Let, $x + \frac{1}{x} + 4 = t$
$\therefore x + \frac{1}{x} = t – 4$
$ \Rightarrow {x^2} + \frac{1}{{{x^2}}} + 2 = {t^2} – 8t + 16$
$ \Rightarrow {x^2} + \frac{1}{{{x^2}}} – 14 = {t^2} – 8t = t(t – 8)$
$\therefore f(t) = t(t – 8)$
So, $f(0) = 0$
Category Archives: IIT JEE
One main scale division of a Vernier caliper is ‘a’ cm ….
One main scale division of a Vernier caliper is ‘a’ cm and $n^{th}$ division of the Vernier scale coincides with $(n-1)^{th}$ division of the main scale. The least count of the caliper in mm is:
(A) $ \frac {10na}{(n-1)} $
(B) $ \frac {10a}{(n-1)}$
(C) $ \frac {10a}{n} $
(D) $ (\frac {n-1}{10n})a$ Continue reading One main scale division of a Vernier caliper is ‘a’ cm ….
An extended object is placed at point O …
An extended object is placed at point O, 10 cm in front of a convex lens $L_1$ and a concave lens $L_2$ is placed 10 cm behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are 20 cm. The refractive index of both the lenses is 1.5. The total magnification of this lens system is
(A) 0.4 (B) 0.8 (C) 1.3 (D) 1.6 Continue reading An extended object is placed at point O …
Let $\theta_1,\theta_1,……..,\theta_{10}$ be …
Let $\theta_1,\theta_1,……..,\theta_{10}$ be positive valued angles (in radian) such that $\theta_1+\theta_2+……..+\theta_{10}=2\pi$. Define the complex numbers $z_1=e^{i\theta_1},z_k=z_{k-1}e^{i\theta_k}$ for k=2, 3, …….., 10 where $i=\sqrt {-1}$. Consider the statements P and Q given below:
P: $|z_2-z_1|+|z_3-z_2|+………..+|z_{10}-z_9|+|z_1-z_{10}|\leq 2\pi $
Q: $|z_2^2-z_1^2|+|z_3^2-z_2^2|+………..+|z_{10}^2-z_9^2|+|z_1^2-z_{10}^2|\leq 4\pi $
Then,
(A) P is TRUE and Q is FALSE
(B) Q is TRUE and P is FALSE
(C) both P and Q are TRUE
(D) both P and Q are FALSE Continue reading Let $\theta_1,\theta_1,……..,\theta_{10}$ be …
Flying Bird ~ Q & A
Q: A bird while flying takes a right turn, where does it get the centripetal force from?
A: The centripetal force is provided by the bird’s wings as it changes the direction of its flight. As the bird turns to the right, it must adjust the angle of its wings to produce a component of the force towards the center of the turn.
Potential Energy of Book ~ Q & A
Q: One person says that the potential energy of a particular book kept in a bookshelf is 25 J and the other says it is 35 J. Is one of them necessarily wrong?
A: It is possible that one of them is wrong, but it is also possible that both are correct.
The potential energy of an object depends on its position and the reference point chosen to calculate it. If both individuals are using different reference points to calculate the potential energy of the book, then they may obtain different values. Continue reading Potential Energy of Book ~ Q & A
Sound Pitch ~ Q & A
Q: If two people talk in a room having Helium gas higher than usual, will they hear any change in the pitch of sound? Continue reading Sound Pitch ~ Q & A