1
IIT-JEE 2011 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$\alpha $$ and $$\beta $$ be the roots of $${x^2} - 6x - 2 = 0,$$ with $$\alpha > \beta .$$ If $${a_n} = {\alpha ^n} - {\beta ^n}$$ for $$\,n \ge 1$$ then the value of $${{{a_{10}} - 2{a_8}} \over {2{a_9}}}$$ is
A
1
B
2
C
3
D
4
2
IIT-JEE 2011 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$\left( {{x_0},{y_0}} \right)$$ be the solution of the following equations
$$\matrix{ {{{\left( {2x} \right)}^{\ell n2}}\, = {{\left( {3y} \right)}^{\ell n3}}} \cr {{3^{\ell nx}}\, = {2^{\ell ny}}} \cr } $$
Then $${x_0}$$ is
A
$${1 \over 6}$$
B
$${1 \over 3}$$
C
$${1 \over 2}$$
D
$$6$$
3
IIT-JEE 2011 Paper 1 Offline
Numerical
+4
-0
Let $${{a_1}}$$, $${{a_2}}$$, $${{a_3}}$$........ $${{a_{100}}}$$ be an arithmetic progression with $${{a_1}}$$ = 3 and $${S_p} = \sum\limits_{i = 1}^p {{a_i},1 \le } \,p\, \le 100$$. For any integer n with $$1\,\, \le \,n\, \le 20$$, let m = 5n. If $${{{S_m}} \over {{S_n}}}$$ does not depend on n, then $${a_{2\,}}$$ is
Your input ____
4
IIT-JEE 2011 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
A straight line $$L$$ through the point $$(3, -2)$$ is inclined at an angle $${60^ \circ }$$ to the line $$\sqrt {3x} + y = 1.$$ If $$L$$ also intersects the x-axis, then the equation of $$L$$ is
A
$$y + \sqrt {3x} + 2 - 3\sqrt 3 = 0$$
B
$$y - \sqrt {3x} + 2 + 3\sqrt 3 = 0$$
C
$$\sqrt {3y} - x + 3 + 2\sqrt 3 = 0$$
D
$$\sqrt {3y} + x - 3 + 2\sqrt 3 = 0$$
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