Straight Lines · JEE Main previous year questions

2005 5 questions

1. Q122005 · 28 Apr 2005 · Shift 1

   If a vertex of a triangle is $(1,1)$ and the mid points of two sides through this vertex are $(-1,2)$ and $(3,2)$ then the centroid of the triangle is :

   1. A.$\left(-1,\frac{7}{3}\right)$
   2. B.$\left(\frac{-1}{3},\frac{7}{3}\right)$
   3. C.$\left(1,\frac{7}{3}\right)$
   4. D.$\left(\frac{1}{3},\frac{7}{3}\right)$
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   Answer: C

2. Q412005 · 28 Apr 2005 · Shift 1

   The angle between the lines $2x=3y=-z$ and $6x=-y=-4z$ is :

   1. A.$0^{\circ }$
   2. B.$90^{\circ }$
   3. C.$45^{\circ }$
   4. D.$30^{\circ }$
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   Answer: B

3. Q532005 · 28 Apr 2005 · Shift 1

   A lizard, at an initial distance of $21\mathrm{cm}$ behind an insect moves from rest with an acceleration of $2cm/{\mathrm{s}}^2$ and pursues the insect which is crawling uniformly along a straight line at a speed of $20cm/s$. Then the lizard will catch the insect after :

   1. A.$20\mathrm{s}$
   2. B.$1\mathrm{s}$
   3. C.$21\mathrm{s}$
   4. D.$24\mathrm{s}$
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   Answer: C

4. Q542005 · 28 Apr 2005 · Shift 1

   Two points $A$ and $B$ move from rest along a straight line with constant acceleration $f$ and $f^{\prime }$ respectively. If $A$ takes $m$ sec. more than $B$ and describes '$n$' units more than $B$ in acquiring the same speed then

   1. A.$(f-f^{\prime })m^2=f{f}^{\prime }n$
   2. B.$(f+f^{\prime })m^2=f{f}^{\prime }n$
   3. C.$\frac{1}{2}(f+f^{\prime })m=f{f}^{\prime }{n}^2$
   4. D.$(f^{\prime }-f)n=\frac{1}{2}f{f}^{\prime }{m}^2$
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   Answer: D

5. Q752005 · 28 Apr 2005 · Shift 1

   $ABC$ is a triangle. Forces $\vec{P},\vec{Q},\vec{R}$ acting along $IA,IB$ and $IC$ respectively are in equilibrium, where $I$ is the incentre of $\Delta ABC$. Then $P:Q:R$ is

   1. A.$\sin A:\sin B:\sin C$
   2. B.$\sin \frac{A}{2}:\sin \frac{B}{2}:\sin \frac{C}{2}$
   3. C.$\cos \frac{A}{2}:\cos \frac{B}{2}:\cos \frac{C}{2}$
   4. D.$\cos A:\cos B:\cos C$
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   Answer: C