1
IIT-JEE 2012 Paper 1 Offline
+3
-1

Let $$f(x) = \left\{ {\matrix{ {{x^2}\left| {\cos {\pi \over x}} \right|,} & {x \ne 0} \cr {0,} & {x = 0} \cr } } \right.$$

x$$\in$$R, then f is

A
differentiable both at x = 0 and at x = 2.
B
differentiable at x = 0 but not differentiable at x = 2.
C
not differentiable at x = 0 but differentiable at x = 2.
D
differentiable neither at x = 0 nor at x = 2.
2
IIT-JEE 2012 Paper 1 Offline
+3
-1

The function $$f:[0,3] \to [1,29]$$, defined by $$f(x) = 2{x^3} - 15{x^2} + 36x + 1$$, is

A
one-one and onto.
B
onto but not one-one.
C
one-one but not onto.
D
neither one-one nor onto.
3
IIT-JEE 2012 Paper 1 Offline
Numerical
+4
-0

The value of $$6 + {\log _{3/2}}\left( {{1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt 2 }}...} } } } \right)$$ is __________.

4
IIT-JEE 2012 Paper 1 Offline
+4
-1
In the determination of Young's modulus $$\left( {Y = {{4MLg} \over {\pi l{d^2}}}} \right)$$ by using Searle's method, a wire of length L = 2 m and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable error of the Y measurement
A
due to the errors in the measurements of d and l are the same.
B
due to the error in the measurement of d is twice that due to the error in the measurement of l.
C
due to the error in the measurement of l is twice that due to the error in the measurement of d.
D
due to the error in the measurement of d is four times that due to the error in the measurement of l.
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