List of top Questions asked in JEE Advanced- 2002

Let T > 0 be a fixed real number. Suppose, f is a continuous function such that for all $x \in R. f(x+T)=f(x). \, If \, I = \int_0^T f(x)dx$ then the value of $\int_3^{3+3T} f(2x)dx$

The sum $\displaystyle \sum_{i-0}^{m} \binom{10}{i} \binom{20}{m-i},$ where $ \binom{p}{q}=0 \, if \, p>q,$ is maximum when m is equal to

The area (in sq units) bounded by the curves $y=|x|-1$ and $y=-|x|+1$ is

The set of all real numbers x for which $x^2-|x+2|+x>0$ is

A 100 W bulb $B_1$ and two 60 W bulbs $B_2 \, and\, B_3$, are connected to a 250 V source, as shown in the figure. Now $W_1, W_2 \, and \, W_3$ are the output powers of the bulbs $B_1, B_2$ and $B_3$ respectively. Then,

A small block is connected to one end of a massless spring of unstretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular frequency to = $\frac{\pi }{3}$ rad/s. Simultaneously at t = 0, a small pebble is projected with speed v from point P at an angle of 45$^{\circ}$ as shown in the figure. Point P is at a horizontal distance of 10 m from O. If the pebble hits the block at / = 1 s, the value of v is $ (take \, \, g = 10 m /s_2 $

Consider the chemical reaction, $N_2(g)+3H_2(g)\rightarrow 2NH_3(g)$ .The rate of this reaction can be expressed in terms of time derivatives of concentration of $N_2(g), H_2(g) or NH_3(g)$. Identify the correct relationship amongst the rate expressions

How many moles of electron weighs 1 kg?

Which of the following molecular species has unpaired electron (s)?

Consider the following equilibrium in a closed container $ N_2 O_4 \, (g) \rightleftharpoons 2NO_2 \, ( g) $ At a fixed temperature, the volume of the reaction container is halved. For this change, which of the following statements hold true regarding the equilibrium constant $ ( K_p ) $ and degree of dissociation $( \alpha)$ ?

An observer can see through a pin-hole the top end of a thin rod of height A, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is

The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed $?$ and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed $?/2$. The ring and disc are separated by frictionless ball bearings. The system is in the x-z plane. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 30$^{\circ}$ with the horizontal. Then with respect to the horizontal surface,

The potential difference applied to an X-ray tube is 5 kV and the current through it is 3.2 mA. Then the number of electrons striking the target per second is

Let f(x) =$\int_1^x \sqrt{2-t^2}dt $ Then, the real roots of the equation $x^2-f'(x)=0$ are

If $a_1,a_2,...,a_n$ are positive real numbers whose product is a fixed number c, then the minimum value of $ a_1 + a_2 +...+ a_{n-1}+2a_n$ is

If $0 < \alpha

Let $\omega=-\frac{1}{2}+i\frac{\sqrt 3}{2},$ then value of the determinant $\begin {vmatrix} 1 & 1& 1 \\ 1 & -1-\omega^2 & \omega^2 \\ 1 & \omega^2 & \omega \\ \end {vmatrix} is $

The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently, is

Let $a, b, c$ be in an AP and $a^2,b^2,c^2$ be in GP, if $a < b < c$ and $a+b+c= \frac{3}{2}$, then the value of a is

The integral $ \int\limits^{1/2}_{-1/2} \bigg ([x] + \log \bigg ( \frac{1+ x}{1 - x} \bigg ) \bigg ) \, dx $ equals

If the nitrogen atom had electronic configuration $1s^7$, it would have energy lower than that of the normal ground state configuration $1s^2 \, 2s^2 \, 2p^3 $ , because the electrons would be closer to the nucleus, yet $1s^7$ is not observed, because it violates

Identify the correct order of boiling points of the following compounds: $CH_3CH_2CH_2CH_2OH(1) \, \, \, \, \, \, \, CH_3CH_2CH_2CHO (2) $ $CH_3CH_2CH_2COOH (3) $

Polyphosphates are used as water softening agents because they

Identify the correct order of acidic strength of $CO_2, CuO, CaO, H_2O$

When the temperature is increased, surface tension of water