1
IIT-JEE 2012 Paper 2 Offline
+4
-1
Let $${{a_n}}$$ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0.Let $${{b_n}}$$ = the number of such n-digit integers ending with digit 1 and $${{c_n}}$$ =the number of such n-digit integers ending with digit 0.

Which of the following is correct?

A
$${a_{17}} = {a_{16}} + {a_{15}}$$
B
$${c_{17}} \ne {c_{16}} + {c_{15}}$$
C
$${b_{17}} \ne {b_{16}} + {c_{16}}$$
D
$${a_{17}} = {c_{17}} + {b_{16}}$$
2
IIT-JEE 2012 Paper 2 Offline
+4
-1
Let $${a_1},{a_2},{a_3},.....$$ be in harmonic progression with $${a_1} = 5$$ and $${a_{20}} = 25.$$ The least positive integer $$n$$ for which $${a_n} < 0$$ is
A
22
B
23
C
24
D
25
3
IIT-JEE 2012 Paper 2 Offline
+4
-1
A tangent PT is drawn to the circle $${x^2}\, + {y^2} = 4$$ at the point P $$\left( {\sqrt 3 ,1} \right)$$. A straight line L, perpendicular to PT is a tangent to the circle $${(x - 3)^2}$$ + $${y^2}$$ = 1.

A possible equation of L is

A
$${x - \sqrt 3 \,y = 1}$$
B
$${x + \sqrt 3 \,y = 1}$$
C
$${x - \sqrt 3 \,y = -1}$$
D
$${x + \sqrt 3 \,y = 5}$$
4
IIT-JEE 2012 Paper 2 Offline
+4
-1
A tangent PT is drawn to the circle $${x^2}\, + {y^2} = 4$$ at the point P $$\left( {\sqrt 3 ,1} \right)$$. A straight line L, perpendicular to PT is a tangent to the circle $${(x - 3)^2}$$ + $${y^2}$$ = 1

A common tangent of the two circles is

A
x = 4
B
y = 2
C
$${x + \sqrt 3 \,y = 4}$$
D
$${x +2 \sqrt 2 \,y = 6}$$
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