Trigonometry · JEE Main previous year questions

2005 4 questions

1. Q42005 · 28 Apr 2005 · Shift 1

   In a triangle $PQR$, $\angle R=\frac{\pi }{2}$. If $\tan \left(\frac{P}{2}\right)$ and $\tan \left(\frac{Q}{2}\right)$ are the roots of $a{x}^2+bx+c=0,a\ne 0$ then

   1. A.$a=b+c$
   2. B.$c=a+b$
   3. C.$b=c$
   4. D.$b=a+c$
   Show answer

   Answer: B

2. Q632005 · 28 Apr 2005 · Shift 1

   In a triangle $ABC$, let $\angle C=\frac{\pi }{2}$. If $r$ is the inradius and $R$ is the circumradius of the triangle $ABC$, then $2(r+R)$ equals :

   1. A.$b+c$
   2. B.$a+b$
   3. C.$a+b+c$
   4. D.$c+a$
   Show answer

   Answer: B

3. Q642005 · 28 Apr 2005 · Shift 1

   If in a $\Delta ABC$, the altitudes from the vertices $A,B,C$ on opposite sides are in H.P, then $\sin A,\sin B,\sin C$ are in :

   1. A.G. P.
   2. B.A. P.
   3. C.A.P.-G.P.
   4. D.H. P
   Show answer

   Answer: B

4. Q652005 · 28 Apr 2005 · Shift 1

   The normal to the curve $x=a(\cos \theta +\theta \sin \theta ),y=a(\sin \theta -\theta \cos \theta )$ at any point '$\theta$' is such that

   1. A.it passes through the origin
   2. B.it makes an angle $\frac{\pi }{2}+\theta$ with the $x$-axis
   3. C.it passes through $\left(a\frac{\pi }{2},-a\right)$
   4. D.it is at a constant distance from the origin
   Show answer

   Answer: D