1
JEE Advanced 2014 Paper 1 Offline
Numerical
+4
-0
Let a, b, c be positive integers such that $${b \over a}$$ is an integer. If a, b, c are in geometric progression and the arithmetic mean of a, b, c is b + 2, then the value of $${{{a^2} + a - 14} \over {a + 1}}$$ is
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2
JEE Advanced 2014 Paper 1 Offline
Numerical
+4
-0
For a point $$P$$ in the plane, Let $${d_1}\left( P \right)$$ and $${d_2}\left( P \right)$$ be the distance of the point $$P$$ from the lines $$x - y = 0$$ and $$x + y = 0$$ respectively. The area of the region $$R$$ consisting of all points $$P$$ lying in the first quadrant of the plane and satisfying $$2 \le {d_1}\left( P \right) + {d_2}\left( P \right) \le 4$$, is
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3
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A circle S passes through the point (0, 1) and is orthogonal to the circles $${(x - 1)^2}\, + \,{y^2} = 16\,\,and\,\,{x^2}\, + \,{y^2} = 1$$. Then
A
radius of S is 8
B
radius of S is 7
C
centre of S is (- 7, 1)
D
centre of S is (- 8, 1)
4
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$f:\left( {0,\infty } \right) \to R$$ be given by $$f\left( x \right) = \int\limits_{{1 \over x}}^x {{e^{ - \left( {t + {1 \over t}} \right){{dt} \over t}}}} .$$ Then
A
$$f(x)$$ is monotonically increasing on $$\left[ {1,\infty } \right)$$
B
$$f(x)$$ is monotonically decreasing on $$(0,1)$$
C
$$f(x)$$ $$ + f\left( {{1 \over x}} \right) = 0$$, for all $$x \in \left( {0,\infty } \right)$$
D
$$f\left( {{2^x}} \right)$$ is an odd function of $$x$$ on $$R$$
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