AIEEE 2002

If \(\alpha \ne \beta\) but \({\alpha ^2} = 5\alpha - 3\) and \({\beta ^2} = 5\beta - 3\) then the equation having \(\alpha /\beta\) and \(\beta /\alpha \,\,\) as its roots is

If \(a,\,b,\,c\) are distinct \(+ ve\) real numbers and \({a^2} + {b^2} + {c^2} = 1\) then \(ab + bc + ca\) is

Product of real roots of equation \({t^2}{x^2} + \left| x \right| + 9 = 0\)

If \(p\) and \(q\) are the roots of the equation \({x^2} + px + q = 0,\) then

\({1^3} - \,\,{2^3} + {3^3} - {4^3} + ... + {9^3} =\)

Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is

Fifth term of a GP is 2, then the product of its 9 terms is

The value of \(\,{2^{1/4}}.\,\,{4^{1/8}}.\,{8^{1/16}}...\infty\) is

If 1, \({\log _9}\,\,({3^{1 - x}} + 2),\,\,{\log _3}\,\,({4.3^x} - 1)\) are in A.P. then x equals

l, m, n are the \({p^{th}}\), \({q^{th}}\) and \({r^{th}}\) term of a G.P all positive, \(then\,\left| {\matrix{ {\log \,l} & p & 1 \cr {\log \,m} & q & 1 \cr {\log \,n} & r & 1 \cr } } \right|\,equals\)

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls?

Locus of mid point of the portion between the axes of
\(x\) \(cos\) \(\alpha + y\,\sin \alpha = p\) where \(p\) is constant is :

If the pair of lines
\(a{x^2} + 2hxy + b{y^2} + 2gx + 2fy + c = 0\)
intersect on the \(y\)-axis then :

The pair of lines represented by
\($3a{x^2} + 5xy + \left( {{a^2} - 2} \right){y^2} = 0\)$
are perpendicular to each other for :

A triangle with vertices \(\left( {4,0} \right),\left( { - 1, - 1} \right),\left( {3,5} \right)\) is :

The number of solution of \(\tan \,x + \sec \,x = 2\cos \,x\) in \(\left[ {0,\,2\,\pi } \right]\) is

If \(\left| {\overrightarrow a } \right| = 4,\left| {\overrightarrow b } \right| = 2\) and the angle between \({\overrightarrow a }\) and \({\overrightarrow b }\) is \(\pi /6\) then $${\left( {\overrightarrow a \times \overrightarrow b } \...

If the vectors \(\overrightarrow c ,\overrightarrow a = x\widehat i + y\widehat j + z\widehat k\) and \(\widehat b = \widehat j\) are such that \(\overrightarrow a ,\overrightarrow c\) and \(\overrightarrow b\) form a right handed system...

If the vectors $\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}$ and $\overrightarrow{\mathbf{c}}$ from the sides $B C, C A$ and $A B$ respectively of a triangle $A B C$, then :

\(\overrightarrow a = 3\widehat i - 5\widehat j\) and \(\overrightarrow b = 6\widehat i + 3\widehat j\) are two vectors and \(\overrightarrow c\) is a vector such that \(\overrightarrow c = \overrightarrow a \times \overrightarrow b\)...

If \(\left| {\overrightarrow a } \right| = 5,\left| {\overrightarrow b } \right| = 4,\left| {\overrightarrow c } \right| = 3\) thus what will be the value of $$\left| {\overrightarrow a .\overrightarrow b + \overrightarrow b .\overrightarr...

If \(\overrightarrow a \,\,,\,\,\overrightarrow b \,\,,\,\,\overrightarrow c\) are vectors such that \(\left[ {\overrightarrow a \,\overrightarrow b \,\overrightarrow c } \right] = 4\) then $$\left[ {\overrightarrow a \, \times \overrighta...