JEE (Advanced) 2008 Paper-1
Let A, B, C be three sets of complex numbersas defined below
$$A = \left\{z : Imz \geq 1\right\}$$
$$B = \left\{z : \mid z - 2 - i \mid = 3\right\}$$
$$C = \left\{z : Re((1 - i)z) = \sqrt{2}\right\}$$
Let z be any point in $$A \bigcap B \bigcap C$$. Then, $$\mid z + 1 - i \mid^2 + \mid z - 5 - i \mid^2$$ lies between
Let z be any point in $$A \bigcap B \bigcap C$$ and let w be any point satisfying $$\mid w - 2 - i \mid < 3$$. Then, $$\mid z \mid - \mid w \mid + 3$$ lies between
For the following questions answer them individually
Students I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of oscillations. The observations are shown in the table.
Least count for length = 0.1 cm
Least count for time = 0.1 s
If $$E_I, E_{II}$$ and $$E_{III}$$ are the percentage errors in g, i.e., $$\left(\frac{\triangle g}{g} \times 100\right)$$ for students I, II and III, respectively,
Figure shows three resistor configurations R1, R2 and R3 connected to 3 V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then
Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?
Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is $$60^\circ$$). In the position of minimum deviation, the angle of refraction will be
An ideal gas is expanding such that $$PT^2 =$$ constant. The coefficient of volume expansion of the gas is
A spherically symmetric gravitational system of particles has a mass density $$\rho = \begin{cases}\rho_0 & for & r \leq R\\0 & for & r > R\end{cases}$$ where $$\rho_0$$ is a constant. A test mass can undergo circular motion underthe influence of the gravitational field of particles. Its speed V as a function of distance $$r(0 < r < \infty)$$ from the center of the system is represented by
Two balls, having linear momenta $$\overrightarrow{p}_1 = p\hat{i}$$ and $$\overrightarrow{p}_1 = -p\hat{i}$$, undergo a collision in free space. There is no external force acting on the balls. Let $$\overrightarrow{p}_1'$$ and $$\overrightarrow{p}_2'$$ be their final momenta. The following option(s) is(are) NOT ALLOWED for any non-zero value of $$p, a_1, a_2, b_1, b_2, c_1$$ and $$c_2$$.
