Trigonometry · JEE Main previous year questions

2014 2 questions

1. Q12014 · 6 Apr 2014 · Shift 1

   Let $f_k(x)=\frac{1}{k}({\sin }^{k}x+{\cos }^{k}x)$ where $x\in R$ and $k\ge 1$. Then $f_4(x)-f_6(x)$ equals :

   1. A.$\frac{1}{4}$
   2. B.$\frac{1}{12}$
   3. C.$\frac{1}{6}$
   4. D.$\frac{1}{3}$
   Show answer

   Answer: B

2. Q262014 · 6 Apr 2014 · Shift 1

   A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point $O$ on the ground is $45^{\circ }$. It flies off horizontally straight away from the point $O$. After one second, the elevation of the bird from $O$ is reduced to $30^{\circ }$. Then the speed (in m/s) of the bird is :

   1. A.$20\sqrt{2}$
   2. B.$20\left(\sqrt{3}-1\right)$
   3. C.$40\left(\sqrt{2}-1\right)$
   4. D.$40\left(\sqrt{3}-\sqrt{2}\right)$
   Show answer

   Answer: B