JEE Advanced 2002 Question Paper with Solutions

Let V → = 2 i → + j → − k → and W → = i → + 3 k → . If U → is a unit vector, then the maximum value of the scalar triple product | U → V → W → | is

If a → and b → are two unit vectors such that a → + 2 b → and 5 a → − 4 b → are perpendicular to each other then the angle between a → and b → is

An ideal spring with spring-constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

If the nitrogen atom has 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 acidic strengths of CO 2 , CuO, CaO, H 2 O

Rutherford's experiment, which established the nuclear model of the atom, used a beam of

Identify the least stable ion amongst the following

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

Which of the following pieces of data does NOT uniquely determine an acute-angled triangle $ABC$ ( $R$ being the radius of the circumcircle)?

The number of integral values of $k$ for which the equation $7\cos x + 5\sin x = 2k + 1$ has a solution is

The equation of the common tangent to the curves ${y^2} = 8x$ and $xy = - 1$ is

A straight line through the origin $O$ meets the parallel lines $4x+2y=9$ and $2x+y+6=0$ at points $P$ and $Q$ respectively. Then the point $O$ divides the segemnt $PQ$ in the ratio

Suppose a , b , c are in A.P. and a 2 , b 2 , c 2 are in G.P. If a < b < c and a + b + c = 3 2 , then the value of a is

The point(s) in the curve ${y^3} + 3{x^2} = 12y$ where the tangent is vertical, is (are)

Let $T>0$ be a fixed real number . Suppose $f$ is a continuous function such that for all $x \in R$ , $f\left( {x + T} \right) = f\left( x \right)$ . If $I = \int\limits_0^T {f\left( x \right)dx}$ then the value of $\int\limits_3^{3 + 3T} {f\left( {2x} \right)dx}$ is

The integral $\int\limits_{ - 1/2}^{1/2} {\left( {\left[ x \right] + \ell n\left( {{{1 + x} \over {1 - x}}} \right)} \right)dx}$ equal to

The area bounded by the curves $y = \left| x \right| - 1$ and $y = - \left| x \right| + 1$ is

Let $T>0$ be a fixed real number . Suppose $f$ is a continuous function such that for all $x \in R$ , $f\left( {x + T} \right) = f\left( x \right)$ . If $I = \int\limits_0^T {f\left( x \right)dx}$ then the value of $\int\limits_3^{3 + 3T} {f\left( {2x} \right)dx}$ is

Specify the coordination geometry around and hybridisation of N and B atoms in a 1 : 1 complex of BF 3 and NH 3