"></mspace> 
   </mrow> 
   <annotation encoding="application/x-tex">
     tan\beta = \frac{5}{20} = \frac{1}{4}\ 
   </annotation> 
  </semantics> 
 </math> </p><p style="text-align:left;">angle with y-axis:<br> 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      t 
    </mi> 
    <mi>
      a 
    </mi> 
    <mi>
      n 
    </mi> 
    <mi>
      α 
    </mi> 
    <mo>
      = 
    </mo> 
    <mfrac> 
     <mn>
       20 
     </mn> 
     <mn>
       5 
     </mn> 
    </mfrac> 
    <mo>
      = 
    </mo> 
    <mn>
      4 
    </mn> 
   </mrow> 
   <annotation encoding="application/x-tex">
     tan\alpha = \frac{20}{5} = 4 
   </annotation> 
  </semantics> 
 </math></p></div>

<div><div><li> <p> The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between t=0 to t=4s?</p> </li></div><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/5cc1e25c-1c5c-4bb1-afc3-49d3be28349e.jpg" style="width:1.92in;height:0.84737in" alt=""> </p></div>

<div><p style="text-align:left;">Displacement Area under the curve<br> 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mo>
     = 
   </mo> 
   <annotation encoding="application/x-tex">
     = 
   </annotation> 
  </semantics> 
 </math></p></div>

<div><div><li> <p>The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is _____ km.</p> </li></div><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/85e56ca4-d565-4517-9f98-a5b9c5ce4505.jpg" style="width:2.51681in;height:1.12107in" alt=""> </p></div>

<div><p style="text-align:left;">distance Area under 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      v 
    </mi> 
    <mo>
      − 
    </mo> 
    <mi>
      t 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     v - t 
   </annotation> 
  </semantics> 
 </math> curve<br> 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mo>
     = 
   </mo> 
   <annotation encoding="application/x-tex">
     = 
   </annotation> 
  </semantics> 
 </math></p></div>

<div><div><li> <p>Two projectiles are fired with same initial speed from same point on ground at angles of (45°-α) and (45°+α), respectively, with the horizontal direction. The ratio of their maximum heights attained is:</p> </li></div></div>

<div><p style="text-align:left;"> 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       θ 
     </mi> 
     <mn>
       1 
     </mn> 
    </msub> 
    <mo>
      = 
    </mo> 
    <msup> 
     <mn>
       45 
     </mn> 
     <mo>
       ∘ 
     </mo> 
    </msup> 
    <mo>
      − 
    </mo> 
    <mi>
      α 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     \theta_{1} = 45^{\circ} - \alpha 
   </annotation> 
  </semantics> 
 </math> </p></div>